m1

m2

37o 37o

m2m

m

3mF

Newton’s Laws of MotionProblems MC Questions

Starting from rest, a 4.0-kg body reaches a speed of 8.0 m/s in 2.0 s. What is the net force acting on the body?

(A) 16 N

(B) 8.0 N

(C) 4.0 N

(D) 32 N

01

maF

tΔvΔa

(A) 250 kg

(B) 24.5 kg

(C) 25.5 kg

(D) 2,450 kg

What is the mass of an object that weighs 250 N on the surface of the Earth where the acceleration due to gravity is 9.80 m/s2?

02

mgW

A stack of books rests on a level frictionless surface. A force F acts on the stack, and it accelerates at 3.0 m/s2. A 1.0 kg book is then added to the stack. The same force is applied, and now the stack accelerates at 2.0 m/s2. What was the mass of the original stack?

(A) 1.0 kg

(B) 2.0 kg

(C) 3.0 kg

(D) 4.0 kg

03

maF

A person of weight 480 N stands on a scale in an elevator. What will the scale be reading when the elevator is accelerating downward at 4.00 m/s2?

(A) 284 N

(B) 196 N

(C) 676 N

(D) 480 N

04

maF

mgW

A person on a scale rides in an elevator. If the mass of the person is 60.0 kg and the elevator accelerates downward with an acceleration of 4.90 m/s2, what is the reading on the scale?

(A) 147 N

(B) 294 N

(C) 588 N

(D) 882 N

05

maF

A person on a scale rides in an elevator. If the mass of the person is 60.0 kg and the elevator accelerates upward with an acceleration of 4.90 m/s2, what is the reading on the scale?

(A) 147 N

(B) 294 N

(C) 588 N

(D) 882 N

06

maF

An object of mass 6000 kg rests on the flatbed of a truck. It is held in place by metal brackets that can exert a maximum horizontal force of 9000 N. When the truck is traveling 15 m/s, what is the minimum stopping distance if the load is not to slide forward into the cab?

(A) 15 m

(B) 30 m

(C) 75 m

(D) 150 m

07

maF

ax2vv 2o

2

In the Atwood machine shown in the

diagram, if m1 = 0.40 kg and m2 = 0.60 kg,

what is the magnitude of the acceleration of the system? (Ignore friction and the mass of the pulley.)

(A) 5.3 m/s2

(B) 3.9 m/s2

(C) 0.98 m/s2

(D) 2.0 m/s2

m1

m2

08

maF

A 10-kg box sitting on a horizontal surface is pulled by a 5.0-N force. A 3.0-N friction force retards the motion. What is the acceleration of the object?

(A) 0.20 m/s2

(B) 0.30 m/s2

(C) 0.50 m/s2

(D) 5.0 m/s2

09

maF

In the Atwood machine shown in the

diagram, if m1 = 0.40 kg and m2 = 0.60 kg,

what is the tension in the string? (Ignore friction and the mass of the pulley.)

(A) 3.1 N

(B) 4.7 N

(C) 7.1 N

(D) 7.5 N

m1

m2

10

maF

A student pulls a box of books on a smooth horizontal floor with a force of 100 N in a direction of 37° above the horizontal. If the mass of the box and the books is 40.0 kg, what is the acceleration of the box?

(A) 1.5 m/s2

(B) 1.9 m/s2

(C) 2.0 m/s2

(D) 3.3 m/s2

11

maF

A traffic light of weight 100 N is supported by two ropes as shown in the diagram. What are the tensions in the ropes?

(A) 50 N

(B) 63 N

(C) 66 N

(D) 83 N

37o 37o

12

0F

Two boxes of masses m and 2m are in contact with each other on a frictionless surface. A force F is applied to the smaller block as shown in the diagram. What is the acceleration of the more massive box?

(A) F/m

(B) F/(2m)

(C) F/(3m)

(D) F/(4m)

m2mF

13

maF

An object slides on a level surface in the +x direction. It slows and comes to a stop with a constant acceleration of 2.45 m/s2. What is the coefficient of kinetic friction between the object and the floor? (A) 0.25

(B) 0.50

(C) 4.9

(D) 1.0

14

Nμf kk

maF

During a hockey game, a puck is given an initial speed of 10 m/s. It slides 50 m on the ice before it stops. What is the coefficient of kinetic friction between the puck and the ice?

(A) 0.090

(B) 0.10

(C) 0.11

(D) 0.12

15

Nμf kk

ax2vv 2o

2

maF

During the investigation of a traffic accident, police find skid marks 90.0 m long. They determine the coefficient of friction between the car's tires and the roadway to be 0.500 for the prevailing conditions. Estimate the speed of the car when the brakes were applied.

