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AP Physics 1
Fall Semester Review
One Dimensional Kinematics
1. Be able to interpret motion diagrams.
a. Assuming there are equal time intervals between each picture shown above, which car in the
diagram above is going faster and how can you tell?
Car B – covers more distance each time interval
b. In the diagram above, give a real life example that would fit the motion depicted in each.
Assume equal time intervals between the depictions.
A. Falling Object
B. Car on cruise control
C. Car slowing down (braking)
c. In the diagram above, what is the object’s displacement between the starting and ending points?
Displacement = final position – initial position = -2 -3 = -5 mi
2. Be able to differentiate between speed and velocity,
a. Compare and contrast speed and velocity. Speed is a scalar quantity. It is how far you have
traveled divided by the time it took. Velocity is a vector quantity. It is your displacement (how
far you ended up from where you started) divide by time. If you are traveling in a straight line
these values are the same.
3. Be able to differentiate between vector and scalar quantities.
a. Compare and contrast vector and scalar quantities. Vector quantities have both magnitude and
direction. Examples are velocity, acceleration, force, etc. Scalar quantities have magnitude
only. Examples are speed, distance traveled, temperature, etc.
4. Be able to draw and analyze position vs time, velocity vs time, and acceleration vs time graphs.
a. Describe (draw) the basic shape of the position vs time graph for on object sitting still, an object
moving with constant positive velocity, an object moving with constant negative velocity, object
moving with constant positive acceleration, and object moving with constant negative
acceleration.
b. How does the fact that one object has a greater speed than another object affect the position vs
time graph of the two objects? It will have a greater slope.
c. On a position vs time graph, how can you find the velocity of an object at a specific time?
slope
d. Describe (draw) the basic shape of the velocity vs time graph for on object sitting still, an object
moving with constant positive velocity, an object moving with constant negative velocity, object
moving with constant positive acceleration, and object moving with constant negative
acceleration.
e. On a velocity vs time graph, how can you find the acceleration of an object at a specific time?
Slope
f. On a velocity vs time graph, how can you find the position of an object at a specific time?
Area between the line / curve and the x axis.
Sitting still + velocity - velocity + accel. - accel
Sitting still + velocity - velocity + accel. - accel
g. Which object in the diagram above had the greatest displacement between zero and two seconds?
How can you tell?
B has the largest area between the line and the x axis
h. How can you find the instantaneous velocity from a position vs time graph of an object that has a
constant acceleration?
Find the slope of the line tangent to the curve at that point. Or find the average acceleration
over a period that has that time at the center.
i. Sketch the velocity time graph that would match the position time graph shown above?
j. How can the average acceleration of an object be determined from a velocity vs time graph?
Slope
k. How can the instantaneous acceleration of an object be determined from a velocity vs time
graph?
Find the slope of the line tangent to the curve at that point. Or find the average acceleration
over a period that has that time at the center.
d
t
l. Describe (draw) the basic shape of the acceleration vs time graph for on object sitting still, an
object moving with constant positive velocity, an object moving with constant negative velocity,
object moving with constant positive acceleration, and object moving with constant negative
acceleration.
m. Use the graph above to answer the following questions.
1. How far has the object moved from 0 to 3 seconds?
(0.5)(20)(3) = 30 m
2. How fast is the object moving at 4 seconds?
10 m/s
3. What is the average velocity of the object between 3 and 5 seconds?
10 m/s
4. What is the object’s acceleration at 10.5 seconds?
20 m/s2
5. What is the object’s average acceleration between 3 and 7 seconds?
-10 m/s
6. At what time will the object be back at its starting position?
Area above = (.5)(20)(3) + (.5)(20)(5-3) = 50
Area below = (.5)(20)(2) + ?(20) = 50 so ? is 1.5
At 8.5 sec it is back at the origin
Sitting still + velocity - velocity + accel. - accel
7. At what time does the object changing directions of travel?
5 sec
8. Rank the magnitude of the object’s acceleration for each of the following time
intervals: 0 – 3, 3 – 5, 5 – 7, 7 – 10, 10 – 11, and 11 – 14.
