1. Example Problems for Newton’s Second Law Answers
1. What force must act on a 75.0-kg mass to give it an
acceleration of 1.2 m/s2?
F = m a
= ( 75.0 kg )( 1.2 m/s2 )
= 90 kg m/s2
= 90 newtons
= 90 N

2. 2. A 2500-kg car starting from rest attains a speed of
15.0 m/s in 30.0 s.
(a) What is the acceleration?
vi = vf = m/s t = s a = ?
vf - vi
15.0 m/s - 0
a = = t
30.0 s
a = m/s2
(b) What force is acting on it?
F = m a
= ( 2500 kg )( 0.50 m/s2 )
F = N

3. 3. A rocket has a mass of 575 kg.
(a) What does the rocket weigh?
Wt. = m g
= ( 575 kg )( 9.80 m/s2 )
Wt. = N

4. (b) What is the minimum force that must
be supplied by the engines in order to
lift the rocket off the pad? FA
Weight acts downward
Applied force by engines acts upward
to counteract gravity
Wt. = N

5. (b) What is the minimum force that must
be supplied by the engines in order to
lift the rocket off the pad? FA
Weight acts downward
Applied force by engines acts upward
to counteract gravity
Remove launch pad:
Wt. = N

6. (b) What is the minimum force that must
be supplied by the engines in order to
lift the rocket off the pad? FA
Weight acts downward
Applied force by engines acts upward
to counteract gravity
Remove launch pad:
Wt. = N
If applied force is less than weight,
gravity wins and rocket falls

7. (b) What is the minimum force that must
be supplied by the engines in order to
lift the rocket off the pad? FA
Weight acts downward
Applied force by engines acts upward
to counteract gravity
Remove launch pad:
Wt. = N
If applied force is greater than
weight, FA wins and rocket goes up

8. (b) What is the minimum force that must
be supplied by the engines in order to
lift the rocket off the pad? FA
Weight acts downward
Applied force by engines acts upward
to counteract gravity
Remove launch pad:
Wt. = N
If FA = Wt., rocket will “hover”
Minimum force to lift rocket off the pad is equal
to the weight
FA = N

9. (c) What additional force must be supplied by the engines in
order to accelerate the rocket upward at 12.0 m/s2?
Additional force will be a net
force that accelerates the rocket FA
Fnet
Fnet = m a
= ( 575 kg )( m/s2 )
a = m/s2
Fnet = N
Wt. = N
m = 575 kg

10. (d) What is the total force exerted by the engines?
Total force does two things: (1) counteracts the weight and
(2) accelerates the rocket
FA = ?
Fnet = N
Total applied force will be the
sum of their magnitudes:
a = m/s2
FA = N N
Wt. = N
FA = N

11. (d) What is the total force exerted by the engines?
A more general (and mathematical) approach:
A net force is always the vector sum
of all the forces acting in a
particular dimension:
Fnet = N
FA = ?
Fnet = F1 + F2 + …
In this case, the dimension is the
vertical dimension and the individual
forces are the applied force and the
weight
Fnet = FA + Wt.
Wt. = N

12. (d) What is the total force exerted by the engines?
Fnet = FA + Wt.
N = FA + ( N )
Fnet = N
N N
FA = N
FA = ?
Wt. = N

13. 4. A rocket having a mass of 1800 kg is pushed upward by its
engine with a force of N.
FA = N
(a) What is the net upward force
acting upon it?
Fnet = ?
Total force of engines must
always counteract the weight
Wt. = m g
= ( 1800 kg )( 9.8 m/s2 )
Wt. = N
m = 1800 kg

14. 4. A rocket having a mass of 1800 kg is pushed upward by its
engine with a force of N.
FA = N
(a) What is the net upward force
acting upon it?
Fnet = ?
Since the force from the engines is
greater than the weight, there is a
net upward force
The net force is the difference
between FA and the weight
m = 1800 kg
Fnet = ( N ) - ( N )
Wt. = N
Fnet = N