(A) 9.49 m/s

(B) 21.0 m/s

(C) 42.0 m/s

(D) 29.7 m/s

16

Nμf kk

ax2vv 2o

2

maF

Boxes of masses m and 3m are pulled to the right by a constant force F as shown in the diagram. The surface between the more massive box and the horizontal surface is smooth and the surface between the boxes is rough. If the less massive box does not slide on the more massive box, what is the static friction force acting on the less massive box?

(A) F

(B) F/2

(C) F/4

(D) F/3

m

3mF

17

maF

A 10-kg mass slides down a flat hill that makes an angle of 10° with the horizontal. If friction is negligible, what is the resultant force on the sled?

(A) 1.7 N

(B) 17 N

(C) 97 N

(D) 98 N

18

Vector Addition

An object with a mass m slides down a rough 37° inclined plane where the coefficient of kinetic friction is 0.20. What is the acceleration of the object?

(A) 4.3 m/s2

(B) 5.9 m/s2

(C) 6.6 m/s2

(D) 7.8 m/s2

19

Nμf kk

maF

An object is placed on an inclined plane. The angle of incline is gradually increased until the object begins to slide. The angle at which this occurs is θ. What is the coefficient of static friction between the object and the plane?

(A) sin θ

(B) cos θ

(C) 1/tan θ

(D) tan θ

20

Nμf kk

maF

01

vΔvΔmFnet

s 0.2m/s 0.8 kg 0.4Fnet N 16

Starting from rest, a 4.0-kg body reaches a speed of 8.0 m/s in 2.0 s. What is the net force acting on the body?

maF

Newton’s 2 nd Law

tΔvΔa

Kinematics

What is the mass of an object that weighs 250 N on the surface of the Earth where the acceleration due to gravity is 9.80 m/s2?

02

gWm 2m/s 9.8

N 250 kg 5.52

mgW

Weight

A stack of books rests on a level frictionless surface. A force F acts on the stack, and it accelerates at 3.0 m/s2. A 1.0 kg book is then added to the stack. The same force is applied, and now the stack accelerates at 2.0 m/s2. What was the mass of the original stack?

03

m

mm

a1

a2

F

F 21 amΔmmaF

21

2aa

maΔm

22

2

m/s 2.0m/s 3.0m/s 2.0 kg 1.0

kg 0.2m

maF

Newton’s 2nd Law

A person of weight 480 N stands on a scale in an elevator. What will the scale be reading when the elevator is accelerating downward at 4.00 m/s2?

04

aN

W

gWm

maNW

ga1WN

agWNW

2

2

m/s 9.8m/s 4.01N 480

N 284N

maF

Newton’s 2nd Law

mgW

Weight

A person on a scale rides in an elevator. If the mass of the person is 60.0 kg and the elevator accelerates downward with an acceleration of 4.90 m/s2, what is the reading on the scale?

05

aN

mg

maNmg

agmN 22 m/s 4.9m/s 9.8kg 60

N 294N

maF

Newton’s 2nd Law

A person on a scale rides in an elevator. If the mass of the person is 60.0 kg and the elevator accelerates upward with an acceleration of 4.90 m/s2, what is the reading on the scale?

06

aN

mg

mamgN

agmN 22 m/s 4.9m/s 9.8kg 60

N 882N

maF

Newton’s 2nd Law

An object of mass 6000 kg rests on the flatbed of a truck. It is held in place by metal brackets that can exert a maximum horizontal force of 9000 N. When the truck is traveling 15 m/s, what is the minimum stopping distance if the load is not to slide forward into the cab?

07

voFm

xmF2v0 2

o

maF

F2mv

x2o

mFa

N 9,000 2

m/s 15 kg 6,000 2 m 75

ax2vv 2o

2

Kinematics

maF

Newton’s 2nd Law

xa2v0 2o

In the Atwood machine shown in the

diagram, if m1 = 0.40 kg and m2 = 0.60 kg,

what is the magnitude of the acceleration of the system? (Ignore friction and the mass of the pulley.)

08

m1

m2a

m1gm2g

TT

mass 1 mass 2amgmT 11 amTgm 22

amgmT 11 amgmT 22

amgmamgm 2211

21

12mm

gmma

kg 60.0kg 40.0m/s 9.8 kg 40.0kg 60.0 2

2m/s 2.0

maF Newton’s 2nd Law

A 10-kg box sitting on a horizontal surface is pulled by a 5.0-N force. A 3.0-N friction force retards the motion. What is the acceleration of the object?