10 – 11 (20 / 1), 3 – 5 and 5 – 7 (20 / 2), 0 – 3 (20 / 3), and 7 – 10 and 11 – 14 (0)
5. Be able to define acceleration.
a. Define acceleration. Rate of change of velocity. Vector quantity
b. An object is accelerating at 5 m/s2 means that each second its velocity will increase by _5__ m/s.
c. For an object to accelerate it can either have a change in __(speed or magnitude)__ or
___direction__ since acceleration is a _vector__ quantity.
6. Be able to solve one dimensional kinematics problems.
a. A hiker walks 500 m to the north in 10 minutes then pauses to admire the view for 2 minutes
before walking another 250 m to the north in 4 minutes before he realizes he dropped his wallet
so he turns around searching for his wallet and a walks 300 m to the south in 15 minutes until he
finds it on the trail. What distance has the hiker traveled? What is the hiker’s displacement from
where the started? What was his average speed (in m/s) for this portion of his hike? What was
the magnitude of his average velocity for this portion of his hike?
Distance = 500 + 250 + 300 = 1050 m
Displacement = 500 + 250 – 300 = 450 m
Speed = 1050 / (31*60) = 0.56 m/s
Velocity = 450 / (31*60) = 0.24 m/s
b. A ball is rolling at 3 m/s when a force acts on it and causes it to accelerate at 0.5 m/s2 for the next
5 seconds. What is the velocity of the ball after the 5 seconds? How far has the ball traveled in
those 5 seconds?
Vf = 3 + (0.5)(5) = 5.5 m/s
X = Xo +vot + 0.5at2 = 0 + 3(5) + (0.5)(0.5)(5
2) = 21.25 m
c. A coin is thrown straight downward at 2 m/s from a height of 8 m. How long will it take the
coin to strike the ground and how fast will it be going?
Vf2 = vo
2 + 2a(x-xo0
Vf2 = (-2)
2 + 2(-9.8)(8)
Vf2 = 160.8
Vf = -12.7 m/s
Vf = Vo + at
-12.7 = -2 + (-9.8)t
t = 1.09 sec
d. A body moving in the positive x direction passes the origin at time t = 0. Between t = 0 and t = 1 second, the body has a constant speed of 14 meters per second. At t = 1 second, the body is given a constant acceleration of 3 meters per second squared in the negative x direction. What is the position of the body at 10 seconds? D = v * t
D = (14)(1) = 14 X = xo + vot + (0.5)at2 X = 14 + (14)(7) + (0.5)(3)(72) X = 38.5 m
Two Dimensional Kinematics 1. Be able to add multiple vectors.
a. A jogger goes 3 km North, then 2 km West, and finally 1 km south. What is the joggers
displacement? (both magnitude and direction).
2.83 km @ 45o North of West
b. A force of 30 N acting at 25
o North of West, a force of 50 N acting at 15
o East of South, and
a force of 75 N acting at 30o East of North all acting on the same object. What is the
resultant force acting on the object?
Vector Horizontal Component Vertical Component
30 cos 25 = 27.2 -20 sin 25 = -8.45
-50 sin 15 = -12.9 50 cos 15 = 48.29
75sin 30 = 37.5 75 cos 30 = 60.6
Resultant 51.8 100.44
Resultant = 11344.1008.51 22 =+ km @ 62.7o north of east
2. Be able to add, subtract and multiply a vector by a scalar quantity.
a. Graphically show the resultant of the following situations for vectors A and B shown below.
BArr
+ BArr
− BArr
3−
b. In the diagram below what is the direction of the acceleration at point P? (v2 – v1)
Av
A
Br
A
P
V2
V1
-V1
v2 – v1 is the direction of the
acceleration
c. In what direction is the average velocity during the time interval shown (t1 to t2) and where
would it be the same as the instantaneous velocity? Halfway between T1 and T2 (midpoint
of the time interval)
d. Graphically show the direction of the acceleration between t1 and t2 (assume v1 is the velocity
at time t1 and v2 is the velocity at time t2)?
3. Be able to calculate the distance traveled, displacement, average speed, average velocity and
acceleration for object moving in two dimensions.
a. A car travels 40 km North in 10 minutes before turning left and moving 30 km East in 5
minutes when it gets to a Y in the road. The car takes the right fork and travels 50 km at 45o
South of East in 20 minutes. How far did the car travel during the trip? What is the car’s
displacement from its origin? What is the car’s average speed for the trip? What is the
magnitude of the car’s average velocity for the trip?
