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Forces & NEWTON’S LAWS HOMEWORK

BASIC CONCEPTS OF MASS VS. WEIGHT VS. VOLUME VS. DENSITY

MULTIPLE CHOICE: You have one kilogram of feathers and one kilogram of lead. Which has more:

1. ______ mass? 3. ______ weight?

a. feathers b. lead c. the same

a. feathers b. lead c. the same

2. ______ volume? 4. ______ density?

a. feathers b. lead c. the same

a. feathers b. lead c. the same

MULTIPLE CHOICE: You have one liter of water and one liter mercury. Which has more:

5. ______ mass? 7. ______ weight?

a. water b. mercury c. the same

a. water b. mercury c. the same

6. ______ volume? 8. ______ density?

a. water b. mercury c. the same

a. water b. mercury c. the same

MULTIPLE CHOICE: You have the dough for a loaf of bread and you put it in

the oven where it bakes. What happens to each of the following after baking?

9. ______ mass? 11. ______ weight?

a. bigger b. smaller c. the same

a. bigger b. smaller c. the same

10. ______ volume? 12. ______ density?

a. bigger b. smaller c. the same

a. bigger b. smaller c. the same

13. If you have the mass of something (say 10 kg) and you want to find its weight, how do you do

it? Show your work. __________________________________________________________.

14. If you have weight of something (say 10 N) and want to find its mass, how do you do it?

Show your work. __________________________________________________________.

Pb

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NEWTON’S FIRST LAW

1. State Newton’s First Law: ______________________________________________________ ____________________________________________________________________________ 2. Give an example of Newton’s First Law at work for an object at rest: ____________________ ____________________________________________________________________________ ____________________________________________________________________________ 3. Give an example of Newton’s First Law at work for an object in motion: _________________ ______________________________________________________________________________ ____________________________________________________________________________ 4. MULTIPLE CHOICE: __________ The more mass an object has the ______ inertia it has. a. more b. less c. inertia is independent of mass 5. In terms of Newton’s First Law, why is it dangerous to have sharp things lying in the rear deck of the car below the back window? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ 6. a. What causes your neck to “whiplash” in a car when you are hit from behind? b. How does the seat head rest help prevent whiplash? ___________________________________________________________________ ___________________________________________________________________

______________________________________________________________________________________________________________________________________

7. An F-18 Hornet of mass 3900 kg is flying at constant velocity in the air. Its thrusters are providing 500,000 N of thrust to the plane. What’s the plane’s acceleration (in m/s2)? ________________

8. An aircraft carrier of mass 250,000,000 kg is moving at a constant speed of 15 m/s. If its engine is providing 260,000,000 N of force to the propellers, how much is the force of water resistance (in N)? ____________________________________

Rear deck

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9. You are an astronaut at zero gravity. Two objects in front of you look identical but one of them has more mass than the other. What simple thing could you do to find out which one has more mass? _______________________________________________.

NEWTON’S SECOND LAW DIRECTIONS: Draw all the real forces (as vector arrows) acting on the GREY block shown in each of the situations. The possible forces are Fg (force of gravity), Ff (the force of friction), FT (force of tension, whenever there are cables, strings, ropes involved), FN (a force between two objects that are in contact like the floor and a block on the floor), and Fp (a pushing or pulling force, like somebody pushing on a block or a car engine

pushing on the tires). The number of vectors () to be drawn for each situation are in parentheses. An example is given here at right. The girl is pushing on the wagon and the boy is too but through a rope. The forces action ON THE WAGON are shown in the force diagram below the picture.

1. (2 vectors) A block at rest on a table

2. (3) A block being accelerated to the right. No friction is present.

3. (4) A block moving to the right at constant velocity. Friction is present.

4. (3) A block at rest with another block on top of it

5. (4) A block with a book leaning against it. The block is not moving. Friction is present.

6. (3) A block on an inclined plane. The block is not sliding. Friction is present.

7. (4) A block on an inclined plane being pulled up the plane. Friction is present.

8. (3) A block at the bottom of an inclined plane butted up against a wall.

9. (2) A block falling through the air at terminal velocity

10. (2) A block hanging from the ceiling by a rope.

11. (3) A block hanging from the ceiling by a rope and with a weight pulling it down.

12. (3) A block hanging from the ceiling by two ropes at angles.

FT FP

Fg

FN

FF

FT FP

Fg

FN

FF

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OVER EASY MATH

FORMULA BANK

𝒂 =𝑭

𝒎 or F = ma x = ±vxot ± ½at2 𝒂 =

𝒗

𝒕=

𝒗𝒇 − 𝒗𝒊

𝒕𝒇 − 𝒕𝒊

Newton’s Second Law. Where a is the acceleration ((in m/s2), F is

the force (in N), and m is the mass (in kg)

Distance travelled in a horizontal direction. Where x

is the distance (in meters), vxo is initial horizontal velocity (in

m/s), t is time (in sec), and a is acceleration (in m/s2)

Acceleration as the slope of velocity. Where a is the

acceleration (in m/s2), vf is the final velocity (in m/s), vi is the initial velocity (in m/s), and t is

the time (in s)

FNET = Fx – Ff Fw = mg FW = FN and Ff = Fx Ff = FN

Net force. Equals the

pushing/pulling force (in N)

one way minus the frictional

force (in N) the other way.

