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Holt McDougal Physics i Sample Problem Set II
Sample Problem Set II Answers
Work and Energy
Additional Practice D
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Holt McDougal Physics ii Sample Problem Set II
Work and Energy continued
Name:______________________________ Class: __________________ Date: _________________
© Houghton Mifflin Harcourt Publishing Company
Holt McDougal Physics 1 Sample Problem Set II
Work and Energy
Problem D
POTENTIAL ENERGY
PROBLEM
A 70.0 kg stuntman jumps from a bridge that is 50.0 m above the water.
Fortunately, a bungee cord with an unstretched length of 15.0 m is attached to the
stuntman, so that he breaks his fall 12.0 m above the water’s surface. If the total
potential energy associated with the stuntman and cord is 3.43 × 10
4
J, what is the
force constant of the cord?
SOLUTION
1. DEFINE
Given: m = 70.0 kg h = 12.0 m
x = 50.0 m − 12.0 m − 15.0 m = 23.0 m
PE
g
= 0 J at river level
PE
tot
= 3.43 × 10
4
J
g = 9.81 m/s
2
Unknown: k = ?
2.
PLAN Choose the equation(s) or situation: The zero level for gravitational
potential energy is chosen to be at the water’s surface. The total potential energy
is the sum of the gravitational and elastic potential energies.
Rearrange the equation(s) to isolate the unknown(s):
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Holt McDougal Physics 2 Sample Problem Set II
3. CALCULATE Substitute the values into the equation(s) and solve:
4.
EVALUATE The situation in this problem is basically the same as that in
Sample Problem 5D in the textbook. In order for the stuntman to have a greater
height above the water, the bungee cord must store more elastic potential energy
with less stretching. This occurs when the spring constant is larger
(98.7 N/m > 71.8 N/m).
ADDITIONAL PRACTICE
1. A highway guardrail is designed so that it can be distorted as much as 5.00 cm
when struck by an automobile. What is the minimum force constant of the
guardrail if it is to withstand the impact of a car with 1.09 × 10
4
J of energy?
2. An arresting cable helps to slow jet planes as they land on an aircraft carrier.
This is accomplished by two springs, each of which is attached to one end of
the cable. Suppose the elastic potential energy stored in the springs while a jet
is landing is 5.78 × 10
7
J. If each spring is stretched 102 m, what is the force
constant of each spring?
3. A produce scale at a supermarket uses a stretched spring to indicate the weight
of fruits and vegetables. If five oranges with a total mass of 0.76 kg are placed
in the scale, the spring will be stretched 2.3 cm. What is the force constant of
the spring?
4. A 5.0 kg stone is slid up a frictionless ramp that has an incline of 25.0° How
long is the ramp if the gravitational potential energy associated with the stone
is 2.4 × 10
2
J?
5. A pogo stick contains a spring with a force constant of 1.5 × 10
4
N/m. Suppose
the elastic potential energy stored in the spring as the pogo stick is pushed
downward is 120 J. How far is the spring compressed?
6. A 1750 kg weather satellite moves in a circular orbit with a gravitational
potential energy of 1.69 × 10
10
J. At the satellite’s altitude above Earth’s
surface, the free-fall acceleration is only 6.44 m/s
2
. How high above Earth’s
surface is the satellite?
7. An automobile to be transported by ship is raised 7.0 m above the dock. If its
gravitational potential energy is 6.6 × 10
4
J, what is the automobile’s mass?
Name:______________________________ Class: __________________ Date: _________________
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Holt McDougal Physics 3 Sample Problem Set II
8. One of the largest planes ever to fly, and the largest to fly frequently, is the
Ukrainian-built Antonov An−124 Ruslan. Its wingspan is 73.2 m and its
length is 69.2 m. The gravitational potential energy associated with the plane
at an altitude of 1.45 km is 3.36 × 10
9
J. What is the airplane’s mass?
9. The force constant of the spring in a child’s toy car is 550 N/m. How much
elastic potential energy is stored in the spring if the spring is compressed a
distance of 1.2 cm?
10. With an elevation of 5334 m above sea level, the village of Aucanquilca,
Chile, is the highest inhabited town in the world. What would be the
gravitational potential energy associated with a 64.0 kg person in
Aucanquilca? Assume that the free-fall acceleration at Aucanquilca is equal to
that at sea level.
