TUTORIAL 4:
CONSERVATION OF ENERGY
Instructors: Kazumi Tolich and Sheh Lit Chang
Relating work and changes in energy:
experiments 1 and 2
2
Two experiments are conducted with identical blocks on a level, frictionless surface. Each block is pushed through
the same distance by the same force. In experiment 1 both blocks end at rest and in 2 both blocks have a final
speed of vf2.
System 1: Two blocks and spring in
experiment 1.
System 2: Two blocks in experiment 2.
Relating work and changes in energy:
Checkpoint 1
3
1.
Determine whether the quantities in the
table are positive, negative, or zero
for each system.
Wnet ext
ΔK
ΔU
ΔEtot
System 1
System 2
2.
With which of the following students, if any, do you agree?
Student 1
The net work done on a system is always equal to the change in kinetic energy of that system.
Student 2
The total energy of a system can change if something is doing work on that system. The net work
done on a system by external forces is equal to the change in total energy of the system.
Student 3
In the absence of friction, the total energy of a system must remain constant. In other words, Ki +
Ui = Kf + Uf or ΔK + ΔU = 0
Relating work and changes in energy:
experiments 1, 2, and 3
4
Experiment 3 is similar to experiment 1, but the spring in experiment 3 is weaker than in experiment 1 (k3 < k1).
At the end of experiment 3, each block has a speed of vf3.
System 3 consists of the two blocks and the spring in experiment 3.
All three experiments are shown together below.
Experiment 1
Each hand pushes
with a constant force
of magnitude Fo
t = t1
Each hand pushes
with a constant force
of magnitude Fo
t = t3
k1
vf 1 = 0
do
A
do
do
B
do
t = t4
vf 2 > 0
do
A
do
do
B
do
Each hand pushes
with a constant force
of magnitude Fo
t = t5
k3
B
A
B
A
t = t2
Experiment 3
Experiment 2
B
A
t = t6
vf 3 > 0
do
A
do
do
B
do
Relating work and changes in energy:
Checkpoint 2
5
Consider systems 1–3.
3.
Rank these systems according to the net work done on each system by external forces, from smallest to
largest. If the net work done on any system is zero, state so explicitly.
4.
Rank these systems according to the change in total energy of the system, from smallest to largest. If the
change in total energy of any system is zero, state so explicitly.
Relating work and changes in energy:
Checkpoint 3
6
5.
Rank these systems according to the change in kinetic energy of the system, from smallest to largest. If the
change in kinetic energy of any system is zero, state so explicitly.
6.
Rank these systems according to the change in potential energy of the system, from smallest to largest. If the
change in potential energy of any system is zero, state so explicitly.
Work and energy in systems
7
A block of mass m on a level, frictionless surface is attached to an ideal
massless spring of constant k, as shown at right. At time ti, the block is released
from rest, and at time tf the spring is at its equilibrium position.
We will account for the change in kinetic energy of the block, ΔKblock by
considering 2 different systems:
System B, which consists of the block alone
System SB, which consists of the spring and the block
Work and energy in systems: Discussion
questions
8
7.
Sketch a free-body diagram for system B and system SB during the interval from ti to tf (after the hand
releases the block).
8.
For each force on your diagrams, determine whether it does positive, negative, or zero work.
9.
For each system, determine whether the net external work is positive, negative, or zero.
Work and energy in systems: Checkpoint 4
9
10.
Two students are considering the work done on the two systems:
Student 1: “I think that the spring does positive work on the block, and the wall does positive work on the
spring-block system.”
Student 2: “But the point where the wall exerts a force on the spring-block system doesn’t move, so how can
the wall do work? The displacement is zero.”
With which student, if either, do you agree?
Work and energy in systems: Checkpoint 5
10
11.
For each system, determine whether Δ𝑈 over the interval from ti to tf is positive, negative, or zero.
12.
Two students are considering an energy analysis of system B (the block alone):
Student 1: “The spring does work on system B, so system B’s spring potential energy changes.”
Student 2: “I agree that the spring does work on system B, but there aren’t any springs in system B, so how
could it have spring potential energy? It’s just a block.”
With which student, if either, do you agree?
Work and energy in systems: Discussion
questions
11
13.
For which system, if either, is the total energy unchanged over the interval from ti to tf?
Explain how you can use the principle of conservation of energy to account for the change in kinetic energy
of the block in this system.
14.
For the system for which the total energy changes, explain how you can account for the change in kinetic
energy of the block in that system.