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ENERGY & MOMENTUM
1. Which of the following best represents the momentum of a small car travelling at a city speedlimit?
A. 1 000 kg ×m sB. 10 000 kg ×m sC. 100 000 kg ×m sD. 1 000 000 kg ×m s
2. A 0.080 kg tennis ball travelling east at 15 m s is struck by a tennis racquet, giving it avelocity of 25 m s, west. What are the magnitude and direction of the impulse given to theball?
MAGNITUDE DIRECTION
A. 0.80 N ×s Eastward
B. 0.80 N ×s Westward
C. 3.2 N ×s Eastward
D. 3.2 N ×s Westward
3. A climber’s gravitational potential energy increases from 14 000 J to 21 000 J whileclimbing a cliff. She expends 18 000 J of energy during this activity. What is the efficiencyof this process?
A. 3%B. 39%C. 61%D. 97%
4. A 40 000 kg rail car travelling at 2.5 m s collides with and locks to a stationary 30 000 kgcar. Determine the speed of the locked cars and state whether the collision is elastic orinelastic.
SPEED OF LOCKED CARS TYPE OF COLLISION
A. 1. 4 m s Elastic
B. 1. 4 m s Inelastic
C. 1.9 m s Elastic
D. 1.9 m s Inelastic
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5. Which of the following correctly describes momentum and impulse?
MOMENTUM IMPULSE
A. vector vector
B. vector scalar
C. scalar vector
D. scalar scalar
6. A stationary object explodes into two fragments. A 4.0 kg fragment moves westwards at3.0 m s. What are the speed and kinetic energy of the remaining 2.0 kg fragment?
SPEED KINETIC ENERGY
A. 4.2 m s 18 J
B. 4.2 m s 36 J
C. 6.0 m s 18 J
D. 6.0 m s 36 J
7. A 1 000 kg vehicle travelling westward at 15 m s is subjected to a 1.0 ×104 N ×s impulsenorthward. What is the magnitude of the final momentum of the vehicle?
A. 5.0 ×103 kg ×m sB. 1.5 ×104 kg ×m sC. 1.8 ×104 kg ×m sD. 2.5 ×104 kg ×m s
.
B. 1. 4 m s Inelastic
C. 1.9 m s Elastic
D. 1.9 m s Inelastic
8. A cyclist increases his kinetic energy from 1100 J to 5 200 J in 12 s. His power outputduring this time is
A. 92 WB. 260 WC. 340 WD. 430 W
- 3 -
9. A force is applied to an 8.0 kg object initially at rest. The magnitude of the net force varieswith distance as shown.
5 10 15
10
20
00
Fnet (N)
Distance (m)
What is the speed of the object after moving 15 m?
A. 5.0 m sB. 6.1 m sC. 7.1 m sD. 8.7 m s
10. A machine rated at 1 500 W lifts a 100 kg object 36 m vertically in 45 s. What is the efficiencyof this machine?
A. 0.053B. 0. 48C. 0.52D. 0.65
11. Two cars collide head-on and come to a complete stop immediately after the collision.Which of the following is correct?
TOTAL MOMENTUM TOTAL ENERGY
A. is conserved is conserved
B. is conserved is not conserved
C. is not conserved is conserved
D. is not conserved is not conserved
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15. A child rolls a ball up a hill as shown. The same child then throws an identical ball up the hill.
Final Position
Initial Position
Thrown Path
Rolled Path
When both balls end up in the same location on the hill, which of the following correctlydescribes the potential energy change for each ball?
A. Both balls have the same potential energy change.B. There is no potential energy change for either ball.C. The thrown ball has a greater potential energy change than the rolled ball.D. The thrown ball has a smaller potential energy change than the rolled ball.
13. A change in kinetic energy is equivalent to
A. work.B. power.C. impulse.D. momentum.
14. A 16 kg object is dropped from a height of 25 m and strikes the ground with a speed of 18 m s.How much heat energy was produced during the fall?
A. 0 JB. 1 300 JC. 2 600 JD. 3 900 J
12. A crane lifts a 3 900 kg shipping container through a vertical height of 45 m in 8.0 s. What isthe minimum average power that the crane motor must supply?
A. 2.7 ×103 WB. 7.7 ×103 WC. 2.1×105 WD. 1.7 ×106 W
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16. A 950 kg elevator ascends a vertical height of 410 m with an average speed of 9.1 m s . Whataverage power must the lifting motor supply?
A. 8.6 ×103 WB. 8.5 ×104 WC. 4.2 ×105 WD. 3.8 ×106 W
17. A 55.0 kg athlete steps off a 10.0 m high platform and drops onto a trampoline. As thetrampoline stretches, it brings him to a stop 1.00 m above the ground.
9.0 m
1.0 m
10.0 m
How much energy must have been momentarily stored in the trampoline when he came to rest?
A. 0 JB. 539 JC. 4 850 JD. 5 390 J
18. An object starts from rest and slides down a frictionless track as shown. It leaves the trackhorizontally, striking the ground at a distance d as shown.
h
2h
d
The same object is now released from twice the height, 2h. How far away will it land?
A. dB. 2 dC. 2dD. 4d
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19. A 0.055 kg bullet was fired at 250 m s into a block of wood as shown in the diagram below.
d
Assuming an average force of 9 500 N brings the bullet to rest in the wood, what distance d didthe bullet penetrate the block?
A. 1. 4 ×10−3 mB. 1. 4 ×10−2 mC. 1.8 ×10−1 mD. 3.6 ×10−1 m
20. An electric winch operates from a 120 V source at 3.5 A. The winch lifts a 360 kg object 2.5 mvertically in 45 s. What is the efficiency of the winch?
A. 4.8%B. 17%C. 19%D. 47%
21. A 0.40 kg ball rolls at 8.5 m s towards a player. The player kicks the ball so that it thentravels at 15.2 m s in the opposite direction. What is the magnitude of the impulse that theball sustained?
A. 1.3 N ⋅ sB. 2.7 N ⋅ sC. 4.7 N ⋅ sD. 9.5 N ⋅ s
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22. A wad of putty is thrown against a wall as shown. The wad of putty sticks against the wall.
Which of the following statements best applies the application of the law of conservation ofenergy to this collision?
A. All energy has been lost.B. Kinetic energy is converted to heat.C. Kinetic energy is converted to momentum.D. Kinetic energy is converted to potential energy.
23. The graph below shows how the force applied to an object varies with distance.
0 5 10 15 20 25 30 35
2
4
6
8
10
0
F (N)
d (m)
What is the work done to move the object from 10 m to 30 m?
A. 40 JB. 80 JC. 120 JD. 240 J
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24. A projectile is fired through a fixed block of wood. The diagram shows the projectile abovepoint P just before it enters the block and again above point Q just after leaving the block.
P Q
Which of the graphs best illustrates how the kinetic energy of the projectile varies over the timeit takes to travel from P to Q?
A.
C.
Ek
t
Ek
t
B.
D.
Ek
t
Ek
t
25. A 1.0 kg cart moves to the right at 6.0 m s and strikes a stationary 2.0 kg cart. After thehead-on collision, the 1.0 kg cart moves back to the left at 2.0 m s and the 2.0 kg cart movesto the right at 4.0 m s. In this collision
A. only momentum is conserved.B. only kinetic energy is conserved.C. both momentum and kinetic energy are conserved.D. neither momentum nor kinetic energy is conserved.
26. A 12.0 kg shopping cart rolls due south at 1.50 m s. After striking the bumper of a car, ittravels at 0.80 m s , 30° E of S. What is the magnitude of the change in momentum sustainedby the shopping cart?
A. 8. 4 kg ×m sB. 9.7 kg ×m sC. 11 kg ×m sD. 27 kg ×m s
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27. Identify momentum and kinetic energy as scalar or vector quantities.
MOMENTUM KINETIC ENERGY
A. scalar scalar
B. scalar vector
C. vector scalar
D. vector vector
28. Which of the following best represents the work-energy theorem?
A. W = ∆E
B. Ek = Ep
C. W = Ff × d
D. Ep = P × t
29. A 1500 kg car moving at 8.0 m s comes to a stop in 16 m when its brakes are applied. Thespeed of the car is now doubled to 16 m s. Assuming the same braking force as before, howfar will the car travel before coming to a stop?
A. 16 mB. 32 mC. 64 mD. 130 m
30. The momentum of a male Olympic sprinter is about
A. 10 kg ⋅ m sB. 100 kg ⋅ m sC. 1000 kg ⋅ m sD. 10 000 kg ⋅ m s
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1. A daredevil is attached by his ankles to a bungee cord and drops from the top of a bridge. Theforce exerted on the daredevil by the bungee cord is measured against the change in length, x ,of the cord as the cord is stretched, slowing the daredevil’s fall.
Force (N) 0 300 600 1 000 1 200 1 700 1 900
x (m) 0 5 10 15 20 25 30
a) Plot a graph of force vs. change in length on the graph below. (2 marks)
x (m)
Force (N)
0
0
b) Use the graph to determine the work done by the bungee cord during its stretch. (3 marks)
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2. A 0.25 kg cart travelling at 3.0 m s collides with and sticks to an identical stationary carton a level track. (Ignore friction.)
v = 3.0 m s
m = 0. 25 kgh
To what height h do the combined carts travel up the hill? (7 marks)
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3. Starting from rest, a farmer pushed a cart 12 m. The graph shows the force F which heapplied, plotted against the distance d.
140
80
7 12d (m)
F (N)
0
a) How much work did the farmer do moving the cart 12 m? (3 marks)
b) After the farmer had pushed the 240 kg cart 12 m, it was moving with a velocity of2.2 m s. What was the cart’s kinetic energy? (2 marks)
c) What was the efficiency of this process? (2 marks)
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4 . A student plots the graph below, showing the kinetic energy E k of a motorbike versus thesquare of its velocity v2 .
20 000
10 000
200 4000
Ek (J)
v2 m2 s2( )
a) What is the slope of this graph? (2 marks)
b) What does the slope represent? (2 marks)
c) Using the axes below, sketch the graph of kinetic energy Ek versus velocity v for thismotorbike. There is no need to plot any data points. (1 mark)
0
Ek
v
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5. A 170 kg cart and rider start from rest on a 20.0 m high incline.
v = 16.0 m s
h = 20. 0 m
60. 0 m
a) How much energy is transformed to heat? (5 marks)
b) What is the average force of friction acting on the cart? (2 marks)
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6. A 0.50 kg ball starting from position A which is 7.5 m above the ground, is projected down anincline as shown. Friction produces 10.7 J of heat energy.
The ball leaves the incline at position B travelling straight upward and reaches a height of13.0 m above the floor before falling back down.
A
B
7.5 m
13.0 m v0
What was the initial speed, v0, at position A? Ignore air resistance. (7 marks)
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7. Sally is driving south in her 2 500 kg pickup truck at 3.8 m s when she collides with Willydriving west in his 1 200 kg car at 4.5 m s.