15. 4. A rocket having a mass of 100 kg is pushed upward by its
engine with a force of 1470 N.
FA = N
(a) What is the net upward force
acting upon it?
Fnet = ?
Fnet = FA + Wt.
= ( N ) + ( N )
Fnet = N
m = 1800 kg
Wt. = N

16. 4. A rocket having a mass of 1800 kg is pushed upward by its
engine with a force of N.
(b) What acceleration does this
force produce?
FA = N
Fnet = m a
Fnet = 7360 N
m m
Fnet
7360 N
a = = m
1800 kg
7360 kg m/s2
m = 1800 kg =
1800 kg
Wt. = N
a = m/s2

17. 5. A box of mass 6.4 kg is pulled across a floor. It requires a
force of 36 N to move the box at constant velocity.
Calculate the coefficient of friction μ. Ff
μ = FN
FA = 36 N
Free-body diagram
(diagram showing all
the forces on an
object) Ff FN
Wt.
For object on horizontal surface, FN equals the Wt.
FN = Wt. = m g = ( 6.4 kg )( 9.8 m/s2 )
FN = N

18. 5. A box of mass 6.4 kg is pulled across a floor. It requires a
force of 120 N to move the box at constant velocity.
Calculate the coefficient of friction μ.
m = 6.4 kg
FA = 36 N Ff Ff
μ = FN
μ = ?
62.72 N
Wt.
constant velocity a = 0
Fnet = 0
Ff = FA
Ff = 36 N

19. 5. A box of mass 25 kg is pulled across a floor. It requires a
force of 120 N to move the box at constant velocity.
Calculate the coefficient of friction μ.
m = 6.4 kg
FA = 36 N Ff
μ =
Ff = 36 N FN
μ = ?
62.72 N
36 N
Wt. =
62.72 N
μ = 0.57

20. 6. If a box has a mass of 24 kg and the coefficient of friction
is 0.40, find the force of friction.
m = 24 kg FA Ff FN Ff FN
μ = FN
μ = 0.40
Wt. FN
Ff = μ FN
FN = Wt. = m g
= ( 0.40 )( N )
= ( 24 kg )( 9.8 m/s2 )
Ff = N
= N
Ff = 94 N

21. 7. The coefficient of starting friction st = 0.45 for steel on a
particular wood floor. What force is needed to begin a steel
box that weighs 1600 N moving across a floor?
FA = ?
Force to begin box
moving must
overcome friction Ff
μ = 0.65
Wt. FN
Ff = μ FN

22. 7. The coefficient of starting friction st = 0.45 for steel on a
particular wood floor. What force is needed to begin a steel
box that weighs 1600 N moving across a floor?
FA = ?
Force to begin box
moving must
overcome friction Ff
μ = 0.45
Wt. FN
Ff = μ FN
FN = Wt. = N
= ( 0.45 )( 1600 N )
Ff = 720 N

23. 8. The coefficient of sliding friction sl = 0.36 for the steel
box in the previous problem. What force is necessary to
keep the box moving at constant speed across the floor?
FA = ? Ff
μ = 0.36
Wt. FN
FN = Wt. = N

24. 8. The coefficient of sliding friction sl = 0.36 for the steel
box in the previous problem. What force is necessary to
keep the box moving at constant speed across the floor?
FA = ? Ff
μ = 0.36
Wt. FN
FN = Wt. = N
constant speed a = 0
Fnet = 0
FA = Ff

25. 8. The coefficient of sliding friction sl = 0.36 for the steel
box in the previous problem. What force is necessary to
keep the box moving at constant speed across the floor?
FA = ? Ff
Ff = μ FN
μ = 0.36
Wt. FN
= ( 0.36 )( 1600 N )
FN = Wt. = N
Ff = 576 N
FA = Ff

26. 9. Calculate the acceleration of the box in the diagram below.
FA = N
Ff = N
5.0 kg
Fnet
Fnet = FA + Ff
= ( N ) + ( - 80 N )
Fnet = N
Fnet = m a
m m
Fnet
+ 40 N
a = =
= a = m/s2 m
5.0 kg