The force of weight. Where

g is the acceleration (in m/s2) due

to gravity, Fw is the force of

weight (in N), and m is the mass (in kg)

Equilibrium. The force of weight (FW) equals the normal

force (FN) and the force of friction (Ff) equals the pulling

force (Fx) in a simple equilibrium situation on a

horizontal surface.

Frictional Force. The Frictional force (Ff) on a block on a flat surface or inclined plane is equal to the coefficient of

friction () times the Normal Force (FN)

Refer to the figure at right to answer the questions following. Assume gravity is 10 m/s2. Assume the strings are massless ______________ 1. What is the block’s weight (in N)?

______________ 2. If an equilibrium situation exists, how much total force (in N) must there be in

the upwards direction?

______________ 3. What is the vertical component of upwards force (in N) provided

by one of the spring scales?

4 kg

4 kg

Ff

FN

FW

FN

Ff Fx

5

______________ 4. If a third spring scale is inserted, how much of the

weight (in N) of the 4-kg mass does each spring

scale now hold up?

Gravity on the moon is 1/6th the gravity on Planet Earth. If you weigh 200 N on the moon… 5. __________________ What is your mass (in kg)? 6. _________________ how much do you weigh (in N) on Planet Earth? 7. _________________ what is your mass (in kg) on the moon? 8. _________________ what is the acceleration due to gravity (in m/s2) on Planet Tupac if

your weight there is 1500 N? A 5-kg block is being pulled along a horizontal surface at a constant velocity by a force of 50 N. Friction is present. Assume gravity is 9.8 m/s2. 9. What is the weight (in N) of the block? __________________ 10. What is the Normal Force (in N) on the block? __________________ 11. If the block is moving at a constant velocity, what is the acceleration (in m/s2) of the 5-kg

block? __________________

12. What must be the frictional force (Ff) acting on the block (in N)? __________________

13. What is the coefficient of friction, , between the block and the surface it rests on? _______

5-kg Fx = 25 N

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Anastacia pulls horizontally on a loaded 120-kg wagon so that its velocity goes from 0 m/s to 4 m/s in 0.5 seconds. Assume gravity is 9.8 m/s2, friction is present, and that the coefficient of friction

between the wagon wheels and the ground is = 0.6. 14. What is the acceleration (in m/s2) of the wagon? __________________ 15. How far (in m) would the wagon move in 5 seconds? __________________ 16. What is the weight (in N) of the wagon? __________________ 17. What is the Normal Force (in N) on the wagon (assuming Anastacia is pulling horizontally)?

__________________ 18. How much frictional force (in N) is acting on the wagon? __________________ 19. What is the net (resultant) force (in N) acting on the wagon? _____________

20. What is the force (in N) applied by Anastacia to the wagon handle to get the net force in Probl. 19? _____________________

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MEDIUM RARE MATH

FORMULA BANK Pythagorean Theorem: a2 + b2 = c2

S.O.H.C.A.H.T.O.A.: 𝐭𝐚𝐧 =

𝒐𝒑𝒑.

𝒂𝒅𝒋. 𝐬𝐢𝐧 =

𝒐𝒑𝒑.

𝒉𝒚𝒑. 𝐜𝐨𝐬 =

𝒂𝒅𝒋.

𝒉𝒚𝒑.

To find the angle : = 𝐭𝐚𝐧𝟏 𝒐𝒑𝒑.

𝒂𝒅𝒋. = 𝐬𝐢𝐧𝟏

𝒐𝒑𝒑.

𝒉𝒚𝒑. = 𝐜𝐨𝐬𝟏

𝒂𝒅𝒋.

𝒉𝒚𝒑.

The set up at right is a signpost holding the sign for a

doctor’s office. The sign post is sticking out of the wall

and is supported by a cable at a diagonal. If the mass

of the sign is 83 kg…

1. __________ What is the weight (in N) of the sign post?

2. __________ What is the vertical force (in N) upwards that must be

present if an equilibrium situation exists?

3. __________ What is the tension (in N) in the cable holding the sign?

4. __________ What is the horizontal force (in N) pushing the

signpost into the wall?

Dr. Love Cardiologist

b =

op

p. a = adj.

= 40

Dr. Love Cardiologist

= 40

T = ?

Dr. Love

Cardiologist

= 40

FX = ?

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Two cables at angles hold an 80-kg mass

from the ceiling as shown at right.

5. __________ What is the weight (in N) of

the hanging mass?

6. __________ What is the vertical force (in N) upwards

that must be present if an equilibrium

situation exists?

7. __________ How much of the vertical force (in N)

upwards from Probl. 6 does each

cable hold?

8. __________ What is the angle (in degrees) between the cables and the ceiling?

= ?

T2 = 500 N T1 = 500 N

m = 80 kg

= ?

= ?

T2 = 500 N T1 = 500 N

80 kg

= ?

= ?

T2 = 500 N T1 = 500 N

80 kg

= ?

FY = ?

FY1=? FY2=?

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WELL-DONE MATH

FORMULA BANK

a = g sin FX = Fwsin FY = Fwcos The acceleration, a, (in m/s2) of a block down an inclined plane is equal to gravity, g, (in m/s2)

times the sine of the angle of the inclined plane

“Horizontal” force. For a block on an inclined plane, the

horizontal component of force (Fx) making the block slide down

the inclined plane equals the weight of the block (Fw) times

the sine of the angle of the inclined plane

“Vertical” force. For a block on an inclined plane, the vertical

component of force (Fy) pushing the block into the inclined plane equals the weight of the block

(Fw) times the cosine of the

angle of the inclined plane

FNET = Fx – Ff On an inclined plane,

FY = FN FX = Ff

Net force. Equals the pushing/pulling force (in N) one way minus the frictional force

(in N) the other way.

Normal Force. The Normal force (FN) in an equilibrium situation on

an inclined plane equals the vertical component of the Force of

Weight (FY).

Friction. In a simple equilibrium situation on a flat surface or inclined plane, the horizontal

component of force of the block’s weight (Fx) equals the

force of friction (Ff).

Fw = mg Ff = FN The force of weight. Where g is the acceleration (in m/s2) due to gravity, Fw is the force of weight (in N), and m is the mass (in kg)

Frictional Force. The Frictional force (Ff) on a block on a flat surface or inclined plane is equal to the coefficient of

friction () times the Normal Force (FN)

Fx

Fw

Fy

Fw

a

Fx

Ff

Fy

Fw

FN

Fx

Ff

Ff FN

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Two blocks are suspended from each other on inclined planes by a cable over a pulley. The inclined

planes have different slopes as can be seen from the figure at right. Assume that there is no friction on the slope Block B is on but there is friction on the slope Block A is on (coefficient of

friction of = 0.1 between the block and the surface of the inclined plane).

1. List what forces “to the left” and what forces “to the right” have to be balanced for an equilibrium situation to exist. HINT: there are three forces. Name them correctly.

___________________________________________________________________________________________________________________

2. Explain how equilibrium still could exist even though Block A is so much more massive than Block B. _______________________________________________________________________________________________________

____________________________________________________________________________________________________________________

____________________________________________________________________________________________________________________

3. What formula(s) you would use to find the force(s) pulling to the left (that you stated in Probl. 1.)_______________________________________________________________________________________________

4. What formula(s) you would use to find the force(s) pulling to the right (that you stated in Probl. 1. _______________________________________________________________________________________________________

5. Find whether or not the system above is actually in equilibrium, by finding the values of the force(s) pulling to the left and comparing them to the force(s) pulling to the right. Show your work for credit.

A = 4.6 kg

B = 0.8 kg

= 22 = 88

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NEWTON’S THIRD LAW

My Third Law states that “for every action, there is an equal and

opposite reaction.” When I shoot a rifle, the rifle recoils backwards

while the bullet goes forwards. QUESTION: Why does the bullet move

forward and the rifle backwards? If they are equal and opposite, don’t

the forces cancel each other out, then?”

ANSWER: __________________________________________

A person is log rolling (see figure) in a river. 1. What is the action? ____________________________________

2. What is the reaction? ____________________________________

A person is running on Planet Earth. 3. What is the action? ____________________________________

4. What is the reaction? ____________________________________

5. How come we can clearly see the effects of the action in the log rolling but no so when the person is

running on Planet Earth? _____________________________________________________________

_____________________________________________________________________________________

6. If you put a rubber band between your thumb and forefinger and stretch, which of the two fingers pulls harder? Explain __________________________________

____________________________________________________________________

7. A hammer strikes a nail, knocking it into a piece of wood.

12 a. How does the force on the hammer by the nail compare to the force on the nail by the hammer? _________________________________________.

b. What does the force on the hammer by the nail make the hammer do? ____________________________________________________________.

c. What does the force on the nail by the hammer make the nail do? ______ ____________________________________________________________. 8. An action hero hits 10 people in a movie with his fist and nothing happens to him.

According to Newton’s Third Law, every time he hits somebody with a certain amount of force… _______________________________________________

________________________________________________________________

________________________________________________________________

9. A speeding truck makes impact with a bug that splatters on the windshield. Because of the sudden force on the unfortunate bug, it undergoes a sudden fatal deceleration

a. Is the corresponding force that the bug exerts on the windshield greater, less than, or the same as that of the bug?

greater than less than the same as

b. Is the deceleration of the two objects the same? Why or why not? _______

_______________________________________________________________

_______________________________________________________________

10. When you jump upwards, the world really does recoil downward. Why can’t

you notice the motion of the earth? Explain. ___________________________ __________________________________________________________________

__________________________________________________________________.

11. We know that the earth pulls on the moon with a force. Does the moon also pull on the earth? If so, which pull is stronger? Explain _________________ __________________________________________________________________

__________________________________________________________________.

12. Identify the action and reaction forces in the case of an object falling without air resistance ___________________________________________________

13 ______________________________________________________________

______________________________________________________________