8
Practice Problems
Energy
1. It is said that Galileo dropped objects off the Leaning
Tower of Pisa to determine whether heavy or light objects fall
faster. If Galileo had dropped a 5.0-kg cannon ball to the
ground from a height of 12 m, what would have been the
change in PE of the cannon ball?
m = 5.0 kg
h = 12 m
g = 10 m/s/s
GPE = mgh
GPE = (5.0 kg)(10 m/s/s)(12 m)
GPE = 600 J
2. On June 5, 2007, Rags to Riches, became the first filly to win the Belmont
Stakes horse race since 1905, running with an average speed of 16.23 m/s. If
Rags to Riches and jockey Johnny Velazquez had a combined mass of 550.0 kg,
what was their KE as they crossed the finish line?
m = 550.0 kg
v = 16.23 m/s
2
KE = ½mv
KE
KE
KE
KE
=
=
=
=
2
(½ * 550.0kg)(16.23 m/s)
(275.0 kg)(263.4129 m/s/s)
72438.5475 J
72440 J
3. Brittany is changing the tire of her car on a steep hill 20.0 m high. She trips and
drops the 10.0-kg spare tire, which rolls down the hill with an initial speed of
2.00 m/s. What is the speed of the tire at the top of the next hill, which is 5.00
m high? (Ignore the effects of rotation KE and friction.)
m = 10.0 kg
h1 = 20.0 m
h2 = 5.00 m
v = 2.00 m/s
g = 10 m/s/s
GPE = mgh
2
KE = ½mv
GPE1 =(10.0 kg)(10 m/s/s)(20.0 m)
GPE1 = 2000 J
GPE2 = (10.0 kg)(10 m/s/s)(5.00 m)
GPE2 = 500 J
ΔGPE = 1500 J
ΔGPE = ΔKE
2
1500 J = ½mv
2
1500 J = (5.00 kg)(v )
5.00 kg
5.00 kg
2
√300 J/kg = √v
√(300 J/kg) = v
17.32050808 m/s = v
17 m/s = v
8
Practice Problems
Energy
4. A Mexican jumping bean jumps with the aid of a small worm that lives inside
the bean. If a bean of mass 2.0 g jumps 1.0 cm from your hand into the air,
how much potential energy has it gained in reaching its highest point.What is its
speed as the bean lands back in the palm of your hand?
m = 0.002 kg
h = 0.01 m
g = 10 m/s/s
GPE = mgh
2
KE = ½mv
ΔGPE = ΔKE
2
mgh = v
½m
2
(0.002 kg)(10 m/s/s)(0.01 m) = v
(0.001 kg)
2
√0.2 J/kg = √v
0.447213595 m/s = v
0.45 m/s = v
5. A 500.-kg pig is standing at the top of a muddy hill on a rainy day. The hill is
100.0 m long with a vertical drop of 30.0 m. The pig slips and begins to slide
down the hill. What is the pig’s speed at the bottom of the hill? Use the law of
conservation of energy.
m = 500. kg
h = 30.0 m
g = 10 m/s/s
GPE = mgh
2
KE = ½mv
ΔGPE = ΔKE
2
mgh = v
½m
2
(500. kg)(10 m/s/s)(30.0 m) = v
(250. kg)
2
√600 J/kg = √v
24.49489743 m/s = v
24 m/s = v
8
Practice Problems
Work and Power
6. On his way off to college, Russell drags his suitcase 15.0 m from the door of his
house to the car at a constant speed with a horizontal force of 95.0 N.
a) How much work does Russell do to overcome the force of friction?
W = (95.0 N)(15.0 m)
F = 95.0 N
W = 1425 J
d = 15.0 m
W = 1430 J
W = Fd
b) If the floor has just been waxed, does he have to do more work or less work
to move the suitcase? Explain.
If the floor has been waxed there is less friction between the floor and
the suitcase, so Russell will do less work because he will not have to use
as much force to move the suitcase.
7. Kevin, a 30.0-kg boy, climbs a tree to rescue his cat who is
afraid to jump 8.0-m to the ground. How much work does Kevin
do in order to reach the cat?
FG = (30.0 kg)(10 m/s/s)
m = 30.0 kg
FG = 300 N
FG = mg
d = 8.0 m
W = (300 N)(8.0 m)
W = Fd
W = 2400 J
W = 2400 J
8
Practice Problems
Work and Power
8. Marissa does 3.2 J of work to lower the window shade in her bedroom a
distance of 0.8 m. How much force must Marissa exert on the window shade?
W = 3.2 J
F = 3.2 J/0.8 m
d = 0.8 m
F=4N
F = W/d
9. Atlas and Hercules, two carnival sideshow strong men, each lift 200.-kg barbells
2.00 m off the ground. Atlas lifts his barbells in 1.00 s and Hercules lifts his in
3.00 s.
a) Which strong man does more work?
m = 200.0 kg
FG = (200.0 kg)(10 m/s/s)
FG = mg
FG = 2000 N
d = 2.00 m
W = Fd
W = (2000 N)(2.00 m)
W = 4000 J
W = 4000 J
Each man does the same work because they both lift the same weight
force to the same height above the ground.
b) Calculate which man
PA =
W = 4000 N
PA =
tA = 1.00 s
PA =
tH = 3.00 s
P = W/t
is more powerful.
W/tA
(4000 N)/(1.00 s)
4000 W
PH
PH
PH
PH
=
=
=
=
W/tH
(4000 N)/(3.00 s)
1333.3333333 W
1330 W
Atlas is more powerful than Hercules because he does the same amount
of work but in a much quicker time amount.