Goal: Link electric fields, work and potential energy
Source: 283-455 Change in Potential Energy when moving a charge
In each of the situations below a negative charge is moved along a path
from point A to point B in the presence of an electric field, as shown.
For which situation is the increase in potential energy the greatest?
Goal: Link work and potential change
Source: 283-450 Move q, do most work
For
the following situations consider moving a positive charge from very far
away to the origin along the y-axis. For which situation would you do
the most work?
(1) Students indicating #7 because they do not know if the masses
are charged should not be disconfirmed. If students key on magnitude
only they will likely choose answer #5.
Goal: Hone the concept of work on a gas
Source: UMPERG-ctqpe220
One mole of an ideal monatomic gas is taken around the cycle shown.
The work done on the system during the process B to C is
(1) Positive work is done ON the system. Since the path on a V-T diagram
is a straight line, the process is isobaric.
Goal: Reasoning about work and energy.
Source: UMPERG-ctqpe72
Consider the two situations shown above. The springs are identical and
are compressed the same amount, but the masses are different with M > m.
The surfaces they sit on have the same non-zero coefficient of friction.
Both start from rest. Which mass has the largest speed when the spring
reaches its relaxed length?
(1) Friction is only a confounding element. The lighter mass will have
the greater speed whether or not there is friction.
Students may correctly reason that the friction force will be less on m
and less of the potential energy stored in the spring will be dissipated
as the spring returns to its relaxed length. While true this is not
relevant for the question.
This is an instance where it is important to elicit student reasoning.
It is a case where students can use wrong reasoning to get the correct
answer.
Goal: Problem solving
Source: UMPERG
A quantity of gas is confined to a cylinder. The cylinder is vertical
and capped by a moveable piston of mass 2 kg and area 0.1 m2.
The gas is heated until the piston rises 20 cm. The amount of work done
by the gas is most nearly
(1) This problem helps interrelate concepts from mechanics and
thermodynamics. The work can be determined from the work done against
the gravitational force.
Goal: Contrast the concepts of impulse and work.
Source: UMPERG-ctqpe127
Consider the following statements:
A. If an object receives an impulse, its kinetic energy must change.
B. An object’s kinetic energy can change without it receiving any impulse.
C. An object can receive a net impulse without any work being done on it.
D. A force may do work on an object without delivering any impulse.
Which of the following responses is most appropriate?
(4) We consider only a simple object with no internal structure. A mass
traveling in a circle with constant speed (mass on a string, satellite
in circular orbit or marble rolling around a hoop on a horizontal
surface) receives a net impulse, say, every quarter circle without any
work being done because the force is perpendicular to the motion.
Students need to sort out the difference between impulse (integral of
force over time) and work (integral of force over displacement). This
question is most easily answered considering the impulse-momentum
theorem and the work-kinetic energy theorem. The example mentioned in
the answer to demonstrate the truth of statement C also serves to
demonstrate the falseness of statement A. As for statement B, if an
object’s KE changes its momentum must change so it must have received an
impulse. Statement D is also false because if a force does work on the
object it must have acted over time.
A book sits at rest on a table. Does gravity do work on the book? Does
gravity provide an impulse?
Compare a satellite in circular orbit around the Earth with a simple
pendulum. Does gravity deliver an impulse over a quarter cycle? a half
cycle? a whole cycle? Does gravity do work on the object over a quarter
cycle? a half cycle? a whole cycle?
Ask students to create physical situations meeting certain
specifications. E.g. A situation for which a force acts over a
particular time causing a change of momentum but no change in kinetic
energy (mass on a spring).
Goal: Interrelate and contrast the concepts of work, kinetic energy and impulse.
Source: UMPERG-ctqpe96
Compare two collisions that are perfectly inelastic. In case (A) a car
traveling with velocity V collides head-on with a sports car having half
the mass and traveling in the opposite direction with twice the speed.
In case (B) a car traveling with velocity V collides head-on with a
light truck having twice the mass and traveling in the opposite
direction with half the speed. In which case is the work done on the
car during the collision the greatest?
(4) The total momentum of both systems is zero, so after the collision
there is no KE in either system. System (A) has more kinetic energy
initially. There is no way, however, to determine how much of the
kinetic energy in the combined system of the two vehicles is dissipated
in the automobile as opposed to the other vehicle.
This question serves only to provoke a discussion of the dissipation of
energy in a collision. Students are tempted to assume that each
vehicle must absorb its own initial KE.
How do the forces acting on the car in the two cases compare?
Which collision takes longer?
Which vehicle do you think will suffer the greatest damage?
Promote a discussion of auto safety.
Goal: Hone the scalar nature of work and distinguish work from impulse.
Source: UMPERG-ctqpe74
A block having mass M travels along a horizontal frictionless surface
with speed v. What is the LEAST amount of work that must be done on
the mass to reverse its direction?
(3) Zero work must be done. Students will likely become entangled in
the sign of the work as well as the interpretation of the requirement to
“reverse its direction”. The most defensible answer after (3) is (2).
Some students may confuse the sign of the work, Students who choose (2)
or (4) have career potential as a lawyer.
This is an excellent problem for engaging students in a discussion of
work and energy. A mass traveling in the opposite direction with the
same speed would have the same kinetic energy. The work-kinetic energy
theorem then states that no net work need be done on the mass. The
work-kinetic energy theorem also resolves any ambiguity in the sign of
the work if the mass is just brought to rest.
Draw a diagram indicating the direction of motion and the direction of
the force acting on the mass. What is the direction of the
displacement?
If the surface had friction and the mass just slid until it stopped, how
much work would the friction force do?
It is easy to demonstrate several situations for which an object
reverses its direction and no new work is done. All it requires is a
conservative force. For example, let a ball roll up an incline and then
back down. Or, allow a mass to encounter a spring. Or, have a marble
roll around a semicircular track. This latter case is interesting
because the force acting on the mass (Normal) does no work.
Goal: Recognize forces that do work, that is those with associated displacement.
Source: UMPERG-ctqpe52
A block having mass m moves along an incline having friction as shown in
the diagram above. The spring is extended from its relaxed length. As
the block moves a small distance up the incline, how many forces do work
on the block?
(4) Four forces do work on the block: gravitation, rope, spring, kinetic
friction (because you are told the block moves). The normal force does
no work.
Recognizing those forces that do work is an important skill for students
to master. They also need to recognize whether the work is positive or
negative.
As the block moves up the plane, which forces do positive work? negative
work? How are you determining which it is? How would your answer to the
above question change if the spring were compressed rather than
extended.
Set up some situations with blocks, springs and ropes and let students
practice identifying all the forces doing work. This is a good activity
to do in conjunction with drawing free body diagrams.
Commentary:
Answer
(2) In case 1 the charge moves to a lower potential energy. In
case 3 the charge returns to a point having the same distance to the
plane of charge as it originally had, meaning no net work. In case 4 the
charge moves along an equipotential and no work is done. Students should
be asked to identify the charge configuration that could account for
each of these field situations. They can also be asked for which case is
the electrostatic potential change the greatest.