Distance traveled = 40 + 30 + 50 = 120 km
Vector Horizontal Component Vertical Components
40 km North 0 40
30 km East 30 0
50 km at 45o
South of East
-50cos45 = - 35.4 50sin45 = 35.4
Resultant -5.4 75.4
Displacement = km6.754.75)4.5( 22 =+− @ 274o
Speed = 120,000 / (35*60) = 57 m/s
Velocity = 75,600 / (35*60) = 36 m/s
t1 t2
V1 V2
V2
-V1
v2 – v1
b. A racecar makes one lap on a round racetrack which has a radius of 150 m. What distance
did the car travel? What is its displacement after the one lap? If the lap took the car 15
seconds to make, what is the average speed of the car and what it its average velocity for the
lap?
Distance Traveled = 2π r = 2π (150) = 942.5 m
Displacement = 0
Speed = 62.8 m/s
Velocity = 0 m/s
4. Be able to solve projectile motion problems.
a. In projectile motion, the horizontal acceleration is _0__ m/s2 and the vertical acceleration is
_-9.8__ m/s2. Therefore, the horizontal velocity is (constant / changing) and the vertical
velocity is (constant / changing).
b. A rock is thrown from the ground so that it has vx = 10 m/s and vy = 5 m/s. What is the speed
of the rock as it hits the ground? How long will the ball remain in the air? How high will the
rock rise? How far away will the rock land?
smv
v
vvv yx
/18.11
510 222
222
=
+=
+=
sec02.12
51.0
)8.9(05
=
=
−+=
+=
t
t
t
atvv of
my
y
attvyy oo
27.1
)51.0)(8.9)(5.0()51.0)(5(0
)5.0(
2
2
=
−++=
++=
md
d
t
dvx
1.10
02.110
=
=
=
c. An arrow is shot at 35 m/s at an angle of 25o with the horizontal. What is the speed of the
rock as it hits the ground? How long will the ball remain in the air? How high will the rock
rise? How far away will the rock land?
Launch velocity = landing velocity if they are the same height. 35 m/s
sec02.32
sec51.1
)8.9(25sin350
=
=
−+=
+=
t
t
t
atvv of
my
y
attvyy oo
16.11
)51.1)(8.9)(5.0()51.1)(25sin35(0
)5.0(
2
2
=
−++=
++=
md
d
t
dvx
8.95
02.325cos35
=
=
=
d. A projectile is launched at 25 m/s at an angle of 30o. One second later, how high and how far
down field is the projectile?
my
y
attvyy oo
6.7
)1)(8.9)(5.0()1)(30sin25(0
)5.0(
2
2
=
−++=
++=
md
d
t
dvx
7.21
130cos25
=
=
=
e. In the diagram below, draw vectors representing the horizontal velocity, vertical velocity,
and acceleration at each location? Keep in mind that the length of a vector is an indication of
its magnitude. Color code the vectors so that you can tell them apart and put a key.
Gravity
Horizontal Velocity
Vertical Velocity
f. To maximize the range of a projectile you should fire it with a (large / small) velocity at an
angle of __45____ degrees.
5. Be able to solve horizontal circular motion problems.
a. If an object is changing speeds as it moves around a corner. It will have both a _radial
(centripetal)___ and a __tangential (linear)_ __ acceleration. The _centripetal__
acceleration will be toward the center of the circle and the _linear__ acceleration will be
along a tangent to the circle.
b. In the diagram below, the object is moving in a horizontal circle at a constant speed. Draw
vectors representing the velocity of the object and the centripetal acceleration at each
position indicated.
c. A 2 kg stone is twirled at a constant rate on the end of a 1.5 m long rope. The stone makes a
complete revolution every 0.5 seconds. What is the speed of the stone? What is the
centripetal acceleration of the stone? What is the centripetal force acting on the stone?
smT
rv /8.18
5.0
)5.1(22===
ππ
222
/6.2355.1
8.18sm
r
vac ===
NmaF cc 3.471)6.235)(2( ===
d. If the speed at which an object is moving around the horizontal circle of constant radius is
tripled, what happens the centripetal force acting on the object? 9 times as much What
happens to the centripetal acceleration? 9 times as much
Velocity
Acceleration
Statics and Free Body Diagrams 7. Be able to draw a free body diagram for an object in a variety of situations.
a. Draw the free body diagram for each of the following situations. Keep in mind that the length of
a vector indicates its magnitude. Do not show any components of vectors.