09

Ffm

mafF

mfFa

kg 10N 0.3N 0.5 2m/s 20.0

maF

Newton’s 2nd Law

In the Atwood machine shown in the

diagram, if m1 = 0.40 kg and m2 = 0.60 kg,

what is the tension in the string? (Ignore friction and the mass of the pulley.)

10

mass 1 mass 2amgmT 11 amTgm 22

1

1m

gmTa

2

2m

Tgma

21

21mm

gmm2T

kg 60.0kg 40.0m/s 9.8 kg 60.0kg 40.02 2

N 4.7

2

2

1

1m

Tgmm

gmT

m1

m2a

m1gm2g

TT

maF Newton’s 2nd Law

A student pulls a box of books on a smooth horizontal floor with a force of 100 N in a direction of 37° above the horizontal. If the mass of the box and the books is 40.0 kg, what is the acceleration of the box?

11

m

F

xmaθcosF

mθcosFax

kg 4037cosN 100 o

2/sm .02

maF

Newton’s 2nd Law

A traffic light of weight 100 N is supported by two ropes as shown in the diagram. What are the tensions in the ropes?

37o 37o

12

T T

W

0WθsinT2

θsin2WT o37sin2

N 100 N 83

0Fy

Vertical Forces

Two boxes of masses m and 2m are in contact with each other on a frictionless surface. A force F is applied to the smaller block as shown in the diagram. What is the acceleration of the more massive box?

m2mF

13

Both boxes move with the same acceleration

am2mF

m3Fa

amF s

maF

Newton’s 2nd Law

An object slides on a level surface in the +x direction. It slows and comes to a stop with a constant acceleration of 2.45 m/s2. What is the coefficient of kinetic friction between the object and the floor?

14

mfk

a

mafk mgμf kk

mamgμk

gaμk 2

2

m/s 8.9m/s 45.2 25.0

Nμf kk

FrictionmaF

Newton’s 2nd Law

During a hockey game, a puck is given an initial speed of 10 m/s. It slides 50 m on the ice before it stops. What is the coefficient of kinetic friction between the puck and the ice?

15

x

vo afk

mgμf kk mafk

mamgμk

gμa k

xgμ2v0 k2o

gx2v

μ2o

k

m 05m/s 9.8 2

m/s 10μ 2

2

k 10.0

xa2v0 2o

v = 0

ax2vv 2o

2

Kinematics

maF

Newton’s 2nd Law

Nμf kk

Friction

During the investigation of a traffic accident, police find skid marks 90.0 m long. They determine the coefficient of friction between the car's tires and the roadway to be 0.500 for the prevailing conditions. Estimate the speed of the car when the brakes were applied.

16

xa2v0 2o

vo

xfk

mgμf kk mafk

mamgμk

gμa k xgμ2v0 k

2o

gxμ2v ko

m 90 m/s 9.8 0.500 2v 2o m/s 29.7

v = 0a

ax2vv 2o

2

Kinematics

maF Newton’s 2nd Law

Nμf kk Friction

Boxes of masses m and 3m are pulled to the right by a constant force F as shown in the diagram. The surface between the more massive box and the horizontal surface is smooth and the surface between the boxes is rough. If the less massive box does not slide on the more massive box, what is the static friction force acting on the less massive box?

F

17

am4F

m4Fa

m fs

maF

m4Fmfk

4Ffk

m3m

maF

Newton’s 2nd Law

A 10-kg mass slides down a flat hill that makes an angle of 10° with the horizontal. If friction is negligible, what is the resultant force on the sled?

18

x

y

mg

NN

mg

mg sin

o2net 10sin 9.8m/s kg 10F

N 17Fnet

Vector Addition

An object with a mass m slides down a rough 37° inclined plane where the coefficient of kinetic friction is 0.20. What is the acceleration of the object?

19

x

y

mg

Nfk

θcosmgμf kk

0θcosmgN

θcosmgN xk mafθsinmg

xk maθcosmgμθsinmg

θcosμθsinga kx

oo2x 37cos20.037sinm/s 9.8a

2x m/s 4.3a

xx maF

Newton’s 2nd LawNμf kk

Friction 0Fy Normal Force

An object is placed on an inclined plane. The angle of incline is gradually increased until the object begins to slide. The angle at which this occurs is θ. What is the coefficient of static friction between the object and the plane?

20

0θcosmgN

θcosmgN Nμf ss

θcosmgμf ss 0fθsinmg s

0θcosmgμθsinmg s

θcosθsinμs θtan

x

y

mg

Nfs

0Fy Normal Force

0Fx X Forces

Nμf ss Static Friction