27. 10. An object of mass 500 kg is resting on the floor. The
coefficient of friction μ = Calculate the force
necessary to accelerate the object at 2.4 m/s2.
FA = ? Ff
500 kg
Fnet
μ = 0.40
a = 2.4 m/s2
Wt. FN
Ff = μ FN
= μ Wt.
= μ m g
= ( 0.40 )( 500 kg )( 9.8 m/s2 )
Ff = N

28. 10. An object of mass 500 kg is resting on the floor. The
coefficient of friction μ = Calculate the force
necessary to accelerate the object at 2.4 m/s2.
FA = ?
Ff = N
500 kg
Fnet
μ = 0.40
a = 2.4 m/s2
Wt. FN
Fnet = m a
= ( 500 kg )( 2.4 m/s2 )
= N
Applied force: (1) overcomes friction
and (2) accelerates the box
FA = ( 1960 N ) + ( 1200 N )
= FA = N

29. 10. An object of mass 500 kg is resting on the floor. The
coefficient of friction μ = Calculate the force
necessary to accelerate the object at 2.4 m/s2.
FA = ?
Ff = N
500 kg
Fnet = N
μ = 0.40
a = 2.4 m/s2
Wt. FN
Fnet = FA + Ff
N = FA + ( N )
N N
N = FA

30. 11. A 6.0-kg mass and a 14.0-kg mass are attached to a
lightweight cord that passes over a frictionless pulley.
The masses are left free to move. Find the acceleration of
the 6.0-kg mass.
F1 = Wt. = m1 g
= ( 6.0 kg )( 9.8 m/s2 )
= N
6.0 kg
14 kg
F2 = Wt. = m2 g
= ( 14.0 kg )( 9.8 m/s2 ) F1
= N F2

31. 11. A 6.0-kg mass and a 14.0-kg mass are attached to a
lightweight cord that passes over a frictionless pulley.
The masses are left free to move. Find the acceleration of
the 6.0-kg mass.
Fnet = N N
Fnet = N
Fnet = m a
6.0 kg
m m
14 kg
Fnet N
a = =
Fnet
58.8 N m
( 6.0 kg + 14 kg )
a = m/s2
137.2 N

32. 12. Two boxes of mass 4.0 kg and 1.5 kg are connected by a rope. The
rope is suspended over a frictionless pulley on the edge of a table.
The coefficient of friction between the 4.0-kg box and the table
is Find the acceleration of the boxes. m1
The force that accelerates the
boxes comes from the
weight of m2.
4 kg
μ = 0.30 m2
Wt. = m2 g
= ( 1.5 kg )( 9.8 m/s2 ) = N
1.5 kg
m2 g

33. 12. Two boxes of mass 4.0 kg and 1.5 kg are connected by a rope. The
rope is suspended over a frictionless pulley on the edge of a table.
The coefficient of friction between the 4.0-kg box and the table
is Find the acceleration of the boxes. m1
The force is transmitted to m1
by the rope
FA = 14.7 N Ff
4 kg
μ = 0.30
Ff = μ FN m2
1.5 kg
FN is the weight of the 4-kg box
= m1 g = ( 4.0 kg )( 9.8 m/s2 ) = N
14.7 N
Ff = μ FN
= ( 0.30 )( 14.7 N ) = N

34. 12. Two boxes of mass 4.0 kg and 1.5 kg are connected by a rope. The
rope is suspended over a frictionless pulley on the edge of a table.
The coefficient of friction between the 4.0-kg box and the table
is Find the acceleration of the boxes.
Fnet m1
FA = N
Ff = N
Fnet = FA + Ff
4 kg
= ( N ) + ( N )
μ = 0.30 m2
1.5 kg
Fnet = N
Both masses accelerate,
so total mass must be
used in equation
Fnet = m a
14.7 N
m m
Fnet N
a = =
= a = m/s2 m
( ) kg