1. A bowling ball rolling down the frictionless lane at a constant speed.
2. An elevator ascending at constant speed.
3. A crate being pulled by a rope angled at 25o with the horizontal across a bumpy
sidewalk (ie has friction).
4. A box sitting on a 10o incline which has friction.
5. A box sliding at constant speed down an incline that has friction.
FN
FW
FT
FW
FN
FW
FF
FT
FF
FN
FW
FF
FN
FW
6. You push a crate across the floor at a constant speed against friction. Assume your
arms make an angle of 30o with the horizontal.
8. Be able to explain the conditions under which an object is in translational equilibrium.
a. An object in translational equilibrium has an acceleration of __0___ m/s2.
b. The net force acting on an object in translational equilibrium is _0__ N.
9. Be able to solve problems for objects in equilibrium.
a. A broom handle inclined at 35o with the horizontal is pushed at a constant speed by a force along
the handle of 100 N. What is the frictional force between the broom and the floor?
NFF xF 9.8135cos100 ===
b. A 100 kg crate is being pulled at constant speed by a rope that makes an angle of 30o with the
horizontal. If the tension in the rope is 200 N, what is the coefficient of friction between the
crate and the floor?
196.0
)30sin200)8.9(100(2.173
2.17330cos200
=
−=
=
===
µ
µ
µ NF
xF
FF
NFF
c. A 50 kg box is suspended by a massless rope from the ceiling. What is the tension in the rope?
Suppose the rope is not massless, how will this affect the tension in the rope?
490 N It will equal the weight of the object if the rope is massless. If the rope is not massless,
the tension will equal the weight of the object where it touch the object and increase to the
weight of the object plus the weight of the rope at the point it attaches to the ceiling.
FN
FW
FF
Fa
d. A 500 N object is suspended from the ceiling as shown below. The slanted cord going to the
ceiling makes a 40o angle with the ceiling. What is the tension in the slanted cord going to the
ceiling? What is the tension in the horizontal cord?
NFT 77840sin
500==
NF
F
T
T
596
50040tan
=
=
e. A 1.5 m long uniform porch swing with a mass of 150 N is hung by a chain at each end. A 500
N person sits 0.3 m from the left end of the swing. The tension in the chain at the right end is
175. What is the tension in the left chain?
475 N Force up = Force down
f. Two teams are playing tug of war. Each team is pulling on the rope with a force of 1500 N, what
is the tension in the rope?
1500 N.
g. A 200 kg sign is suspended equally by two ropes which make an angle of 35o with each other.
What is the tension in each rope?
NF
F
F
F
6.1027
2
)8.9)(200(
)5.72sin(
=
=
h. As 600 N student is on a bathroom scale in an elevator that is descending at constant speed.
What is the reading on the bathroom scale?
NF
F
maFF
N
N
wN
600
)0(8.9
600600
=
=−
=−
Dynamics 1. Be able to solve problems for objects accelerating across level ground, vertically, and on an incline
both with and without friction.
a. A 50 kg cart is being pulled across level ground by force of 200 N applied parallel to the ground.
The coefficient of kinetic friction between the cart and the ground is 0.1. What is the
acceleration of the cart?
2/02.3
50)1.0)(8.9(50200
sma
a
maFF Fa
=
=−
=−
b. A cart of mass m is being pulled across level ground by force of F applied at an angle of θ with
the horizontal. The coefficient of kinetic friction between the cart and the ground is µ. What is
the acceleration of the cart in terms of m, F, θ and µ.
am
FmF
maFmF
=−−
=−−
)sin8.9(cos
)sin8.9(cos
θµθ
θµθ
c. A 60 kg crate is being pulled up a 15o incline by force applied parallel to the incline. The
coefficient of kinetic friction between the cart and the ground is 0.15. To give the cart an
acceleration of 0.5 m/s2 up the ramp, what force must be applied?