2 500 kg
1 200 kgvW = 4. 5 m s
vS = 3. 8 m s
The two vehicles lock together and slide over the wet parking lot. Find the speed and directionof the damaged vehicles immediately after the collision. (7 marks)
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8. Two steel pucks are moving as shown in the diagram. They collide inelastically.
θ30°
m1 = 4.2 kg
v1 = 1.8 m s
m2 = 1.3 kg
′v = 2. 3 m s
v2
Before Collision After Collision
Determine the speed and direction (angle θ ) of the 1.3 kg puck before the collision. (7 marks)
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9. A space vehicle made up of two parts is travelling at 230 m s as shown.
v = 230m s1 200 kg 450 kg
An explosion causes the 450 kg part to separate and travel with a final velocity of 280 m sas shown.
v = 280m s1 200 kg 450 kg
a) What was the momentum of the space vehicle before the explosion? (2 marks)
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b) What was the magnitude of the impulse on the 1 200 kg part during the separation?(3 marks)
c) Using principles of physics, explain what changes occur, if any, to the
i) momentum of the system as a result of the explosion. (2 marks)
ii) kinetic energy of the system as a result of the explosion. (2 marks)
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10. A 3.00 kg object initially at rest explodes into three fragments as shown in the diagram below.
0.80 kg
θ
v
1.30 kg
15 m s south
20 m s west
What are the speed and direction of the 0.80 kg fragment? (7 marks)
- 21 -
11. A 5.20 kg block sliding at 9.40 m/s across a horizontal frictionless surface collides head on with astationary 8.60 kg block. The 5.20 kg block rebounds at 1.80 m/s. How much kinetic energy is lostduring this collision? (7 marks)
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12. In sports such as golf, tennis and baseball, a player exerts a force over a time interval on a ball,as shown on the graph, in order to give it a high speed.
F(N)
t(s)00
Players are instructed to “follow through” on their swing. A weaker player may not exert aslarge a force but may give the ball a higher speed than a stronger player.
a) Sketch on the graph below how a weaker player can overcome the force handicap.(1 mark)
F(N)
t(s)00
b) Explain how the player can impart a greater impulse on a ball. (3 marks)
EQUILIBRIUM AND TORQUE
2. Two forces, 12 N west and 5.0 N north, act on an object. What is the direction of a third force
that would produce static equilibrium?
A. 23° south of east
B. 23° north of west
C. 67° south of east
D. 67° north of west
- 1 -
1. State the condition for translational equilibrium.
A. ΣF = 0
B. ΣF ≠ 0
C. Στ = 0
D. Στ ≠ 0
A 110 kg object is supported by two ropes attached to the ceiling. What is the tension T in
the right-hand rope?
110 kg
Right-hand rope
60° 25°
A. 460 N
B. 540 N
C. 930 N
D. 1 300 N
3.
4. A mass suspended by a string is held 24° from vertical by a force of 13.8 N as shown. Find themass.
240
F = 13.8 N
string
A. 0.57 kgB. 1.5 kgC. 3.2 kgD. 3.5 kg
5. A mass of 5.0 kg is suspended from a cord as shown in the diagram below. What horizontal force F
is necessary to hold the mass in the position shown?
cord
mass
350
F
A. 28 NB. 34 NC. 40 ND. 70 N
6. A 220 N bag of potatoes is suspended from a rope as shown in the diagram. A person pulls
horizontally on the bag with a force of 80 N.
80 NWhat is the tension in the rope?
A. 1. 4 ×102 N
B. 2.2 ×102 N
C. 2.3×102 N
D. 3.0 ×102 N
- 2 -
7. Two forces act on an object as shown. Find the magnitude of the third force required to achieve
translational equilibrium.
F1 = 25 N
F2 = 40 N
A. 15 N
B. 33 N
C. 47 N
D. 65 N
8. A 25 kg block is pulled by a horizontal force. The supporting rope can withstand a maximum
tension force of 620 N.
Rope
F T= 620 N
m = 25 kg
θ
To what maximum angle, θ , can the block be pulled without the rope breaking?
A. 22°
B. 23°
C. 67°
D. 88°
9. An 85.0 kg mountaineer remains in equilibrium while climbing a vertical cliff. The tension
force in the supporting rope is 745 N.
Find the magnitude of the reaction force, F, which the cliff exerts on the mountaineer's feet.
A. 88.0 N
B. 373 N
C. 479 N
D. 546 N - 3 -
F
F T = 745 N40°
10. An artist must push with a minimum force of 75 N at an angle of 45° to a picture to hold it
in equilibrium. The coefficient of friction between the wall and the picture frame is 0.30.
What is the mass of the picture?
45°
F = 75 N
A. 1.6 kg
B. 2.3 kg
C. 3.8 kg
D. 7.0 kg
11. A uniform 1.60 m board rests on two bricks as shown below. The left brick exerts an upward
force of 12 N on the board.
0.40 m1.20 m
What upward force does the right brick exert?
A. 3.0 N
B. 12 N
C. 24 N
D. 36 N
- 4 -
12. A uniform beam of mass 25 kg rests on supports P and Q, as shown in the diagram below.
6.0 m
8.0 m
P Q
What force is exerted by support Q on the beam?
A. 1.2×102 N
B. 1.6×102 N
C. 3.3×102 N
D. 4.9×102 N
16. In which direction should a force act at point P to hold the boom in equilibrium so that the
force will be a minimum?
1
2
34
P
A. 1
B. 2
C. 3
D. 4
13. What are the units of torque?
A. N × m
B . N m
C. N × s
D. N s
15. A body is in rotational equilibrium when
A. Στ = 0B. ΣF = 0C. Σ p = 0D. ΣEk = 0
14. A body is in static equilibrium when
A. Στ = 0 only.
B. ΣF = 0 only.
C. ΣF = 0 and Στ = 0.
D. ΣF = 0 and Στ ≠ 0.
- 5 -
17. A uniform ladder leans against a frictionless wall as shown.
Which of the following diagrams best shows the forces acting on the ladder?
A. C.B. D.
18. A uniform 15 kg pipe of length 5.0 m has a 160 N force applied 4.0 m from its lower
end as shown.
42°
34°
FT = 160 N
1.0 m
Using the point where the pipe touches the ground as a pivot, calculate the sum of the torques
acting on the pipe.
A. 180 N ×m in a clockwise direction.
B. 270 N ×m in a clockwise direction.
C. 120 N ×m in a counter-clockwise direction.
D. 270 N ×m in a counter-clockwise direction.
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- 7 -
19. Which of the four problems shown requires the application of torque?
A.
C.
What is the tension in the supporting cables?
What is the acceleration of the puck?
B.
D.
What is the friction force acting on the block?
What force does the wall exert on the board?
20. A force F is applied to a uniform horizontal beam as shown in the diagram below.
dPθ
F
Which of the following is a correct expression for the torque on the beam about pivot point P
due to this force?
A. F sinθ ⋅dB. F sinθ ⋅d lC. F cosθ ⋅dD. F cosθ ⋅d l
21. A beam is to be kept horizontal by a cord. In which of the four situations shown below will the
tension in the cord be least?
A.
C.
B.
D.
22. A uniform 25 kg bar, 6.0 m long, is suspended by a cord as shown.
cordwall
270
6.0 m
What is the tension in the cord?
A. 1.2 x 102 N
B. 2.7 x 102 N
C. 3.7 x 102 N
D. 5.4 x 102 N
23. A boom hinged at P is held stationary, as shown in the diagram below.
cord
600
boom
P
If the tension in the supporting cord, attached three-quarters of the way along the boom from P,
is 720 N, what is the weight of the boom?
A. 720 N
B. 1 080 N
C. 1 440 N
D. 2 160 N
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- 9 -
24. A uniform 3.0 kg shelf of width 0.50 m is supported by a bracket, as shown in the diagram below.
500
bracket
0.50 m0.20 m
What force does the bracket exert on the shelf?
A. 7.4 NB. 38 NC. 48 ND. 57 N
25. The motorcycle shown has a mass of 200 kg and a wheel base of 1.8 m.
1.8 m
If the rear wheel exerts a 1200 N force on the ground, find how far the motorcycle's centre ofgravity is located from the front wheel.
A. 0.70 mB. 0.90 mC. 1.1 mD. 1.2 m
26. The diagram shows a horizontal beam of negligible mass. The wall exerts a 42.0 N horizontal forceon the lever. Find the weight of the load.
load
string
280
1.30 m
1.80 m
A. 16.1 NB. 22.3 NC. 34.4 ND. 47.6 N
27. A uniform 18 kg beam hinged at P is held horizontal by a vertical string that can withstand a
maximum tension of 350 N. A 5.0 kg mass is suspended from the end of the beam as shown.
string
1.4 m
x
5.0 kg
P
At what minimum distance, x, can the string be attached without breaking?
A. 0.16 m
B. 0.20 m
C. 0.55 m
D. 0.70 m
- 10 -
28. A 35 kg uniform plank is balanced at one end by a 55 kg student as shown.
L
1.3 m
55 kg
What is the overall length of this plank?
A. 2.6 m
B. 3.3 m
C. 5. 4 m
D. 6.7 m
- 11 -
29. A uniform 1.5 kg beam hinged at one end supports a 0.50 kg block. The beam is held level
by a vertical 0.80 kg rod resting on a Newton scale at the other end.
Newtonscale
0.20 m 0.60 m
0.50 kg
1.5 kg beam
0.80 kg rod
What is the reading on the scale?
A. 8.6 N
B. 9.1 N
C. 16 N
D. 27 N
31. A uniform 2.5 kg beam, pivoted at its right end, is held in a horizontal position by a cable as
shown in the diagram.
500ˇ
T = 24 N
0.10 m2.5 kg
center of mass
If the cable is attached 0.10 m to the left of the beam's centre of gravity, how long is the beam?
A. 0.34 m
B. 0.60 m
C. 1.2 m
D. 9.6 m
30. An 85 kg object is suspended from a ceiling and attached to a wall.
85 kg
65°
70°
Left-hand rope
What is the tension in the left-hand rope?
A. 280 N
B. 350 N
C. 500 N
D. 1100 N
- 12 -
32. The diagram shows the forces acting on a massless ladder resting on the floor and a frictionless
F N1
F g
F f
F N 2
As a person walks up the stationary ladder, what happens to the magnitude of the forces
FN1 and FN2
?
MAGNITUDE OF FN1MAGNITUDE OF FN2
A. Decreases Decreases
B. Decreases Increases
C. Increases Decreases
D. Increases Increases
33. A trailer carrying a boat is supported by a scale which initially reads 48 kg. The boat (and therefore
its centre of gravity) is moved 0.15 m further back on the trailer. The scale now reads 37 kg. Find
the mass of the boat.
scale
0.15 m
6.0 m
A. 440 kgB. 1600 kgC. 1700 kgD. 3400 kg
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- 14 -
1. A 25 kg droid rests on a 5.0 m long shelf supported by two cables as shown. The mass of
the shelf is 12 kg.
