Question

Example 4: The gravitational potential energy of a 15-kilogram
object is 294 joules. What is the height of the object
above the ground?
Given: PE � 294 J
m � 15 kg
g � 9.8 m/s2
Unknown: Height (h)
Equation: PE � mgh
Solution: Solve the equation for h, and then substitute
the given values in the new equation:
h � ; h � � 2.0 m
Practice Exercises
Exercise 1: Find the kinetic energy of a 0.1-kilogram toy truck
moving at a speed of 1.1 meters per second.
Exercise 2: What is the speed of a 48-kilogram dog running across
a lawn with 216 joules of kinetic energy?
294 J
15 kg � 9.8 m>s2
PE
mg
64 Physical Science Math Skills and Problem Solving Workbook



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Exercise 3: A book on a shelf 2.0 meters above the floor has a mass
of 1.5 kilograms. What is the gravitational potential
energy of the book?
Exercise 4: Find the mass of a ball on a roof 30 meters high, if the
ball’s gravitational potential energy is 58.8 joules.
Exercise 5: Which runner has greater kinetic energy: a 46-kilogram
runner moving at a speed of 8 meters per second or a
92-kilogram runner moving at a speed of 4 meters per
second?
Exercise 6: If a 6-kilogram box is moved from the floor to a storage
compartment 2 meters above the floor, by how many
joules does its gravitational potential energy change?
Exercise 7: A 0.1-kilogram ball rolls across the floor at a speed of
2 meters per second. Another 0.1-kilogram ball rests on
a shelf 1 meter above the floor. Which ball has more
energy?

Answer 1

Here are the solutions.

Use KE = 1/2 m v^2 and PE = m g h with g = 9.8 m/s^2.

Exercise 1
m = 0.1 kg, v = 1.1 m/s
KE = 1/2 m v^2 = 0.5(0.1)(1.1^2) = 0.0605 J ≈ 0.061 J.

Exercise 2
KE = 216 J, m = 48 kg
v = sqrt(2 KE / m) = sqrt(2·216 / 48) = sqrt(9) = 3.0 m/s.

Exercise 3
m = 1.5 kg, h = 2.0 m
PE = m g h = 1.5·9.8·2.0 = 29.4 J.

Exercise 4
PE = 58.8 J, h = 30 m
m = PE / (g h) = 58.8 / (9.8·30) = 58.8 / 294 = 0.20 kg.

Exercise 5
Runner A: m = 46 kg, v = 8 m/s
KE_A = 1/2·46·8^2 = 23·64 = 1472 J.
Runner B: m = 92 kg, v = 4 m/s
KE_B = 1/2·92·4^2 = 46·16 = 736 J.
Runner A has the greater kinetic energy.

Exercise 6
m = 6 kg, Δh = 2 m
ΔPE = m g Δh = 6·9.8·2 = 117.6 J ≈ 118 J (increase).

Exercise 7
Moving ball: m = 0.1 kg, v = 2 m/s
KE = 1/2·0.1·2^2 = 0.2 J.
Ball on shelf: PE = 0.1·9.8·1 = 0.98 J.
The ball on the shelf has more energy (0.98 J > 0.2 J).