NF
F
mmgmgF
1217
15cos)8.9(60)15.0(15sin)8.9(60)5)(.60(
)5.0()cos(15.0sin
=
++=
=−− θθ
d. A 75 kg cart is being pushed across level ground by force of 200 N applied at an angle of 30o
with the horizontal. The coefficient of kinetic friction between the cart and the ground is 0.2.
What is the magnitude of the acceleration of the cart?
2/827.0
75))30sin(200)8.9(75(2.030cos200
sma
a
=
=+−
e. A 500 kg elevator is speeding up as it ascends at a rate of 2 m/s2. What is the tension in the cable
on the elevator?
NF
F
maFF
T
T
WT
5900
)2)(500()8.9)(500(
=
=−
=−
θ
30o
f. A 600 kg elevator is accelerating downward at 3 m/s2. What is the tension in the cable?
NF
F
maFF
T
T
WT
4080
)3)(500()8.9)(600(
=
−=−
=−
g. As 600 N student is on a bathroom scale in an elevator that is descending with an acceleration of
1.0 m/s2. What is the reading on the bathroom scale?
NF
F
maFF
N
N
WN
1100
)1)(500()600(
=
=−
=−
2. Be able to combine linear motion problems with dynamics problems.
a. Due to friction, a 5 kg cart is slowing down from 6 m/s. If the coefficient of kinetic friction
between the cart and the ground is 0.2, how far will the cart travel before coming to a stop?
mx
x
xxavv
a
NF
of
F
18.9
)0)(96.1(260
)(2
96.15
8.9
8.9)8.9)(5)(2.0(
22
0
22
=
−−+=
−+=
−=−
=
==
3. Be able to explain the affect of air resistance on the speed of a falling object and calculate terminal
velocity.
a. The faster an object falls, the air resistance (increases / decreases / remains the same) until the
object reaches terminal velocity therefore the terminal velocity cause the actual acceleration of
the object to be (greater than / less than / equal to) 9.8 m/s2, downward.
b. A tiny particle of mass 4 x 10-4 kg (so Fdrag = bv) has a drag coefficient,
b = 3.3 x 10-2 kg/s. What is this particle's terminal velocity?
smv
v
b
mgv
bvmg
/119.0
103.3
)8.9)(104(2
4
=
×
×=
=
=
−
−
4. Be able to find the acceleration of systems of objects connected by ropes and find the tension in the
rope. Examples: Atwood machine, two objects moving across the floor, and one object on a table
attached to an object hanging off the table.
a. Find the tension in the cord between the two objects.
NF
F
sma
a
T
T
13.26
)27.3(2)8.9(2
/27.3
6)8.9(2)8.9(4
2
=
=−
=
=−
b. Find the tension in the cord between the two objects.
NF
F
sma
a
T
T
7.666
)3.13)(50(
/3.13
751000
2
=
=
=
=
c. Find the tension in the cord between the two objects.
NF
F
sma
a
T
T
53.6
)27.3(2
/27.3
3)8.9(1
2
=
=
=
=
5. Be able to explain Newton’s first, second and third law as well as apply them to problem
situations.
a. What is the quantitative measure of an object’s inertia? mass
b. Which has more inertia and why?
• a loaded semi tractor trailer going 10 m/s or a Corvette going 50 m/s It has more
mass
c. If the net force acting on an object is doubled, what happens to the acceleration of the object?
doubles
2
kg 4
kg
50 kg 25 kg 1000 N
2 kg
1 kg
d. A 1200 kg pick up truck is pulling a 600 kg trailer and accelerating down the road at 2 m/s2. If
the pick up truck exerts a force 3000 N on the trailer, what force does the trailer exert on the pick
up truck? 3000 N. The forces are equal and opposite according to Newton’s Third Law
e. A person pushes with force of 15 N on Box A which has a mass of 5 kg. Box A then pushes
against box B, whose mass is 10 kg, with a force of 10 N. What force does box B exert on box
A? 10 N. The force of A on B is equal but opposite to the force on B.
Universal Gravitation and Circular Motion
1. Be able to make calculations using the law of universal gravitation.
a. What is the force of attraction does a 150 kg object feel to a 2 kg object that is 0.5 m to its right?
What force of attraction does the 2 kg object feel?