0.60 m 0.60 m0.80 m
Q2D2
3.8 m
droid
Find the tension in each cable. (7 marks)
- 15 -
Peter exerts a horizontal force F on a 12 kg bucket of concrete so that the supporting rope
makes an angle of 20° with the vertical.
20°
F
a) Find the tension force in the supporting rope. (3 marks)
b) Peter now exerts a new force which causes the rope to make a greater angle with the
vertical. How will the tension force in the supporting rope change?
p The tension force will increase.
p The tension force will decrease.
p The tension force will remain the same.
(Check one response.) (1 mark)
c) Using principles of physics, explain your answer to b). (3 marks)
2.
- 16 -
3. A uniform 4.8 m long ladder of mass 16 kg leans against a frictionless vertical wall as shown in
the diagram below.
4.8 m
65°
a) Draw and label a free body diagram showing the forces acting on the ladder. (2 marks)
b) What minimum force of friction is needed at the base of the ladder to keep it from sliding?
(5 marks)
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4. A uniform beam 6.0 m long, and with a mass of 75 kg, is hinged at A. The supporting cable keeps
the beam horizontal.
37˚
load
cable
2.0 m
3.5 m
6.0 m
A
If the maximum tension the cable can withstand is 2.4 ×103 N , what is the maximum mass
of the load? (7 marks)
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A 6.0 m uniform beam of mass 25 kg is suspended by a cable as shown. An 85 kg object
hangs from one end.
75°
67°
85 kg4.0 m
Cable
Beam 6.0 m)(25 kg,
What is the tension in the cable? (7 marks)
5.
- 19 -
6. The diagram shows the rear door of a station wagon supported horizontally by a strut. The mass of
the door is 18 kg and the compression force in the strut is 450 N.
F = 450 N
strut
32°
centre of gravityx
0.36 m
b) At what distance, x, from the hinge is the centre of gravity of the door located? (7 marks)
- 20 -
7. A 0.75 kg board of length 2.60 m initially rests on two supports as shown.
0.40 m 1.40 m x
a) What maximum distance, x, from the right-hand support can a 1.20 kg bird walk before theboard begins to leave the left-hand support? (5 marks)
b) What force does the right-hand support exert on the board at that instant? (2 marks)
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8. An object of mass, m, is suspended by two cords connected to a wall and to a 5.0 kg block
resting on a table as shown.
32°
5.0 kg
m
µ = 0. 47
A coefficient of friction of 0.47 exists between the 5.0 kg block and the table. What is the
maximum mass, m, that can be hung from the cords before the 5.0 kg block begins to move?
(7 marks)
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A 6.0 m uniform beam of mass 32 kg is suspended horizontally by a hinged end and a
cable. A 93 kg object is connected to one end of the beam.
93 kg object
6.0 m beam, 32 kg
4.0 mHinge
Cable
48°R
What is the magnitude and direction of the reaction force R that the hinge exerts on the beam? (10 marks)
9.
- 24 -
10. A 65 kg person is 34 of the way up a 25 kg uniform ladder as shown in the diagram below. The ladder
ÿ
is leaning against a frictionless surface inclined at 600 to the horizontal. What is the minimum coefficient
of friction between the ladder and the floor necessary to maintain equilibrium? (10 marks)
600400
- 25 -
11. A wire is stretched between two posts. A mass is suspended near the centre as shown below.
If the tension in the wire were increased, is it possible to make the wire perfectly horizontal?
Explain your answer in terms of forces. (4 marks)
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CIRCULAR MOTION AND GRAVITATION
- 1 -
1. Which of the following graphs shows how the gravitational field of a body varies with distancefrom its centre? (Assume d is greater than the radius of the body.)
A. C.g
d
g
d
B. D.g
d
g
d
2. A rock drops from a very high altitude towards the surface of the moon. Which of thefollowing is correct about the changes that occur in the rock's mass and weight?
MASS WEIGHT
A. decreases decreases
B. decreases increases
C. remains constant decreases
D. remains constant increases
3. Cavendish's historic experiment is set up as shown to determine the force between twoidentical sets of masses. What would be the net force of attraction between one set of masses?
0.30 m
m2 = 2.0 kg
M1 = 25 kg
A. 1.1 ×10- 8 NB. 1.9 ×10- 8 NC. 2.2 ×10- 8 ND. 3.7 ×10- 8 N
4. A satellite experiences a gravitational force of 228 N at an altitude of 4.0 ×107 m above Earth.
Altitude
What is the mass of this satellite?
A. 23 kgB. 650 kgC. 910 kgD. 1 200 kg
An object travels along a circular path with a constant speed v when a force F acts on it. Howlarge a force is required for this object to travel along the same path at twice the speed (2v)?
A. 12 F
B. FC. 2FD. 4F
- 2 -
Oberon is a satellite of the planet Uranus. It has an orbital radius of 5.83 ×108 m and anorbital period of 1.16 ×106 s. What is the mass of Uranus?
A. 2.6 ×108 kgB. 5.9 ×1014 kgC. 1.5 ×1017 kgD. 8.7 ×1025 kg
5.
6.
7. Find the gravitational force of attraction between a 75 kg physics student and her 1500 kg car whentheir centres are 10 m apart.
A. 7.5 ×10- 8 NB. 7.5 ×10- 7 NC. 740 ND. 1.5 ×103 N
- 3 -
8. A certain planet has a mass of 3.3 ×1023 kg and a radius of 2.6 ×106 m. What is the accelerationdue to gravity on the surface of this planet?
A. 0.54 m/s2
B. 3.3 m/s2
C. 4.0 m/s2
D. 9.8 m/s2
9. A space shuttle orbits the earth at an altitude where the acceleration due to gravity is 8.70 m s2.What is the shuttle's speed at this altitude?
A. 2.65 ×103 m sB. 7. 45 ×103 m sC. 7.68 ×103 m sD. 7.91 ×103 m s
10. Which of the following graphs shows how the gravitational force varies with the distance ofseparation between two objects?
A.
C.
F
d
F
d
B.
D.
F
d
F
d
- 4 -
11. A planet travels in an elliptical path around a star as shown.
star planet X
Describe the magnitude of the velocity and the acceleration of the planet at X.
MAGNITUDE OFVELOCITY
MAGNITUDE OFACCELERATION
A. least leastB. least greatestC. greatest leastD. greatest greatest
12. What is the gravitational field strength at the surface of a star of mass 4.8 ×1031kg andradius 2.7 ×108 m?
A. 9.8 N/kgB. 4. 4 ×104 N/kgC. 4.9 ×106 N/kgD. 1.2 ×1013 N/kg
13. A satellite's orbit is maintained by a
A. normal force.B . frictional force.C. centrifugal force.D. gravitational force.
14. Kepler's third law r3 ∝ T 2( )can be derived from the law of
A. inertia.B. universal gravitation.C. conservation of energy.D. conservation of momentum.
- 5 -
A planet of radius 7.0 ×107 m has a gravitational field strength of 68 N kg at its surface. What isthe period of a satellite orbiting this planet at a radius of 1. 4 ×108 m (twice the planet's radius)?
A. 9.0 ×103 sB. 1.3 ×104 sC. 1.8 ×104 sD. 2. 4 ×104 s
16. On Earth, the maximum speed without skidding for a car on a level circular curved track of radius40 m is 15 m/s. This car and track are then transported to another planet for the Indy Galactic 500.The maximum speed without skidding is now 8.4 m/s. What is the value of the acceleration due togravity on this other planet?
A. 1.8 m/s2
B. 3.1 m/s2
C. 4.3 m/s2
D. 5.5 m/s2
A satellite travels around a planet at 9. 0 × 103 m s with an orbital radius of 7.4 × 106 m.What would be the speed of an identical satellite orbitting at one half this radius?
A. 4. 5 × 103 m sB . 9.0 × 103 m sC. 1.3 × 104 m sD. 1.8 × 104 m s
18. A satellite orbits a planet of mass 4.0 ×1025 kg at a velocity of 5.8 ×103 m/s. What is the radius ofthis orbit?
A. 6.4 ×106 mB. 7.9 ×107 mC. 1.6 ×108 mD. 1.2 ×1019 m
17.
15.
- 6 -
19. The orbital radius of Mars around the Sun is 1.52 times that of Earth's orbital radius. In Earthyears, what is the period of revolution for Mars in this orbit?
A. 0.66 yearsB. 1.5 yearsC. 1.9 yearsD. 3.5 years
20. What is the centripetal acceleration of the Moon in its orbit around the Earth?
A. 0 m/s2
B. 2.7 x 10-3 m/s2
C. 1.6 m/s2
D. 9.8 m/s2
21. The equation Ep = mgh, in which g is 9.8 m s2 , can not be used for calculating thegravitational potential energy of an orbiting Earth satellite because
A. the Earth is rotating.B. of the influence of other astronomical bodies.C. the Earth's gravity disappears above the atmosphere.D. the Earth's gravitational field strength varies with distance.
22. A 1570 kg satellite orbits a planet in a circle of radius 5.94 ×106 m. Relative to zero at infinitythe gravitational potential energy of this satellite is - 9.32 ×1011 J. What is the mass of the planet?
A. 5.29 ×1025 kgB. 8.31 ×1028 kgC. 3.14 ×1031 kgD. 4.93 ×1034 kg
Relative to zero at infinity, what is the gravitational potential energy of a 7.2 ×102 kg satellite thatis at a distance of 3. 4 ×107 m from earth's centre?
A. - 2. 4 ×1011 JB. - 8. 4 ×109 JC. 8. 4 ×109 JD. 2. 4 ×1011 J
23.
- 7 -
24. A planet is in orbit as shown in the diagram below.
planet
SR
The planet's gravitational potential energy will
A. be constant throughout its orbit.B. always be equal to its kinetic energy.C. increase as the planet goes from point R to point S.D. decrease as the planet goes from point R to point S.
A 450 kg piece of space debris initially at rest falls from an altitude of 6.2 ×105 m abovethe earth's surface. What is its kinetic energy just before impact with the surface? (Ignore airresistance.)
7. 0 106 m×0
6. 8 106 m×3
6. 105 m×2
A. 2.5 ×109 JB. 2.7 ×109 JC. 2.6 ×1010 JD. 2.9 ×1011 J
25.
- 8 -
A 5.2 ×104 kg rocket is initially at rest on the surface of the earth. If 3.0 ×1011 J of workis done on this rocket, what maximum altitude h will the rocket reach? (Assume the rocket'smass does not change.)
h
A. 5.9 ×105 mB. 6.5 ×105 mC. 5.8 ×106 mD. 6.9 ×107 m
A stationary 25 kg object is released from a position 8.9 ×106 m from the centre of the earth.
8.9 ×106 m
What is the speed of the object just before impact? Ignore air resistance.
A. 6.0 ×103 m sB. 7.0 ×103 m sC. 1.3 ×104 m sD. 1.8 ×104 m s
26.
