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Chapter 1 Problems
1. When offensive lineman Aaron Gibson reported to the Buffalo Bills in 2006, he was the
largest NFL player ever with a mass of 186 kg. What was Aaron’s weight?
2. At the 2008 Beijing Olympics, Matthias Steiner of Germany won the gold medal in
weightlifting in the unlimited weight class (>105 kg). He lifted 203 kg in the snatch and
258 kg in the clean and jerk for a total of 461 kg. How much does 461 kg weigh?
3. Fitness instructor Kim weighs 491 N. What is her mass?
4. Mairin is a 55 kg road cyclist. Her bicycle weighs 100 N. What is the combined weight of
Mairin and her bicycle?
5. The coefficient of static friction between Jimmy’s hand and his tennis racket is 0.45.
How hard must he squeeze the racket (what is R?) if he wants to exert a total force of
200 N along the longitudinal axis of the racket?
6. The coefficient of static friction between the sole of Ken’s shoes and the basketball
court floor is 0.67. If Ken exerts a normal contact force of 1400 N when he pushes off
the floor to run down the court, how large is the friction force exerted by Ken’s shoes on
the floor?
7. Emma is working in a shoe test lab measuring the coefficient of friction for tennis shoes
on a variety of surfaces. The shoes are pushed against the surface with a force of 400 N,
and a sample of the surface material is then pulled out from under the shoe by a
machine. The machine pulls with a force of 300 N before the material begins to slide.
From P. McGinnis, 2013, Biomechanics of Sport and Exercise Student Web Resource, Third Edition (Champaign, IL:
Human Kinetics).
When the material is sliding, the machine has to pull with a force of only 200 N to keep
the material moving.
a. What is the coefficient of static friction between the shoe and the material?
b. What is the coefficient of dynamic friction between the shoe and the material?
8. Billy is trying to slide an 80 kg box of equipment across the floor. The coefficient of static
friction between the box and the floor is 0.55. If Billy pushes only sideways (horizontally)
against the box, how much force must he push with to initiate movement of the box?
9. A sprinter is just coming out of the starting block, and only one foot is touching the
block. The sprinter pushes back (horizontally) against the block with a force of 800 N
and pushes down (vertically) against the block with a force of 1000 N.
a. How large is the resultant of these forces?
b. What is the direction of the resultant force?
From P. McGinnis, 2013, Biomechanics of Sport and Exercise Student Web Resource, Third Edition (Champaign, IL:
Human Kinetics).
10. The sprinter from problem 9 is now out of the blocks and running. If the coefficient of
static friction between the track shoe and the track is 0.80, and the sprinter exerts a
vertical force of 2000 N downward on the track, what is the maximum horizontal force
he can generate under his shoe?
11. Katie exerts a 400 N upward force on a 700 N barbell that is resting on the floor. The
barbell does not move. How large is the normal contact force exerted by the floor on
the barbell?
12. Daisy walks across a force platform, and the forces exerted by her foot during a step are
recorded. The peak vertical reaction force is 1200 N (this force acts upward on Daisy). At
the same instant, the braking frictional force is 200 N (this force acts backward on
Daisy).
a. How large is the resultant of these forces?
b. What is the direction of the resultant force?
13. The quadriceps pulls on the patella with a force of 1000 N while the patellar tendon
pulls on the patella with a force of 1000 N also. The knee is in a flexed position, so the
angle between these two forces is 120°. A compressive force from the femoral condyles
is the only other significant force acting on the patella. If the patella is in static
equilibrium, how large is the compressive force exerted by the femoral condyles on the
patella?
From P. McGinnis, 2013, Biomechanics of Sport and Exercise Student Web Resource, Third Edition (Champaign, IL:
Human Kinetics).
14. The ground reaction force acting on Carter during his long jump is 4500 N acting forward
and upward at an angle of 78° from horizontal. Carter’s mass is 70 kg. Other than
gravity, this is the only external force acting on Carter.
a. What is the vertical component of this ground reaction force?
b. What is the horizontal component of this ground reaction force?
c. How big is the net force, the sum of all the external forces, acting on Carter?
From P. McGinnis, 2013, Biomechanics of Sport and Exercise Student Web Resource, Third Edition (Champaign, IL:
Human Kinetics).
15. Three athletes are tugging on a ring. Martha pulls with a force of 150 N directly north.
Evelyn pulls with a force of 100 N directly east. Sara pulls with a force of 200 N directly
southwest (225° clockwise from north).
a. How big is the resultant of the three forces?
b. What is the direction of the resultant force?
16. Brian is trying to pull Julie on a sled across a flat, snowy field. Brian pulls on a rope
attached to the sled. His pulling force is directed forward and upward at an angle of 30°
above horizontal. Julie’s mass is 50 kg, and the sled's mass is 8 kg. If the coefficient of
From P. McGinnis, 2013, Biomechanics of Sport and Exercise Student Web Resource, Third Edition (Champaign, IL:
Human Kinetics).
static friction between the sled runners and the snow is 0.10, how much force must
Brian exert on the rope to start moving the sled?
17. Amy is in a tuck and skiing straight down a 30° slope. Air resistance pushes backward on
her with a force of 10 N. The coefficient of dynamic friction between her skis and the
snow is 0.08. Amy’s mass is 60 kg. What is the resultant of the external forces that act
on Amy?
18. A golf club makes impact with a 0.045 kg golf ball during a drive off the tee. The loft
angle of the club (the angle between the club face and vertical) is 10°. The normal
contact force exerted by the club on the ball is a 7500 N force directed forward and
upward 10° above horizontal. The friction force exerted by the club on the ball is 700 N
directed forward and downward 80° below horizontal.
a. What is the magnitude of the vector sum of the two club head forces acting on
the golf ball?
From P. McGinnis, 2013, Biomechanics of Sport and Exercise Student Web Resource, Third Edition (Champaign, IL:
Human Kinetics).
b. What is the direction of this resultant force?
From P. McGinnis, 2013, Biomechanics of Sport and Exercise Student Web Resource, Third Edition (Champaign, IL:
Human Kinetics).