NF
F
d
mGmF
8
2
11
2
21
10*8
5.0
)2)(150)(10*67.6(
−
−
=
=
=
Forces are equal in magnitude but opposite in direction
b. The force of gravitational attraction between you and the planet earth is called your
___weight__.
c. Suppose the mass of one object is tripled and the distance between them is doubled. How does
this affect the force of attraction between them?
4
3
2
32
= times as much
2. Be able to make calculations for the acceleration due to gravity at different locations.
a. A 1000 kg satellite is circling the earth at an altitude of 100 km. What is the acceleration due to
gravity at this location?
2
26
2411
2
/56.9
)10*36.6000,100(
)10*98.5)(10*67.6(
smg
d
Gmg e
=
+==
−
b. The mass of the Jupiter is approximately 300 times that of Earth and has a radius of
approximately 7 times that of Earth. In terms of the Earth’s gravity (g), what is the acceleration
due to gravity on Jupiter?
g1.67
3002
=
A
B
c. As an object moves further and further from the center of the Earth, what happens to the
acceleration due to gravity? Decreases. Inverse square relationship
d. The acceleration due to gravity does not change by a noticeable amount when you move from a
height of 10 m above the surface to 1000 m above the surface. Why is this?
Relative to the distance to the center of the earth the additional 1000 m is negligible.
e. Rank the following planets according to the acceleration due to gravity.
Acceleration due to gravity is directly related to the mass and inversely related to the square of the
radius. Largest to smallest acceleration due to gravity – 1, 3, 4, 2, 5
3. Be able to make calculations for the period of a satellite and orbital speed.
a. The moon has a period of 28 days. What is the orbital radius for the moon?
mr
r
r
Gm
dT
e
8
253
2411
3
3
10*896.3
10*91.5
)10*98.5)(10*67.6(2)60)(60)(24)(28(
2
=
=
=
=
−π
π
b. Suppose the moon was only half its current distance away, how would this affect the period of
the moon?
It would have a smaller period. It would be 8
1times as much
c. A 500 kg satellite is in orbit 1500 m above the surface of the earth. What is its orbital velocity?
What is its period?
smv
v
r
Gmv e
/7918
)10*36.61500(
)10*98.5)(10*67.6(6
2411
=
+=
=
−
==
+=
=
−
sec4.803
)10*98.5)(10*67.6(
)10*36.61500(2
2
2411
36
3
T
T
Gm
dT
e
π
π
d. Rank the planets below according to their orbital speed (fastest to slowest). Then rank them
according to period (longest to shortest)
r
Gmv e= small radius = big velocity - 2, 5, 3, 1, 4
eGm
dT
3
2π= big radius = big period - 4, 1, 3, 5, 2
4. Be able to make calculations for object rotating at a constant speed.
a. How does the rotational velocity of an object 2 cm for the center compare to the rotational
velocity of an object 4 cm from the center? Would the same be true if you were looking at
tangential (linear) velocity of the two points?
The rotational (angular) velocity does NOT depend on the radius so they are the same. The
linear velocity does depend on the radius so the one closer to the center has a smaller linear
velocity.
b. A record player makes 45 revolutions per minute. What is the angular velocity of a point 3 cm
from the center of the record?
sradrev
rev/71.4
sec60
min1
1
2
min1
45=××
π
c. A particle moves uniformly around the circumference of a circle whose radius is 8 cm with a
period of π / 10 seconds. What is the angular velocity of the particle?
srad /2010/
2==
π
πω
d. A bicycle wheel has an angular velocity of 6 rad / s. If the wheel is 0.75 m in diameter, what is
the linear speed of the bike? How far does the bike travel in 3 seconds?
smrv /5.4)75.0)(6( === ω
md 5.13)3(5.4 ==
Work, Power, and Energy
1. Be able to calculate the work done on an object.
a. How much work is done in accelerating a car from 30 m/s to 60 m/s? Answer in terms of m.
W = ∆K
W = (0.5)m(602-30
2) = 1350 * m J
b. How much work is done in moving an object from a height of 3 m to a height of 1.5 m? Answer
in terms of m.
W = ∆U
W = (m)(9.8)(3 – 1.5) = 14.7*m J
c. A 5 kg crate slides down a 15o incline for a distance of 2 m. The coefficient of sliding friction is
0.1. How much work does the weight of the object do? How much work does the normal force
do? How much work does the frictional force do?