27.
28. A 620 kg satellite orbits the earth where the acceleration due to gravity is 0.233 m s2. What isthe kinetic energy of this orbiting satellite?
A. - 5.98 ×109 JB. - 2.99 ×109 JC. 2.99 ×109 JD. 5.98 ×109 J
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30. An object is located on the surface of a planet. The work required to remove this object from theplanet's gravitational field depends on which combination of the following three variables:mass of the planet, mass of the object, and radius of the planet?
MASS OF PLANET MASS OF OBJECT RADIUS OF PLANET
A. Yes Yes Yes
B . Yes Yes No
C. Yes No Yes
D. No Yes Yes
What minimum kinetic energy would a spacecraft of mass 1.2 ×104 kg need at the surface of theEarth so that it could escape to infinity?
A. 1.1 ×104 JB. 1.2 ×105 JC. 7.5 ×1011 JD. An infinite amount
31. A 120 kg astronaut stands on the surface of an asteroid of radius 600 m. The astronaut leaves thesurface with 15 J of kinetic energy and reaches a maximum height of 300 m above the surface.What is the mass of the asteroid?
A. 5.6 ×1011 kgB. 2.2 ×1012 kgC. 3.4 ×1012 kgD. 5.1 ×1012 kg
29.
- 10 -
34. Which of the following is a correct expression for the total energy of the orbiting satellite shownbelow?
M
m
A. ET = - G Mmr
B. ET = G Mmr
C. ET = 12
mv2 + mgr
D. ET = 12
mv2 + -G Mmr
⎛⎝
⎞⎠
33. Which of the indicated areas of the graph represent the work needed to send an object fromseparation distance r to infinity?
A1
A2
A3
Separation Distance
GravitationalForce
rA. A1+ A2B. A2C. A2 + A3
D. A3
32. The work required to move an object in a planet's gravitational field can be determined graphicallyby calculating
A. the slope of a graph of gravitational force versus separation distance.B. the area under a graph of gravitational force versus separation distance.C. the slope of a graph of gravitational potential energy versus separation distance.D. the area under a graph of gravitational potential energy versus separation distance.
35. A satellite orbits the earth with a kinetic energy of 2.0 × 1010 J . Its gravitational potentialenergy in this orbit is -4.0 × 1010 J. What is the total energy of the satellite?
A. -6.0 × 1010 JB. -2.0 × 1010 JC. 2.0 × 1010 JD. 6.0 × 1010 J
36. The shaded area shown in the diagram represents
(Gravitational force exerted by the earth)
F
r(distance from the centre of the earth)
A. the gravitational field strength near the earth.B. the gain in kenitic energy.C. the centripetal acceleration of an object orbiting the earth.D. the work required to move an object in the earth's gravitational field.
37. A 2.0 ×103 kg satellite is in a circular orbit around the earth. The satellite has a speed of3.6 ×103 m s at an orbital radius of 3.1 ×107 m. What is the total energy of this orbitingsatellite?
A. - 2.6 ×1010 JB. - 1.3 ×1010 JC. 1.3 ×1010 JD. 3.9 ×1010 J
- 11 -
- 12 -
38. Which graph shows gravitational potential energy plotted as a function of distance r from thecentre of the earth?
A.
C.
Ep
r
Ep
r
B.
D.
Ep
r
Ep
r
39. A satellite is in a stable circular orbit around the earth. Another satellite in a stable circularorbit at a greater altitude must have
A. a smaller speed and a shorter period.B. a smaller speed and a longer period.C. a greater speed and a shorter period.D. a greater speed and a longer period.
40. Which of the following could represent the kinetic energy, the gravitational potential energyand the total energy for an orbiting satellite in a stable circular orbit?
KINETIC ENERGY GRAVITATIONAL POTENTIAL ENERGY TOTAL ENERGY
A. 40 000 J - 80 000 J - 40 000 J
B. 40 000 J 40 000 J 80 000 J
C. -80 000 J 40 000 J -120 000 J
D. 80 000 J - 40 000 J 40 000 J
-
- 13 -
1. A 4.2 ×103 kg spacecraft orbits a 5.6 ×1026 kg planet. If it takes the spacecraft 8.9 ×104 s tocomplete one orbit, how far is it from the planet’s centre? (7 marks)
- 14 -
2. a) The space shuttle orbits the Earth in a circular path where the gravitational field strengthis 8.68 N kg. What is the shuttle’s orbital radius? (5 marks)
b) A space station that has 10 times the mass of the shuttle in a) orbits Earth at the same altitude.How does the orbital speed of the space station compare to that of the shuttle?(Check one response.) (1 mark)
The space station’s speed is less than the shuttle’s speed.
The space station’s speed is the same as the shuttle’s speed.
The space station’s speed is greater than the shuttle’s speed.
c) Using principles of physics, explain your answer to b). (3 marks)
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
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3. An 884 kg satellite in orbit around a planet has a gravitational potential energy of −5. 44 ×1010 J .
The orbital radius of the satellite is 8.52 ×106 m and its speed is 7.84 ×103 m s.
a) What is the mass of the planet? (3 marks)
b) What is the kinetic energy of the satellite? (2 marks)
c) What is the total energy of the satellite? (2 marks)
- 16 -
4. A spacecraft of mass 470 kg rests on the surface of an asteroid of radius 1 400 m and mass2.0 ×1012 kg. How much energy must be expended so that the spacecraft may rise to a heightof 2 800 m above the surface of the asteroid? (7 marks)
- 17 -
5. a) Mars has a mass of 6.37 ×1023 kg and a radius of 3. 43 ×106 m . What is the gravitationalfield strength on its surface? (4 marks)
b) What thrust force must the rocket engine of a Martian lander exert if the 87.5 kg spacecraftis to accelerate upwards at 1.20 m s2 as it leaves the surface of Mars? (3 marks)
- 18 -
6. A space shuttle is placed in a circular orbit at an altitude of 3.00 ×105 m above Earth’ssurface.
a) What is the shuttle’s orbital speed? (5 marks)
- 19 -
b) The space shuttle is then moved to a higher orbit in order to capture a satellite.
The shuttle’s speed in this new higher orbit will have to be
greater than in the lower orbit.
less than in the lower orbit.
the same as in the lower orbit.
(Check one response.) (1 mark)
c) Using principles of physics, explain your answer to b). (3 marks)
- 20 -
7. A 650 kg satellite in circular orbit around Earth has an orbital period of 1.5 ×104 s.
a) What is the satellite’s orbital radius? (5 marks)
b) What is the gravitational potential energy of this satellite? (2 marks)
- 21 -
8. A 1 200 kg space probe is in a circular orbit around the Sun. The orbital radius is7.0 ×109 m .
a) What is the orbital speed of this satellite? (5 marks)
b) If the Sun collapsed to one-tenth its present radius without a change to its mass, the spaceprobe’s orbital radius will
increase.
decrease.
stay the same.
(Check one response.) (1 mark)
c) Using principles of physics, explain your answer to b). (3 marks)
- 22 -
9. What minimum energy is required to take a stationary 3.5 ×103 kg satellite from the surface ofthe Earth and put it into a circular orbit with a radius of 6.88 ×106 m and an orbital speed of7.61 ×103 m s? (Ignore Earth’s rotation.) (7 marks)
- 23 -
10. A 720 kg communication satellite is in a geosynchronous orbit around the planet Mars.
What is the orbital radius of this satellite? (7 marks)
Planetary Data for Mars
Mass: 6. 42 ×1023 kg
Period of rotation: 8.86 ×104 s
- 24 -
11. Geostationary satellites appear to remain stationary to an observer on Earth. Such satellites areplaced in orbit far above the equator.
Satellite above equator
Using principles of physics, explain why such satellites all have the same orbital radius.(4 marks)
ELECTROSTATICS
1. Which one of the following represents correct units for electric field strength?
A. TB. N/CC. J / CD. N • m2 / C2
2. The diagram below shows two positive charges of magnitude Q and 2Q.
Q 2Q
P
Which vector best represents the direction of the electric field at point P, which is equidistantfrom both charges?
A. B.
C. D.
- 1 -
3. A 6.0 x 10-6 C charge is located 4.0 m from a -3.0 x 10 -6 C charge.
Q1 = 6.0 x 10-6 CP
Q2 = -3.0 x 10 -6 C
2.0 m2.0 m
What is the electric potential at P, halfway between the charges?
A. - 4.1 x 10-2 VB. 6.8 x 103 VC. 1.4 x 104 VD. 4.1 x 104 V
4. The diagram below shows the electric field near two point charges L and R.
L R
What is the polarity of each charge?
CHARGE L CHARGE R
A. positive positive
B. positive negative
C. negative positive
D. negative negative
5. The electric field 2.0 m from a point charge has a magnitude of 8.0 ×104 N/C. What is the strengthof the electric field at a distance of 4.0 m?
A. 2.0 ×104 N/CB. 4.0 ×104 N/CC. 1.6 ×105 N/CD. 3.2 ×105 N/C
6. When a charge is accelerated through a potential difference of 500 V, its kinetic energy increasesfrom 2.0 ×10−5 J to 6.0 ×10−5 J . What is the magnitude of the charge?
A. 4.0 ×10−8 CB. 8.0 ×10−8 CC. 1.2 ×10−7 CD. 1.6 ×10−7 C
- 2 -
- 3 -
8. A negative charge in an electric field experiences a force accelerating it due south. What is thedirection of the electric field?
A. eastB. westC. northD. south
9. A − 2.3×10−6 C charge exerts a repulsive force of magnitude 0.35 N on an unknown charge0.20 m away. What are the magnitude and polarity of the unknown charge?
MAGNITUDE POLARITY
A. 6.8 ×10−7 C Negative
B. 6.8 ×10−7 C Positive
C. 1.2 ×10−6 C Negative
D. 1.2 ×10−6 C Positive
10. Two point charges, 2.5 ×10−6 C and −5.0 ×10−6 C , are placed 3.0 m apart as shown below.
1.5 m
P+
−5.0 10− 6 C×2.5 10−6 C ×_
1.5 m
What is the magnitude of the electric field at point P, midway between the two charges?
A. 0 N / CB. 1.0 ×104 N / CC. 2.0 ×104 N / CD. 3.0 ×104 N / C
7. What is the electric potential energy of an electron located 5.3×10−11 m from the proton in ahydrogen atom?
A. −8.2 ×10−8 JB. − 4.3×10−18 JC. − 2.2 ×10−18 JD. −1.6 ×10−19 J
- 4 -
11. A 4.0 ×10−9 C charge is initially located 3.0 m from a stationary 6.0 ×10−8 C charge. How muchwork is required to move the 4.0 ×10−9 C charge to a point 0.50 m from the stationary charge?
