# A2L Item 155

Goal: Problem solving

Source: UMPERG-ctqpe84

A mass of 0.5 kg moving along a horizontal frictionless surface
encounters a spring having k = 200 N/m. The mass compresses the spring
by 0.1 meters before reversing its direction. Consider the total time
the mass is in contact with the spring. What is the total impulse
delivered to the mass by the spring?

1. -4 N-s
2. -2 N-s
3. 0 N-s
4. 2 N-s
5. 4 N-s
6. none of the above
7. cannot be determined.

### Commentary:

(2) This problem requires students to put together the concepts
of kinetic and potential energy, and change of momentum. Some may be
tempted to resort to the definition of impulse and try to determine the
force due to the spring.

# A2L Item 145

Goal: Reasoning with energy

Source: UMPERG-ctqpe64

Two
masses, M > m, travel down the surfaces shown. Both surfaces are
frictionless. Which mass has the largest speed at the bottom?

1. m
2. M
3. Both have the same speed
4. Cannot be determined

### Commentary:

(3) By energy considerations, both would have the same speed.
Students frequently get confused about the mass, thinking that the
larger mass has the greatest potential energy change and therefore has
the greatest speed.

# A2L Item 144

Goal: Reasoning with kinematics

Source: UMPERG-ctqpe63

Two
masses, M > m, travel down the surfaces shown. Both surfaces are
frictionless. Which mass has the largest average speed during
their motion?

1. m
2. M
3. Both have the same average speed
4. Cannot be determined

### Commentary:

(1) This problem is intended to promote discussion of average
speed. Both masses have the same speed at the bottom. Mass m has a
larger acceleration in the beginning because the circular track is
vertical at the outset. Although the angle of the incline is not
specified, the angle is irrelevant. All inclines will have the same
average speed. A simple graph of the speed of each mass versus time
shows that m will have the larger average speed.

# A2L Item 143

Goal: Reasoning with energy

Source: UMPERG-ctqpe62

Two
identical blocks fall a distance H. One falls directly down, the other
slides down a frictionless incline. Which has the largest speed at the
bottom?

1. The one falling vertically
2. The one on the incline
3. Both have the same speed
4. Cannot be determined

### Commentary:

(3) The only force doing work is gravity and both block undergo
the same vertical displacement.

# 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 132

Goal: Link energy conservation and electromagnetism

Source: 283-421 Change of total energy

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 total energy, E?

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

### Commentary:

(5) Students often forget to include the kinetic energy,
especially after a lot of discussion of potential energy. Many will
simply misinterpret the energy to mean potential energy. Teasing apart
these issues is important.

# A2L Item 105

Goal: Problem solving

Source: UMPERG-ctqpe147

A hoop of mass 4 kg and radius r rolls
without slipping down an incline 30° to the horizontal. The hoop is
released from rest. What is the speed of the hoop after its center has
fallen a distance h?

1. (4g(h-r))1/2
2. (2gh)1/2
3. (gh)1/2
4. (0.5g(h+r))1/2
5. none of the above
6. cannot be determined

### Commentary:

(3.) Students should realize that the speed cannot depend upon the
radius. Answer #2 is the speed that a falling point mass would have and
the hoop must have less than that.

# A2L Item 100

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. m
2. M
3. Both have the same speed.

### Commentary:

(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

# A2L Item 093

Goal: Problem solving

Source: UMPERG-ctqpe88

Two blocks, M=2m, sit on a horizontal frictionless surface with a
compressed massless spring between them. After the spring is released
M has velocity v. The total energy initially stored in the spring was:

1. mv2
2. 2mv2
3. 3mv2
4. 4mv2
5. 5mv2
6. None of the above.
7. Cannot be determined

### