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Chapter 3 Problems
1. Quentin is lifting a 10 kg dumbbell by pulling upward on it with a 108.1 N force. What is the
acceleration of the dumbbell as a result of this force?
2. Grant accelerates a 1 kg ball 5.0 m/s2 horizontally. The vertical acceleration of the ball is zero.
The force of gravity is the only external force acting on the ball other than the forces Grant
exerts on it.
a. How large is the horizontal force Grant exerts on the ball at this instant to cause its 5.0
m/s2 horizontal acceleration?
b. How large is the vertical force Grant exerts on the ball at this instant?
3. During a fastball pitch, the maximum horizontal acceleration of the 146 g baseball is 1000 m/s2.
What horizontal force is the pitcher exerting on the baseball at this instant to cause this
acceleration?
4. Tonya crashes into Nancy while they are practicing their figure skating routines. Tonya's mass is
60 kg and Nancy's mass is 50 kg. Just before the collision occurs, Tonya's velocity is 5 m/s and
Nancy's velocity is 6 m/s in the opposite direction. During the collision, Tonya exerts an average
force of 1000 N against Nancy.
a. How big is the average force Nancy exerts against Tonya during the collision?
b. If this is the only horizontal force acting on each skater during the collision, what
average horizontal acceleration does each skater experience during the collision?
c. If the collision is perfectly inelastic, how fast and in what direction will Tonya and Nancy
be moving immediately after the collision?
5. Doris is trying to lift a stack of books off the table. The stack of books has a mass of 15 kg. What
minimum upward force must Doris exert on the books to lift the books off the table?
6. Blanche, a 100 kg shot-putter, is putting the 4 kg shot in a track meet. Just before she releases
the shot, Blanche is in the air (her feet are off the ground). At this instant, the only force she
exerts against the shot is an 800 N horizontal force directed forward.
a. What is Blanche’s horizontal acceleration at this instant?
b. What is Blanche’s vertical acceleration at this instant?
c. What is the shot’s horizontal acceleration at this instant?
From P. McGinnis, 2013, Biomechanics of Sport and Exercise Student Web Resource, Third Edition (Champaign, IL: Human
Kinetics).
d. What is the shot’s vertical acceleration at this instant?
7. Jay is gliding north on his cross-country skis across a flat section of snow at 7 m/s. Jay’s mass is
100 kg. The coefficient of dynamic friction between the skis and the snow is 0.10. The coefficient
of static friction between the skis and the snow is 0.12. The force of air resistance is 1.9 N acting
backward (south) on Jay. If friction between the skis and snow and air resistance are the only
horizontal forces acting on Jay, what is his horizontal acceleration?
8. Mary is trying to stop a 5 kg bowling ball that is rolling toward her. Its horizontal velocity is 8.0
m/s when she begins to stop it. It takes her 2.0 s to stop the ball. What average force did Mary
exert on the ball during this 2.0 s to stop it?
From P. McGinnis, 2013, Biomechanics of Sport and Exercise Student Web Resource, Third Edition (Champaign, IL: Human
Kinetics).
9. A 0.43 kg soccer ball is stationary on the field when Darryl kicks it. Darryl’s foot is in contact with
the ball for 0.01 s during the kick. The horizontal velocity of the ball as it leaves his foot is 25
m/s. What is the average horizontal force exerted by Darryl’s foot on the ball during the 0.01 s
of contact (assume that friction between the ball and the field is zero)?
10. Peter, a 100 kg basketball player, lands on his feet after completing a slam dunk and then
immediately jumps up again to celebrate his basket. When his feet first touch the floor after the
dunk, his velocity is 5 m/s downward; when his feet leave the floor 0.50 s later, as he jumps back
up, his velocity is 4 m/s upward.
a. What is the impulse exerted on Peter during this 0.50 s?
b. What is the average net force exerted on Peter during this 0.50 s?
c. What is the average reaction force exerted upward by the floor on Peter during this 0.50
s?
11. Scott is rolling down a 30° slope on his skateboard. The total mass of Scott and the skateboard is
75 kg. The rolling friction between the skateboard wheels and the concrete is 9 N acting
backward against the skateboard. The drag force due to air resistance is 11 N acting backward
against Scott. What is Scott’s acceleration?
12. To earn the FIFA Approved label, a soccer ball must bounce at least 135 cm high and no more
than 155 cm high when dropped from a height of 200 cm onto a steel plate.
a. What is the minimum coefficient of restitution of a FIFA Approved soccer ball?
b. What is the maximum coefficient of restitution of a FIFA Approved soccer ball?
From P. McGinnis, 2013, Biomechanics of Sport and Exercise Student Web Resource, Third Edition (Champaign, IL: Human
Kinetics).
13. A warm hockey puck has a coefficient of restitution of 0.50, while a frozen hockey puck has a
coefficient of restitution of only 0.35. In the NHL, the pucks to be used in games are kept frozen.
During a game, the referee retrieves a puck from the cooler to restart play but is told by the
equipment manager that several warm pucks were just put into the cooler. To check to make
sure he has a game-ready puck, the referee drops the puck on its side from a height of 2 m. How
high should the puck bounce if it is a frozen puck?
14. A 0.15 kg baseball collides with a 1.0 kg bat. The ball has a velocity of 40 m/s immediately before
the collision. The center of mass of the bat also has a velocity of 40 m/s, but in the opposite
direction, just before the collision. The coefficient of restitution between the bat and the ball is
0.50. Estimate how fast the baseball is moving as it leaves the bat following the collision.
15. Maddie is standing still when her dancing partner, Paul, begins to lift her up and throw her into
the air. Maddie’s mass is 40 kg. Paul exerts an average vertical force of 500 N for 1.0 s on
Maddie during the lift and throwing motion.
a. What is Maddie’s vertical velocity when Paul releases her?
b. If Maddie’s center of gravity was 1.5 m above the floor when Paul released her, what
peak height will she reach?
From P. McGinnis, 2013, Biomechanics of Sport and Exercise Student Web Resource, Third Edition (Champaign, IL: Human
Kinetics).