+
0.50 m
3.0 m4.0 × 10− 9 C 6. 0 ×10−8 C+
A. 6.0 ×10−7 JB. 8.6 ×10−7 JC. 3.6 ×10−6 JD. 4.3×10−6 J
12. Two parallel plates 4.0 ×10−2 m apart have a potential difference of 1000 V. An electron isreleased from the negative plate at the same instant that a proton is released from the positive plate.Which of the following best compares their speed and kinetic energy as they strike the oppositeplate?
SPEED OFELECTRON AND PROTON
KINETIC ENERGY OFELECTRON AND PROTON
A. same sameB. same differentC. different sameD. different different
13. Two long, parallel plates are separated by 0.028 m and have a potential difference between them of80 V, as shown below.
P80 V
0 V0.014 m
0.028 m
Point P is located midway between the plates. What is the potential difference between point P andone of the plates?
A. 0 VB. 40 VC. 80 VD. 160 V
- 5 -
15. Two positive charges, equal in magnitude, are separated as shown below.
1 2 3 4⊕⊕
In which location would the electric field strength be zero?
A. 1B. 2C. 3D. 4
16. An electron is positioned in an electric field. The force on the electron due to the electric field isequal to the force of gravity on the electron. What is the magnitude of this electric field?
A. 8.93 ×10−30 N/CB. 5.69 ×10−12 N/CC. 5.58 ×10−11 N/CD. 1. 44 ×10−9 N/C
14. A particle with a charge of 2.4 ×10−5C is accelerated from rest through a potential differenceof 6.2 ×104 V. If the final speed of this particle is 9.3×103 m/s, what is the mass of the particle?
A. 7.7 ×10−10 kgB. 5.2 ×10−9 kgC. 3. 4 ×10−8 kgD. 1.5 ×10−1 kg
17. Two 3.0 ×10−6 C point charges are placed 5.0 m apart as shown below.
5.0 m
5.0 m
5.0 m⊕ ⊕
P
3.0 ×10−6 C 3.0 ×10−6 C
What is the potential at point P due to the two charges?
A. 0 VB. 5. 4 ×103 VC. 7.6 ×103 VD. 1.1×104 V
- 6 -
18. Which of the following diagrams best shows the electric field between two equal negative charges?
A. B.
C. D.
19. In a hydrogen atom, the electron and proton are separated by a distance of 5.3 ×10-11 m. What isthe electric force exerted on the proton by the electron?
A. 0 NB. 4. 4 ×10−18 NC. 8.2 ×10−8 ND. 1.0 ×1012 N
20. A 2.5 C charge is moved from a point with a potential of 12 V to another point of potential 75 V.How much work was done on this charge?
A. 30 JB. 160 JC. 180 JD. 220 J
- 7 -
21. An electron is travelling in an electric field as shown.
parallel plates
electron_ v
+ + + + + + + + + + +
_ _ _ _ _ _ _ _ _ _ _ _
Describe the electrostatic force acting on the electron while in the field.
MAGNITUDE OF FORCE DIRECTION OF FORCE
A. Changing Upward
B. Changing Downward
C. Constant Upward
D. Constant Downward
22. A proton initially at rest is accelerated between parallel plates through a potential differenceof 300 V .
+ 300 V0.040 m
0 V
proton
+
What is the maximum speed attained by the proton?
A. 7.5 ×103 m/sB. 1.7 ×105 m/sC. 2. 4 ×105 m/sD. 1.2 ×106 m/s
- 8 -
23. An electron experiences an electric force of 1.8 ×10−11 N at a distance of 5.0 ×10−9 m from thenucleus of an ion. The electron is moved farther away, to a distance of 2.0 ×10−8 m from the ion.What is the new electric force on the electron?
A. 1.1×10−12 NB. 4.5 ×10−12 NC. 7.2 ×10−11 ND. 2.9 ×10−10 N
24. What is the magnitude of the electric field at point P due to the two fixed charges as shown?
P+
+
5.0 ×10−6 C
8.0 ×10−6 C
3.0 m
3.0 m
A. 3.0 ×103 N / CB. 9. 4 ×103 N / CC. 1.3×104 N / CD. 3.9 ×104 N/C
25. Which of the following is an equivalent unit for the volt?
A. Cs
B. JC
C. NC
D. J
- 9 -
26. An object with a charge of + 4.0 ×10−18 C and a mass of 1.1×10−15 kg is held stationary bybalanced gravitational and electric forces midway between horizontal charged plates as shown.What is the applied voltage V?
1.2 × 10−2 m
charged object
V
A. 16 V
B. 32 V
C. 65 V
D. 2.7 ×102 V
27. What are the magnitude and direction of the electric force on the +2.0 ×10−6 C charge shownbelow?
q = +2. 0 ×10−6 CQ1 = −6.0 ×10−6 C Q2 = −7.0 ×10−6 C
_ + _
4.0 m 4.0 m
MAGNITUDE OF FORCE DIRECTION OF FORCE
A. 1.1×10−3 N Left
B. 1.1×10−3 N Right
C. 1.5 ×10−3 N Left
D. 1.5 ×10−3 N Right
- 10 -
28. Which diagram shows the electric field between a pair of charged parallel plates?
A.
C.
- - - - - - - - - -
+ + + + + + + + + +
- - - - - - - - - -
+ + + + + + + + + +
B.
D.
+ + + + + + + + + +
- - - - - - - - - -
+ + + + + + + + + +
- - - - - - - - - -
29. In the diagram below, a 2.0 ×10−6 C charge experiences forces of 3.0 N and 8.0 N at its locationbetween charges Q1 and Q2 .
2 .0 × 10 C− 6
= 3.0 N1F = 8.0 N2F
Q1 Q2+
Find the magnitude of the net electric field strength at the location of the 2.0 ×10−6 C charge.
A. 2.5 ×106 N CB. 2.8 ×106 N CC. 5.5 ×106 N CD. 1.2 ×107 N C
30. How much work is done moving the −2.0 ×10−6 C charge, Q1, from S to T in the diagram shownbelow?
−+ −= − 2.0 × 10−6 C
S T
= 8.0 × 10− 6 C
5.0 m 2.0 m
Q 1Q 2
A. 5.6 ×10−3 JB. 8.2 ×10−3 JC. 1.2 ×10−2 JD. 7.2 ×10−2 J
31. A 1.60 ×10- 19 C ion is accelerated from rest through a potential difference of 750 V reaching amaximum speed of 8.50 ×104 m s. What is the mass of this ion?
A. 9.11×10- 31 kgB. 1.67 ×10- 27 kgC. 3.32 ×10- 26 kgD. 4.84 ×10- 20 kg
32. Which of the following shows the electric field between two opposite charges of unequalmagnitude?
A.
C.
B.
D.
33. Three point charges of equal magnitude but opposite sign are arranged as shown in the diagrambelow.
+Q1
_
Q2
+ Q3
Which of the diagrams below best represents the electric forces acting on Q3 due to the othertwo charges?
A. + Q3 B.
+
Q3
C.
+
Q3
D.
+ Q3
- 11 -
- 12 -
34. What is the acceleration of a proton in a uniform 2.5 ×105 N C electric field as shown below?
E
proton
MAGNITUDE OF ACCELERATION DIRECTION OF ACCELERATION
A. 2. 4 ×1013 m s2 Right
B. 2. 4 ×1013 m s2 Left
C. 1.5 ×1032 m s2 Right
D. 1.5 ×1032 m s2 Left
35. How much work is needed to move a −2.0 ×10−6 C charge from position S to position T as shownbelow?
−+
2.0 mT
3.0 m
−S
8.0 × 10−6 C −2. 0 × 10−6 C
fixed
A. 4.3×10−2 JB. 4.8 ×10−2 JC. 9.1×10−2 JD. 1.1×10−1 J
36. An electron, initially at rest, is accelerated through a potential difference of 600 V as shown.
600 V
0 V
m4 .2 × 10−2v
What is the maximum kinetic energy of the electron?
A. 3.7 ×10−31 JB. 9.6 ×10−17 JC. 6.0 ×102 JD. 1. 4 ×104 J
- 13 -
37. A cathode ray tube is adjusted so as to deflect the beam as shown.
Side View Front View
If the deflecting voltage is held constant and the accelerating voltage is then decreased , whichdiagram displays the new deflection?
A.
C.
B.
D.
- 14 -
39. Two 2.0 ×10−6 C charges are positioned as shown in the diagram below.
2 .0 10− 6 C×2 .0 10 6 C× −
X
Y
0.60
m 0 .60m
0 .40 m0 .40 m
What work must be done to move a 1.2 ×10−7 C charge from location X to location Y?
A. 3.6 ×10−3 JB. 1.5 ×10−2 JC. 1.8 ×10−2 JD. 3.9 ×10−2 J
38. A cathode ray tube beam deflects to the location as shown in Diagram I when a certain voltageis applied to the deflecting plates.
Diagram II
1
23
4
C R T S creen
Diagram I
C R T S creen
The connections to the deflecting plates are then r ever sed and the deflecting voltage isr educed. Which location in Diagram II best represents the new beam position?
A. Location 1B. Location 2C. Location 3D. Location 4
40. An electron orbits the nucleus of an atom with velocity v. If this electron were to orbit thesame nucleus with twice the previous orbital radius, its orbital velocity would now be
A. v2
B. v2
C. v
D. 2v
41. In a cathode ray tube,
A. protons are accelerated from anode (positive) to cathode (negative).B. protons are accelerated from cathode (negative) to anode (positive).C. electrons are accelerated from anode (positive) to cathode (negative).D. electrons are accelerated from cathode (negative) to anode (positive).
42. Which pair of values will cause the greatest deflection of an electron beam in a cathoderay tube?
ACCELERATING VOLTAGE DEFLECTION (PLATE) VOLTAGE
A. 400 V 20 V
B. 400 V 40 V
C. 800 V 20 V
D. 800 V 40 V
- 15 -
43. Which diagram shows the electric field near a negative point charge?
A.
C.
_
_
B.
D.
_
_
- 16 -
46. A moving proton has 6. 4 ×10−16 J of kinetic energy. The proton is accelerated by a potentialdifference of 5 000 V between parallel plates.
0 V - 5 000 V
+proton
v
+v0
The proton emerges from the parallel plates with what speed?
A. 8.8 ×105 m sB. 9.8 ×105 m sC. 1.3×106 m sD. 1.8 ×106 m s
44. In an experiment, a positively charged oil droplet weighing 6.5 ×10−15 N is held stationary bya vertical electric field as shown in the diagram.
+
EIf the electric field strength is 5.3 ×103 N C, what is the charge on the oil droplet?
A. 1.2 ×10−18 CB. 3. 4 ×10−11 CC. 4.1×104 CD. 8.2 ×1017 C
45. A proton with kinetic energy of 2.1×10−17 J is moving into a region of charged parallel plates.The proton will be stopped momentarily in what region?
0 V 100 V
v
200 V 300 V 400 V
+
proton
2.1× 10−17 J
K L M N
. .. . . . . . . .. . . .. . . . . . . .. . . .. . . . . . . .. . . .. . . . . . . .. . . . . . . .
