Download X - Newtons Laws Problems MC

Newton’s Laws of Motion
Problems MC Questions
m2
m1
37o
37o
m
3m
2m
m
F
01
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
 F  ma
Δv
a
Δt
02
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?
(A) 250 kg
(B) 24.5 kg
(C) 25.5 kg
(D) 2,450 kg
W  mg
03
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
 F  ma
04
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
 F  ma
(D) 480 N
W  mg
05
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
 F  ma
06
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
 F  ma
07
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
 F  ma
(B) 30 m
(C) 75 m
(D) 150 m
v 2  vo2  2ax
08
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.)
m2
m1
(A) 5.3 m/s2
(B) 3.9 m/s2
(C) 0.98 m/s2
(D) 2.0 m/s2
 F  ma
09
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
 F  ma
10
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
m2
m1
 F  ma
11
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
 F  ma
12
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
(A) 50 N
(B) 63 N
(C) 66 N
(D) 83 N
F  0
13
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)
F
2m
m
 F  ma
14
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
 F  ma
(C) 4.9
fk  μ k N
(D) 1.0
15
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
 F  ma
fk  μ k N
v 2  vo2  2ax
16
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
 F  ma
(B) 21.0 m/s
fk  μ k N
(C) 42.0 m/s
v 2  vo2  2ax
(D) 29.7 m/s
17
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
 F  ma
m
(C) F/4
(D) F/3
3m
F
18
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
Vector Addition
19
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
 F  ma
fk  μ k N
20
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
 F  ma
fk  μ k N
01
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?
Newton’s 2 nd Law
Kinematics
 F  ma
a
Δv
Δt
 Δv 
Fnet  m 
 Δv 
 8.0 m/s 
Fnet  4.0 kg 

 2.0 s 
 16 N
02
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?
Weight
W  mg
250 N
W

m
g
9.8 m/s 2
 25.5 kg
03
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?
Newton’s 2nd Law
F
m
 F  ma
F  ma1  m  Δm a 2

F

Δma 2
1.0 kg 2.0 m/s 2
m

a1 - a 2 3.0 m/s 2 - 2.0 m/s 2
m  2.0 kg
Dm
m
a1
a2
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?
N
Newton’s 2nd Law
a
Weight
W
F

ma

W  mg
W - N  ma
W
m
W
W - N   a
g
 g 
 4.0 m/s 2 
 a

N  W 1 -   480 N 1 2
 9.8 m/s 
 g
N  284 N
04
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?
N
Newton’s 2nd Law
mg
 F  ma
mg - N  ma

N  mg - a   60 kg 9.8 m/s 2 - 4.9 m/s 2
N  294 N

05
a
06
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?
N
Newton’s 2nd Law
 F  ma
a
mg
N - mg  ma

N  mg  a   60 kg 9.8 m/s 2  4.9 m/s 2
N  882 N

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
vo
the load is not to slide forward into the cab?
F
Kinematics
Newton’s 2nd Law
m
v 2  vo2  2ax
 F  ma
0  vo2  2- a x
F  ma
F
a
m
 F
0  v o2  2 -  x
 m
mv o2 6,000 kg 15 m/s 2
x

2F
2 9,000 N 
 75 m
07
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.) Newton’s 2nd Law
 F  ma
mass 1
T - m1g  m1a
mass 2
m 2 g - T  m 2a
T  m1g  m1a
T  m 2 g - m 2a
08
T
T
m2
m1
m 1g
m 2g
m1g  m1a  m 2g - m 2a
a
m 2 - m1 g
m1  m 2

0.60 kg - 0.40 kg  9.8 m/s 2

0.40 kg  0.60 kg
 2.0 m/s 2
a
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?
Newton’s 2nd Law
 F  ma
F
f
m
F - f  ma
F-f
5.0 N - 3.0 N
a

m
10 kg
 0.20 m/s 2
09
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.)
Newton’s 2nd Law
mass 1
T - m1g  m1a
T - m1g
a
m1
 F  ma
mass 2
m 2 g - T  m 2a
10
T
T
m2
m1
m 1g
m 2g
m 2g - T
a
m2
T - m1g m 2g - T

m1
m2
T
2m1m 2 g
m1  m 2
20.40 kg 0.60 kg  9.8 m/s 2

0.40 kg  0.60 kg
 4.7 N
a
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?
q
Newton’s 2nd Law
m
 F  ma
F cos θ  ma x
F cos θ
ax 
m
100 N cos 37o

40 kg
 2.0 m/s 2
11
F
12
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
Vertical Forces
q
 Fy  0
q
T
T
2T sin θ - W  0
W
100 N
T

2 sin θ
2 sin 37o
 83 N
W
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?
Newton’s 2nd Law
 F  ma
Both boxes move with
the same acceleration
F  m sa
F  m  2m a
F
a
3m
F
2m
m
13
14
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?
Friction
fk  μ k N
fk  μk mg
Newton’s 2nd Law
 F  ma
fk
a
m
- fk  ma
- μk mg  ma
- 2.45 m/s 2
a
μk  9.8 m/s 2
g
 0.25
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
v=0
vo
fk
Kinematics
x
v 2  vo2  2ax
Newton’s 2nd Law
Friction
0  vo2  2- a x
0  vo2  2- μk g x
v o2
μk 
2gx

10 m/s 2
μk 
2 9.8 m/s 2 50 m


 F  ma
fk  μ k N
fk  ma
fk  μk mg
μk mg  ma
a  μk g
 0.10
15
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
a
v=0
v
when the brakes were applied.
o
f
Kinematics
v 2  vo2  2ax
0  vo2  2- a x
0  vo2  2- μk g x
vo  2μk gx
x
k
Newton’s 2nd Law
 F  ma
fk  ma
μk mg  ma
a  μk g
vo  2 0.500  9.8 m/s 2 90 m 
 29.7 m/s
Friction
fk  μ k N
fk  μk mg
16
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?
m
F
3m
Newton’s 2nd Law
 F  ma
F  4m a
F
a
4m
m
fs
 F  ma
 F 
f k  m

 4m 
F
fk 
4
17
18
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?
y
Vector Addition
N
q
N
q
q
x
mg
mg
mg sin q


Fnet  10 kg 9.8m/s 2 sin 10o
Fnet  17 N
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?
Normal Force
Friction
Newton’s 2nd Law
 Fy  0
fk  μ k N
F

ma
 x
N - mg cos θ  0
x
mg sin θ - fk  ma x
N  mg cos θ
fk  μk mg cos θ
mg sin θ - μk mg cos θ  ma x
N
a x  gsin θ - μk cos θ 

a x  9.8 m/s 2 sin 37o - 0.20cos 37o
a x  4.3 m/s 2
y
fk

q
q
mg
x
19
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?
X Forces
 Fx  0
Normal Force
 Fy  0
Static Friction
mg sin θ - fs  0
mg sin θ - μsmg cos θ  0
fs  μ s N
fs  μ s N
N - mg cos θ  0
N  mg cos θ
fs  μsmg cos θ
y
N
sin θ
μs 
cos θ
 tan θ
fs
q
q
mg
x
20