Work, Energy, and Conservation of Energy ​–​ Practice Test A
W = F d cos ​θ
K = ​½ ​m v2​
Work-Energy Theorem:
U​g​ = m g y
U​s​ = ​½​ k x2​
E​total​ = K + U​g​ + U​s
W​net​ = ​½​ m v​f2​ ​ – ​½​ m v​i2​
Conservation of Energy:
W​NC​ = E​f​ - E​i
“​NC​” ​is “nonconservative”: the work by nonconservative forces is the work done by forces ​other ​than
gravity and spring forces, which ​do​ conserve energy and store it as potential energy.
1)
A rollercoaster starts at a point 30.0 m above the bottom of a dip with a speed of 25.0 m/s. Neglecting
friction, what will be the speed of the roller coaster at the top of the next hill, which is 45.0 m above the
bottom of the dip? ​Answer: 18.2 m/s
2)
Calculate the work required to compress an initially uncompressed spring with a spring constant of 25 N/m
by 10 cm. ​Answer: 0.125 J (Note: A Joule [J] is equal to a Newton-meter [N ​⋅​ m].)
3)
What work is required to stretch a spring of spring constant 40 N/m from ​x​ = 0.20 m to
0.25 m? (The unstretched position is at ​x​ = 0.) ​Answer: 0.45 J
4)
A pendulum bob is released from some initial height such that the speed of the bob at the bottom of the
swing is 2.6 m/s. What is the initial height of the bob? ​Answer: 0.345 m = 34.5 cm
5)
A worker pulls a 40.0-kg crate with a rope at a 30.0​°​ angle above the horizontal. The coefficient of sliding
friction between the crate and the floor is 0.55. If he moves the crate with a constant velocity through a
distance of 7.00 m, how much work does the worker do on the crate? ​Answer: 1150 J
6)
A horizontal force of 150 N is used to push a 40.0 kg packing crate a distance of 6.00 m on a rough
horizontal surface. If the crate moves at constant speed, find the following.
a) The work done by the 150 N force
Answer: 900 J
b) The work done by gravity
Answer: 0
c) The work done by the normal force
Answer: 0
d) The work done by friction
Answer: -900 J
e) The total (net) work done by all the forces
Answer: 0
f) The coefficient of kinetic friction between the crate and surface
Answer: 0.383
7)
An archer pulls her bowstring back 0.400 m by exerting a force that increases linearly from zero to 230 N.
What is the equivalent spring constant of the bow? ​Answer: 575 N/m
8)
A 0.250 kg block along a horizontal track has a speed of 1.50 m/s immediately before colliding with a light
spring of force constant 4.60 N/m located at the end of the track.
a) What is the spring’s maximum compression if the track is frictionless? ​Answer: 0.350 m = 35 cm
b) If the track is not frictionless, would the spring’s maximum compression be greater than, less than,
or equal to the value obtained in part (a)?
Answer: Less Than
W​net​ = 0 on an object moving at constant speed. This includes uniform circular motion (UCM).
W = ​Fd​ if F and d are in the same direction.
(​θ​ = 0​°​)
W=0
if F and d are perpendicular.
(​θ​ = 90​°​)
W = ​–Fd​ if F and d are in opposite directions.
(​θ​ = 180​°​)
W​g​ = ​–mg ​Δ​y