A. Region KB. Region LC. Region MD. Region N
- 17 -
1. a) A 2.5 ×10−7 C charge is initially located 7.0 m from a fixed 8.0 ×10−6 C charge. What isthe minimum amount of work required to move the 2.5 ×10−7 C charge 2.0 m closer asshown? (5 marks)
+ +2.5 ×10−7 C 8.0 ×10−6 C
+
2.0 m
7.0 m
- 18 -
b) If the 2.5 ×10−7 C charge is moved a further 2.0 m closer to the 8.0 ×10−6 C charge, will theadditional work required be less than, the same as or greater than the work required in (a)?Using principles of physics, explain your answer. (4 marks)
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
- 19 -
2. A proton is located at A, 1.0 m from a fixed +2.2 ×10−6C charge.
+
proton
v2.2 ×10−6 C
+
1.0 m10 m
a) What is the change in potential energy of the proton as it moves to B, 10 m from the fixedcharge? (5 marks)
b) If the proton started from rest at A , what would be its speed at B ? (2 marks)
A B
- 20 -
3. A −4.2 ×10−6 C charge is placed between two stationary charges, Q1 and Q2 , as shown below.
4.2 × 10−6 C−
0.030 m
++ −7.3 × 10−6 C=Q22.5 × 10−6 C=Q1
0.020 m
What is the magnitude and direction of the net force on the −4.2 ×10−6 C charge due to the twostationary charges? (7 marks)
- 21 -
4. An electron passing between parallel plates 0.025 m apart experiences an upwardelectrostatic force of 5.1×10−16 N.
F
electron
a) What is the magnitude of the electric field between the plates? (3 marks)
b) What is the potential difference between the plates? (2 marks)
c) On the diagram below draw in the connections to the power supply necessary for theelectron to experience this upward force. (2 marks)
F
electron
- 22 -
5. Two charges are positioned as shown in the diagram below.
+ _
4.0 m 2.0 m
Q1 = 8. 0 μC Q2 = −2.0 μC A
a) Find the magnitude and direction of the electric field at A. (Note: 1.0 μC = 1.0 ×10−6 C)(4 marks)
b) A charge placed at A experiences a force of 4.0 ×10−3 N towards the right. What arethe magnitude and polarity of this charge? (3 marks)
- 23 -
6. A charge q of 30.0 µC is moved from point X to point Y.
Q1
8.00
3.00
70. 0 µC+= + = 30. 0 µC
+
How much work is done on the 30.0 µC charge? 1 µC = 1 ×10−6 C( ) (7 marks)
150
0.025 m
V = 500 V
7. A small 4.0 × 10-3 kg charged sphere is suspended by a light thread between parallel plates, as shownin the diagram below. When the plates are connected to a 500 V source, the thread makes a 150 anglewith the vertical.
What is the charge on the sphere? (9 marks)
- 24 -
900
8. Two small, indentically-charged conducting spheres each of mass 2.5 × 10-4 kg hang from the samepoint on insulating threads of length 0.50 m as shown in the diagram below. If the enclosed angle
between the threads is 900, what is the charge on each sphere? (9 marks)
- 25 -
- 26 -
9. In a cathode-ray tube, electrons are accelerated from the cathode towards the anode by anaccelerating voltage Va. After passing through the anode, the electrons are deflected by the twooppositely-charged parallel plates.
+ + + deflection
Cathode Anode
– – –
If the accelerating voltage Va is increased, will the deflection increase, decrease, or remain thesame? Using principles of physics, explain your answer. (4 marks)
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_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
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_______________________________________________________________________________
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_______________________________________________________________________________
ELECTROMAGNETISM
- 1 -
1. A compass is positioned at each of the following locations near a bar magnet.
1
2
3
4
N S
In which location will the compass needle point to the right-hand side of the page?
A. 1B. 2C. 3D. 4
2. A current-carrying conductor is placed in a uniform magnetic field as shown.
I
B
What is the direction of the magnetic force on this conductor?
A. Into the pageB. Out of the pageC. Towards the top of the pageD. Towards the bottom of the page
3. A 5.0 A current flows through a 0.20 m long solenoid that contains 1 500 loops.
5.0 A
What are the magnitude and direction of the magnetic field at the centre of the solenoid?
MAGNITUDE DIRECTION
A. 9. 4 ×10−3 T left
B. 9. 4 ×10−3 T right
C. 4.7 ×10−2 T left
D. 4.7 ×10−2 T right
- 2 -
4. Four conductors of different lengths are moved through a uniform magnetic field at the samespeed.
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
v
×
×
×
×
×
×
v
v
1
23
4
B×
×
×
×
×
×
v
Which conductor will induce the greatest emf?
A. 1B. 2C. 3D. 4
5. A motor has an armature resistance of 3.5 Ω and is connected to a 12.0 V source. At fullspeed the current through the armature is 0.18 A . What is the back emf at full speed?
A. 0 VB. 0.63 VC. 11. 4 VD. 12.0 V
6. A step-down transformer has a 500 turn primary that operates at 120 V ac. Which of thefollowing sets of conditions best describes the number of secondary turns and secondaryvoltage of this transformer?
SECONDARY TURNS SECONDARY VOLTAGE
A. 40 9.6 V ac
B. 40 1 500 V ac
C. 2 000 30 V ac
D. 2 000 480 V ac
- 3 -
7. A flexible loop of wire of area 4.5 ×10−2 m2 is positioned in a 0.17 T magnetic field asshown in Figure A. The loop is then stretched until its area is zero in a time of 0.35 s(Figure B). What is the average induced emf in the circuit and the direction of the currentthrough resistor R?
× × × ×
× × × ×
× × × ×
× × × ×
× × × ×
× × × ×
× × × ×
P
R
Q
Figure A
B
Figure B
× × × ×
× × × ×
× × × ×
× × × ×
× × × ×
× × × ×
× × × ×
P
R
Q
B
AVERAGE EMF DIRECTION OF CURRENT THROUGH R
A. 2.2 ×10−2 V P to Q
B. 2.2 ×10−2 V Q to P
C. 4.9 ×10−1 V P to Q
D. 4.9 ×10−1 V Q to P
8. An electron enters a uniform magnetic field as shown below.
–
B
The path of the electron upon entering the field would be
A. linear.B. circular.C. parabolic.D. hyperbolic.
- 4 -
9. The diagram below represents a cross-sectional view from the side of a cathode ray tube. Whatis the purpose of the coils in a functional cathode ray tube?
coil
coil
A. They increase the speed of the electrons.B. They focus the electrons into a fine beam.C. They deflect the electrons into or out of the page.D. They deflect the electrons toward the top or bottom of the page.
10. A solenoid of length 0.35 m and diameter 0.040 m carries a current of 5.0 A through itswindings. If the magnetic field in the centre of the solenoid is 2.8 ×10−2 T , what is thenumber of turns per metre for this solenoid?
A. 1.8 ×102 turns mB. 7.8 ×102 turns mC. 1.6 ×103 turns mD. 4.5 ×103 turns m
11. A 1.2 m length of wire is pulled through a uniform 0.045 T magnetic field at 6.7 m s asshown. What emf is generated between the ends of the wire?
B
1.2 m 6.7 m s 1.5 m
A. 0 VB. 0.090 VC. 0.36 VD. 0. 45 V
- 5 -
12. A dc motor is connected to a 12.0 V power supply. When the armature is rotating, the currentthrough it is 0.78 A and the back emf is 10.6 V . What is the resistance of the armature?
A. 1. 4 ΩB. 1.8 ΩC. 14 ΩD. 15 Ω
13. In which of the following diagrams is the secondary current greater than the primary current?
A.
B.
C.
D.
acPrimary Secondary
dc
Primary Secondary+–
Primary Secondary
ac
Primary Secondary+–dc
- 6 -
14. An electron circulates in a uniform 5.0 ×10−4 T magnetic field as shown. If the electron has3.2 ×10−18 J of kinetic energy, what is its radius of orbit, r ?
× ××××
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
r
B
A. 2.3 ×10−7 mB. 4.6 ×10−4 mC. 2.5 ×10−3 mD. 3.0 ×10−2 m
15. Which of the following diagrams shows the magnetic field produced by a longcurrent-carrying wire?
A. B.
×
C. × × × × × ××
× × × × × × ×I
D. × × × × × ××
× × × × × × ×I
16. Which of the following devices commonly uses a solenoid?
A. kettleB. televisionC. batteryD. incandescent bulb
- 7 -
17. An electric motor is connected to a constant source of potential. Considering back emf, whichof the following observations is correct?
A. At full speed the applied voltage increases.B. At full speed the armature resistance increases.C. If the motor is kept from rotating at full speed, the armature heats up.D. If the motor is kept from rotating at full speed, the armature temperature decreases.
19. In a step-up transformer, how does the secondary voltage Vs compare with the primaryvoltage Vp , and the number of turns in the secondary Ns compare with the number of turnsin the primary Np ?
VOLTAGE NUMBER OF TURNS
A. Vs < Vp Ns > Np
B. Vs > Vp Ns > Np
C. Vs < Vp Ns < Np
D. Vs > Vp Ns < Np
18. Which of the following are correct units for magnetic flux?
A. TB. WbC. V mD. N ⋅ m2
20. An ideal transformer has a potential difference of 130 V ac across the primary windings and apotential difference of 780 V ac across the secondary windings. There are 390 turns in thesecondary. The secondary current is
A. twice the primary current.B. one half the primary current.C. six times the primary current.D. one-sixth the primary current.
- 8 -
21. Two particles Y and Z with equal mass and speed enter a uniform magnetic field and follow thepaths as shown. How do their magnitude and polarity of charge compare?
× ××××
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
Y
Z
B
MAGNITUDE OF CHARGE POLARITY
A. Y < Z same charge
B. Y < Z opposite charge
C. Y > Z same charge
D. Y > Z opposite charge
22. A wire carrying a current of 5.0 A is in a uniform 3.2 × 10− 2 T magnetic field as shown.What is the force on the 0.15 m length of wire?
5.0 A
0 .15 m0 .25 m
B
A. 0 NB. 1.6 ×10−2 NC. 2. 4 ×10−2 ND. 4.0 ×10−2 N
- 9 -
23. A single coil of wire of area 6.0 ×10−3 m2 is positioned in a uniform 0.18 T magnetic fieldas shown. The coil is rotated 90° about axis XY in 4.2 ×10−3 s . What average emf isinduced by the coil?
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
X
Y
B
A. 0 VB. 0.13 VC. 0.26 VD. 43 V
24. A part of a coil of wire is placed in a uniform magnetic field as shown. Which two directionsof motion would immediately induce an emf in the coil?
× ××××
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
× × × × ×
1
2
3
4
B
A. 1 and 2B. 1 and 3C. 2 and 3D. 2 and 4
- 10 -
25. Which of the following diagrams best shows the magnetic field lines between the poles of twopermanent magnets?
A.
C.
N S
N N
B.
D.