W = (5)(9.8)(2) cos (90 – 15) = 25.36 J
W = (5)(9.8)(cos 15) (2) cos 90 = 0 J
W = (0.1)(5)(9.8)(cos15) (2) cos 180 = -9.47 J
d. According to the graph below, how much work is done from 0 to 12 sec? How much work is
done from 0 to 20 seconds?
W = (4)(12) = 48 J
W = 48 + (4)(8) = 80 J
e. Identical twins both run up a flight of stairs. John makes it to the top of the stairs in half the time
it takes his brother Joseph. How does the work done by John compare to the work done by
Joseph?
They both do the same amount of work. Work does not depend on time or speed
2. Be able to calculate potential energy, kinetic energy, and changes in each.
a. A 2 kg book is located on a desktop which is 0.75 m from the floor in a room with a ceiling
located 2.5 m above the floor. What is the potential energy of the book relative to the floor?
What is the potential energy of the book relative to the ceiling? The book is then moved to a
location 1 m above the floor. How does the change in potential energy with reference to the
floor compare to the change in potential energy with reference to the ceiling?
U = (2)(9.8)(0.75) = 14.7 J respect to the floor
U = (2)(9.8)(- 1.75) = - 34.3 J respect to the ceiling
The change in potential energy will be the same in both cases, it does not depend on the
reference point.
b. A 1500 kg car is moving at 20 m/s. What is its kinetic energy? If it then accelerates to 30 m/s,
what is its change in kinetic energy? How much work was done on the object to change its
kinetic energy?
K = (.5)(1500)(202) = 300,000 J
∆K = (0.5)(1500)(302 – 20
2) = 375,000 J
W = ∆K = 375,000 J
c. A spring is compressed a distance of 0.25 m from its equilibrium position. At this location, the
spring has stored potential energy of 1.25 J. What is the spring constant? The spring is then
compressed further to 0.5 m. What is the change in potential energy stored in the spring?
U = 0.5kx2
1.25 = (0.5) k (0.252)
k = 40 N / m
∆U = (0.5)(40)(0.52 – 0.25
2)
∆U = 3.75 J
d. You and a friend both decide to hike to the top of a mountain. You decide to take the winding
road up the mountain and your friend decides to take the direct path to the top of the mountain.
After reaching the top of the mountain, compare your gravitational potential energies (assume
you both have the same mass) and the work each of you did.
You both have the same potential energy and you both did the same work to get there. Work
does not depend on the path taken only on the displacement.
3. Be able to apply conservation of energy to problem situations.
a. An object loses 30 J of gravitational potential energy as it falls 3 m, how much kinetic energy did
it gain?
30 J of kinetic energy if there is no friction. Less than 30 J if there is friction present.
b. A marble is released from rest at the top of a 0.5 m high ramp. What is the speed of the marble
at the bottom of the ramp?
(m)(9.8)(0.5) = (0.5)(m)v2
v =3.13 m/s c. The rollercoaster in the diagram below has a velocity of 5 m/s at point A. What is its velocity at
point B? Assume the friction is negligible.
(700)(9.8)(90) + (0.5)(700)(52) = 700(9.8)(50) + (0.5)(700)v
2
v = 28.44 m/s
d. In the diagram below, use lowest point on the track as the reference point for measuring potential
energy. What is happening to the potential energy and to the kinetic energy as the object moves
from point B to point C? What is happening to the potential energy and to the kinetic energy as
the object moves from point C to point D? From B to C Potential energy is turning into kinetic
energy. From C to D kinetic energy is turning into potential energy
4. Be able to calculate power
a. Identical twins both run up a flight of stairs. John makes it to the top of the stairs in half the time
it takes his brother Joseph. How does the average power demonstrated by John compare to the
average power by Joseph?
John demonstrates twice as much power as Joseph
b. Motor A has a power rating of 50 watts and motor B has a power rating of 150 watts. How does
the amount of work done by motor B compare to the amount of work done by motor A in 30
minutes?
Motor B does 1.5 times as much work as motor A.
c. A 100 Watt motor runs uninterrupted for one minute. How much work does it do?
JW
W
t
WP
6000
60100
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