# A2L Item 149

Goal: Reason with potential energy

Source: UMPERG-ctqpe68 Consider three spring systems having identical springs and
masses. Which of the 3 systems has the largest amount of stored energy?

1. A
2. B
3. C
4. A and C
5. All have the same potential energy
6. Cannot be determined

### Commentary:

(2) Students often forget to include the gravitational potential
energy and also have difficulty selecting a good reference point.

# A2L Item 148

Goal: Hone the concept of conservative force

Source: UMPERG-ctqpe67 The
potential energy function for a certain body is shown at right. The
force associated with this potential is …

1. conservative.
2. dissipative.
3. neither conservative or dissipative.
4. Cannot be determined

### Commentary:

(1) It is remarkable how many students will select one of the
other answers. Many students do not recognize that you cannot have a
potential function unless the force is conservative.

# A2L Item 146

Goal: Hone the concept of potential energy functions

Source: UMPERG-ctqpe65 The
potential energy function for a certain body is shown at right. If the
body is released from rest at a location corresponding to point 4, the
object would …

1. move towards larger values of x.
2. move towards smaller values of x.
3. remain stationary.
4. oscillate back and forth.
5. None of the above
6. Cannot be determined

### Commentary:

(2) At position 4 the object experiences a force toward the
origin given by the negative of the slope of the potential curve.
Frequently students interpret the fact that U is zero at point 4 to mean
that there is no force.

# A2L Item 140

Goal: Link potential energy with work needed to assemble a charge configuration.

Source: 283-460 Lowest potential energy

Which of the following charge distributions has the lowest potential
energy? ### Commentary:

(2) Encourage students to reason to the answer rather than write
formal expressions for each case. They should be able to perceive that
cases #1, #3 and #5 all have positive PE. Situation #4 has zero energy
as can be seen by assembling subunits, then moving the two positive
charges along the zero equipotential of the charges on the y-axis.
Finally, situation #2 is clearly negative.

A good follow-up question is to ask students to order the cases
according to increasing potential energy.

# A2L Item 135

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? ### Commentary:

(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.

# A2L Item 129

Goal: Hone the concept of electrostatic potential

Source: 283-420 Change of PE A uniform volume distribution of
charge has radius R and total charge Q. A point charge -q is released
from rest at point b, which is a distance 3R from the center of the
distribution. When the point charge reaches a, which of the following is
true regarding the potential energy, U?

1. Ua = -Ub
2. Ua = -2Ub/3
3. Ua = -3Ub/2
4. Ua = -9Ub/4
5. Ua = Ub
6. Ua = 2Ub/3
7. Ua = 3Ub/2
8. Ua = 9Ub/4
9. None of the above
10. Cannot be determined