N S
SS
26. A wire carrying 12 A of current is placed in a magnetic field of strength 0.63 T.
×
×
×
×
×
×
×
×
×
×
×
×
B×
×
×
×I
0.15 m
0.25 m
What are the magnitude and direction of the magnetic force acting on the wire?
FORCE DIRECTION
A. 1.1 N down the page
B. 1.1 N up the page
C. 1.9 N down the page
D. 1.9 N up the page
- 11 -
27. A particle having a charge of 3.2 ×10−19 C follows a circular path of 0. 45 m radius whiletravelling at a speed of 1.2 ×104 m s in a 0.78 T magnetic field. What is the mass of theparticle?
A. 7.8 ×10−28 kgB. 9. 4 ×10−24 kgC. 1.1 ×10−19 kgD. 3.0 ×10−15 kg
28. A 460-turn solenoid having a diameter of 0.024 m is 0.14 m long. What is the magneticfield at the centre of the solenoid when a 13 A current flows through it?
A. 0 TB. 5. 4 ×10−2 TC. 3.1 ×10−1 TD. 6.3 ×10−1 T
29. A conducting rod is moving perpendicular to a uniform magnetic field of 0.23 T at a velocityof 9.2 m s. What emf is generated during this motion?
N
N
S
S
0.25 m
0.012 m
0.15 mv=9.2 m s
A. 0 VB. 0.025 VC. 0.32 VD. 0.53 V
- 12 -
30. A rectangular coil measuring 0.12 m by 0.080 m is placed perpendicular to a 0.85 Tmagnetic field as shown.
B×
×
×
×
×
×
×
×
×
×
×
×
××× ×
0.080 m
0.12 m
What is the magnetic flux through the coil?
A. 0 WbB. 8.2 ×10−3 WbC. 6.8 ×10−2 WbD. 1.0 ×10−1 Wb
31. A single loop of wire of radius 0.23 m is placed in a 0.75 T magnetic field as shown. Themagnetic field is changed to a strength of 0.50 T in the opposite direction in 0.61 s.
B×
×
×
×
×
×
×
×
×
×
×
×
0.23 m
B
0.23 m
Before After
What is the average emf induced in the coil?
A. 0.068 VB. 0.094 VC. 0.34 VD. 0. 47 V
- 13 -
32. With the electromagnet turned off, electrons in a cathode ray tube strike the centre of the screenas shown.
Electron GunCRT
1
4
3
2
+
−
Electromagnet
When the electromagnet is turned on, where will the electron beam now strike the screen?
A. 1B. 2C. 3D. 4
I
What is the direction of the magnetic field inside the solenoid?
A.
C.
B
B
B.
D.
B
B
33. An electric current flows through a solenoid as shown below.
- 14 -
34. Which of the following diagrams best shows the magnetic field due to a long straight wirecarrying a conventional current I as shown?
A.B
I
B.B
I
C.B
I
D.B
I
35. A proton is travelling at 2.3 ×106 m s in a circular path in a 0.75 T magnetic field. What isthe magnitude of the force on the proton?
A. 1.6 ×10−24 NB. 2.9 ×10−21 NC. 2.8 ×10−13 ND. 1.7 N
36. A solenoid of length 0.75 m has a radius 0.092 m . A current of 25 A flows through its4 700 turns. Within this solenoid a 0.10 m long conductor moves at 4.3 m s perpendicularto the field in the solenoid.
v
What emf is induced between the ends of the conductor?
A. 0.085 VB. 0.197 VC. 0. 430 VD. 4.80 V
- 15 -
37. In which of the following situations would the greatest emf be induced in the coil? All changesoccur in the same time interval.
A.
C.
B
coil moves
B
coil changes shape
B.
D.
B
coil changes shape
B
coil moves
38. A motor is connected to a 12 V dc supply and draws 5.0 A when it first starts up. What willbe the back emf when the motor is operating at full speed and drawing 1.2 A?
A. 7.0 VB. 7.8 VC. 9.1 VD. 10.8 V
- 16 -
39. A long conductor is placed in a 0.65 T magnetic field as shown below.
×
×
×
×
×
×
×
×
×
×
×
B
×
= 0.65 T
0.22 m
0.56 m
××××
××××
0.35 m
What are the magnitude and direction of the current that produces a 1.6 N force on the wiredirected up the page?
MAGNITUDE OF CURRENT DIRECTION OF CURRENT
A. 4. 4 A Right
B. 4. 4 A Left
C. 11 A Right
D. 11 A Left
40. A proton has a speed of 5.0 ×106 m s while travelling perpendicular to a 0.14 T magneticfield. What is the magnetic force on the proton?
A. 1.6 ×10−26 NB. 8. 4 ×10−21 NC. 2.2 ×10−20 ND. 1.1 ×10−13 N
41. The flux through a circular coil with a radius of 0.075 m is 0.013 Wb when placedperpendicular to a magnetic field. What is the strength of the magnetic field?
A. 0 TB. 0.17 TC. 0.74 TD. 2.3 T
- 17 -
42. The diagram below shows an aluminum ring and the current induced in it by the nearby magnetthat is free to move along its central axis.
I
Magnet
Aluminum ring
Central axisNS
The magnet must be
A. stationary.B. moving to the left.C. moving to the right.D. spinning about its central axis.
43. A computer adapter contains a transformer that converts 120 V ac across its primary windingsto 24 V ac across its secondary windings. The primary current is 1.2 A. What is thesecondary current and what is the type of transformer?
MAGNITUDE OF CURRENT DIRECTION OF CURRENT
A. 0.24 A Step-up
B. 0.24 A Step-down
C. 6.0 A Step-up
D. 6.0 A Step-down
44. A charged particle travels in a circular path in a magnetic field. What changes to the magneticfield and to the velocity of the particle would both cause the radius of its path to decrease?
CHANGE TO THE MAGNETIC FIELD CHANGE TO THE VELOCITY
A. increase increase
B. increase decrease
C. decrease increase
D. decrease decrease
- 18 -
45. A loop of wire of area 0.32 m2 is placed in a 0.75 T magnetic field as shown. Themagnetic field is changed to 0.35 T in the opposite direction in 0. 45 s.
×
×
×
×
×
×
×
×
× ×
×
×
×
×
×
×
×
×
× ×
×
×
×
×
×
X Y
R = 15 Ω
Before
B B
Y
After
R = 15 Ω
X
What are the magnitude and direction of the current through the 15 Ω resistor?
MAGNITUDE OF CURRENT DIRECTION OF CURRENT
A. 0.019 A X to Y
B. 0.019 A Y to X
C. 0.052 A X to Y
D. 0.052 A Y to X
46. The direction of a magnetic field is determined to be the direction in which
A. a positive charge would tend to move.B. a negative charge would tend to move.C. the north end of a compass needle would point.D. the south end of a compass needle would point.
47. Which diagram shows the magnetic field created near a conductor carrying current towardsthe right?
A.
C.
I
I
B.
D.
I
I
- 19 -
48. A beam of positively and negatively charged particles enters a magnetic field as shown. Whichpaths illustrate the positive and negative charges leaving the magnetic field region?
Beam of chargedparticles
I
IIB
PATH OF POSITIVE CHARGES PATH OF NEGATIVE CHARGES
A. I I
B. I II
C. II I
D. II II
49. A solenoid has a length of 0.30 m, a diameter of 0.040 m and 500 windings. The magneticfield at its centre is 0.045 T. What is the current in the windings?
A. 2.9 AB. 3.0 AC. 21 AD. 170 A
50. An aircraft with a wingspan of 24 m flies at 85 m s perpendicular to a magnetic field.An emf of 0.19 V is induced across the wings of the aircraft. What is the magnitude of themagnetic field?
A. 9.3 ×10−5 TB. 5. 4 ×10−2 TC. 6.7 ×10−1 TD. 3.9 ×102 T
- 20 -
51. As a carpenter drills into a beam, friction on the drill bit causes the armature of the drill toslow down. How will the back emf and the current through the armature change as the drillslows down?
BACK EMF CURRENT
A. Increase Increase
B. Increase Decrease
C. Decrease Increase
D. Decrease Decrease
52. The diagram shows a bar magnet falling through an aluminum pipe. Electric currents areinduced in the pipe immediately above and below the falling magnet. In which direction dothese currents flow?
S
N
1 2
3 4
Falling bar magnet
Aluminum pipe
ABOVE THE MAGNET BELOW THE MAGNET
A. 1 3
B. 1 4
C. 2 3
D. 2 4
54. A 0.75 m conducting rod is moved at 8.0 m s across a 0.25 T magnetic field along metal rails.The electrical resistance of the system is 5.0 Ω .
5.0 Ω8.0 m s
B = 0.25 T
0.40 m
X
0.75 m
What are the magnitude and direction of the current through point X?
MAGNITUDE OF CURRENT DIRECTION OF CURRENT THROUGH X
A. 0.16 A Left
B. 0.16 A Right
C. 0.30 A Left
D. 0.30 A Right
53. A metal block moves with a constant speed in a uniform magnetic field.
J K
LM
vB
Which side of the block is positive?
A. JKB. KLC. LMD. MJ
- 21 -
- 22 -
55. The diagram shows a magnet suspended near a solenoid. After the solenoid has beenconnected to a power supply, the magnet rotates to a new position with its south pole pointingtowards the solenoid.
Before
After
Which arrows show the direction of the current in the solenoid and the direction of themagnetic field caused by this current?
DIRECTION OF CURRENT DIRECTION OF MAGNETIC FIELD
A. 1 3
B. 1 4
C. 2 3
D. 2 4
56. The diagram shows a 0.010 kg metal rod resting on two long horizontal frictionless railswhich remain 0. 40 m apart. The circuit has a resistance of 3.0 Ω and is located in a uniform0.20 T magnetic field.
m = 0. 010 kg
B = 0.20 T
V = 15 V
0.40 m
Find the initial acceleration and maximum velocity for the rod.
INITIAL ACCELERATION MAXIMUM VELOCITY
A. 40 m s2 190 m s
B. 40 m s2 300 m s
C. 120 m s2 190 m s
D. 120 m s2 300 m s
- 23 -
57. A coil of 25 turns of wire is suspended by a thread. When a current flows through the coil, thetension in the thread is reduced by 4.0 ×10−2 N.
0.25
m0.15 m
B = 0.065 T
What are the magnitude and direction of the current?
MAGNITUDE OF CURRENT DIRECTION OF CURRENT
A. 0.16 A clockwise
B. 0.16 A counter-clockwise
C. 4.1 A clockwise
D. 4.1 A counter-clockwise
58. A bar magnet is moving toward a solenoid.
G
N S
X Y
P
What is the direction of the current through the galvanometer and what is the direction of themagnetic field produced by this current at location P inside the solenoid?
DIRECTION OF THE CURRENTTHROUGH THE GALVANOMETER
DIRECTION OF THE MAGNETICFIELD AT P
A. From X to Y Right
B. From X to Y Left
C. From Y to X Right
D. From Y to X Left
- 24 -
1. A single loop of wire of area 5.0 ×10−3 m2 and resistance 1.8 Ω is perpendicular to auniform magnetic field B. The field then decreases to zero in 1.2 ×10−3 s inducing anaverage current of 8.3 ×10−2 A in the loop. What was the initial value of the magneticfield B? (7 marks)
- 25 -
2. An electron is accelerated from rest through a potential difference of 750 V. It then enters auniform 2.3 ×10−3 T magnetic field at right angles to the field.
a) What is the speed of the electron? (3 marks)
b) What is the radius of its path in the magnetic field? (4 marks)
- 26 -
3. An electric device operates on 9.0 V ac and has a total resistance of 21 Ω. An idealtransformer is used to change the incoming line voltage of 120 V ac to the operating voltageof 9.0 V ac.
a) Is the transformer a step-up or step-down transformer? (1 mark)
b) What is the current in the primary side? (6 marks)
- 27-
4. An electric motor is connected to a 9.0 V power supply. The data table below shows howthe back emf of the motor, Vback , varies with the current through the armature, I , as themechanical load changes.
Back emf Vback (V) 7.5 6.0 4.5 3.0 1.5 0
Current I (A) 1.0 2.0 3.0 4.0 5.0 6.0
a) Plot this data on the graph below. (2 marks)
I (A)
Vb (V)
00
b) Determine the slope of this graph. (2 marks)
c) What property of the motor does the slope of this graph represent? (1 mark)
x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x
BV75
SwitchGlider
0.12 m
5. The diagram below shows a pair of horizontal parallel rails 0.12 m apart with a uniform magnetic fieldof 0.055 T directed vertically downward between the rails. There is a glider of mass 9.5 ×10−2 kg acrossthe rails. the internal resistance of the 75 V power supply is 0.30 ohms and the electrical resistance of therails and the glider is negligible. Assume friction is also negligible.
(a) When the switch is closed, what is the initial accleration of the glider? (5 marks)
(b) What is the value of the terminal velocity as limited by the back emf produced by the moving glider? (4 marks)
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6. A rectangular loop is suspended by a spring scale between magnetic poles. The loop is0.060 m wide by 0.120 m high. As the current in the loop is varied, the readings of the spring scale
N
S
0.120 m0.060 m
Vdc
and current are plotted on a graph.
0 1.0 2.0 3.0 4.0 5.0 6.0
For
ce o
f Spr
ing
Sca
le (
N)
Current in Loop (A)
1.0
2.0
3.0
6.0
5.0
4.0
0
a) What is the weight, in newtons, of the loop? (1 mark)
b) What is the slope of the best fit line? (2 marks)
c) What is the magnitude of the magnetic field? (2 marks)
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7. A coil of wire containing 50 loops is lying on a flat surface in a 0.60 T magnetic field pointingdirectly into the surface.
r = 0. 40 m
The magnetic field then changes to a value of 0.10 T in the opposite direction in 2.10 s.What is the average emf induced in the coil during the time that the magnetic field waschanging? (7 marks)
1.5 Ω
0.12 m
End View Side View
S N
8. A rectangular conducting loop of mass 4.5 x 10 -2 kg and resistance 1.5 Ω is dropped in thedirection shown through a uniform horizontal magnetic field of 1.8 T.
At what speed will this loop be falling through the magnetic field when it stops accelerating? (7 marks)
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SPECIAL RELATIVITY
Vector Problems
1. How far east has a person walked if he travels 350 m in a direction 25° E of N?2. What would be the resulting displacement if a snail crawls 2.0 m north and then 3.0 m east?
What is the snail's direction from the starting point?3. Find the magnitude and direction from the horizontal of a 40.0 N upward force and 17.0 N
horizontal force.
4. A boat travels east at 13 km/hr when a tide is flowing north at 1.2 m/s. Find the actualvelocity and heading of the boat.
5. A person that swims at 3.2 m/s swims straight across a river with a current of 1.4 m/s. Whatis the resulting velocity of the swimmer (across and down stream)? At what angle comparedto straight across is the swimmer moving?
6. The swimmer above decides to swim into the current at such an angle that he will travelstraight across. Find the angle (compared to straight across) at which he would have toswim. Calculate the velocity across the stream.
7. If the river above is 1.58 km across how long will it take for each of the swimmers inquestion 5 & 6 to cross the river? How far downstream will the swimmer in question 5 land?
8. A plane with an air speed of 400 km/hr wants to go north but a wind of 70 km/hr is blowingwest. What must be the plane's heading (to go north)? What will be its resulting groundspeed?
9. A plane is traveling at 650 km/hr in a direction 37° east of north. Find the how fast the planeis traveling north and east. Find how far north and how far east it would travel in 90 minutes.
10. A boat has a speed of 9.0 km/hr, in still water and is traveling down a river with a current of2.0 m/s. What will be its "riverbank" velocity going downstream? At what angle would thisboat have to travel across the river in order to move straight across and what will be itsresultant velocity as measured from the riverbank?
MoreVector problems
1. A seagull flying with an air speed of 10 km/h is flying north but suddenly encounters a windof 5 km/h at 20° south of east. What will be the new direction and airspeed of the seagull?
2. A pilot wishes to reach a city 600.0 km away in a direction of 15° S of W in two hours. Ifthere is a wind of 70 km/h blowing at 10° W of S. What must be the heading and air speed ofthe plane?
3. A plane that can fly at 250 km/h wishes to reach an airport that has a bearing of 25° W of Nfrom its present location. If there is a 50.0 km/h wind blowing directly to the west whatshould be the heading of the plane. What will be its ground speed? How long would it taketo get to the airport if it were 560 km away?
4. A pilot of an airplane with an air speed of 300. km/h is on a heading of due north but finds heis actually traveling 350 km/h 8° W of N. What must be the wind velocity and direction?
5. A plane heading due north with an air speed of 250 km/h is blown off course by a windblowing at 50 km/h to the NE. What will be the ground speed and direction of the plane?
6. A boat capable of 10.5 knots in still water wishes to cross a narrows at a bearing of 23° N ofE. If the current in the narrows is at 3.7 knots at 8° E of S. What must be the heading of theboat and what will be its chart speed?
Special Relativity Review
Multiple Choice Identify the letter of the choice that best completes the statement or answers the question.
____ 1. Time is
a. dependent on the observer d. simultaneous in all cases b. absolute e. never changing c. the same for different observers
____ 2. Newtonian mechanics are valid a. in all frames of reference d. on Earth only b. in relativistic frames of reference e. both b and c c. in inertial frames of reference
____ 3. In Newtonian mechanics, the speed of light a. is 3 × 108 m/s d. will be faster than c b. can be infinite e. none of the above c. will be slower than c
____ 4. Michelson-Morely proposed that when Earth was moving opposite to the ether wind it would a. slow the speed of light b. make the speed of light increase c. not be detectable d. be massless, and therefore would not affect the speed e. be nonexistent
____ 5. A beam of light is shone forward from a moving vehicle. The speed of light leaving the vehicle will be a. dependent on the speed of the vehicle b. the addition of the speed of light plus the speed of the vehicle c. constant at the speed of light d. slower so that the addition of the vehicle’s speed corrects it e. none of the above
____ 6. The length of a horizontal metre stick moving at 0.75c is a. 1.00 m d. 0.56 m b. 0.66 m e. 1.51 m c. 0.44 m
____ 7. The pendulum of a grandfather clock in a ship moving at 0.6c was set to have a period of 1.0 s. What period did it appear to have to an observer on the ground? a. 1.67 s d. 1.00 s b. 0.64 s e. 0.80 s c. 1.25 s
____ 8. The length contraction will apply to which of the following dimensions of an object: a. height relative to direction d. all dimensions equally b. length relative to direction e. no contraction occurs c. width perpendicular to direction
____ 9. A scientist in a very fast spaceship wants to do an experiment to determine whether he is moving. Which quantity can be measured to find out whether the scientist is moving or at rest? a. Time can be measured accurately. b. Length can be measured accurately. c. Time and length can be measured together. d. An object can be observed going by the window. e. Nothing can be measured which would indicate this.
____ 10. What length will a vertical metre stick moving sideways at 0.99c appear to be? a. 100 cm d. 1 cm b. 99 cm e. 0.01 cm c. 14 cm
____ 11. An astronaut flying at 0.65c takes a 3-h sleep period. How long does mission control think that the astronaut has slept? a. 4.61 h d. 3 h b. 3.90 h e. 2.28 h c. 3.58 h
____ 12. A computer can make a calculation in 0.25µs. If the computer is in a ship moving at 0.95c, how long will each calculation take relative to Earth? a. 0.80 µs d. 0.18 µs b. 0.24 µs e. 0.08 µs c. 0.26 µs
____ 13. Mission control would like an cosmonaut to check her heart rate. She is flying at 0.50c. If a normal heart rate is 72 beats/min, what would a normal heart rate appear to be for the cosmonaut? a. 288 beats/min d. 72 beats/min b. 62 beats/min e. 18 beats/min c. 83 beats/min
____ 14. A ship flies by at 0.82c and is observed by ground-based radar to be 55 m in length. What is the ship’s proper length? a. 96 m d. 43 m b. 73 m e. 31 m c. 45 m
Completion Complete each sentence or statement.
25. A frame of reference in which the law of inertia holds is called a(n) ____________________________
26. A(n) ____________________frame of reference is a frame of reference that is accelerating relative to an inertial frame.
27. All laws of physics are the ____________________in all frames of reference.
28. The Michelson–Morley interferometer experiment was performed to prove the existence of a(n) ____________________.
29. The slowing of a clock on a moving object is called ____________________.
Short Answer
35. A plane is dropping medical supplies to a village. Describe the path of the supplies relative to an observer on
the ground watching the plane travel from left to right.
36. Looking out a train window, you see a train on the adjacent track. Explain why you think it might be the other train moving when it is really your train that has started to move.
37. Suppose that an ether wind did exist. What would happen to the speed of light if it were projected into an oncoming ether wind?
38. A car moving forward at 0.5c turns on its headlights. What would the speed of light appear to be to the driver and to a pedestrian in front of the car?
39. If a scientist looks out the window while flying by a clock on Earth at nearly the speed of light, how would she perceived time on Earth?
40. A spacecraft is travelling between two stars at 0.9c. Would the pilot of the ship notice any changes to the shape or length of the ship?
41. A person sees an UFO fly by at 0.9c and describes the ship to be the classic “flying saucer” shape. What shape of ship would you look for if the ship had landed on the ground?
42. What would happen to the relativistic momentum of any object with mass as it approached the speed of light?
43. What happens to the total energy of an object as the speed of the object increases?
Problem
44. Bonus: Two 30 m long spaceships are flying toward each other. One ship is travelling at 0.30c and the
other at 0.42c. What do each of the pilots observe the others ship’s length to be?
45. Bonus: For an electron with speed 0.880c, calculate its kinetic energy if its total energy is 0.980 MeV.
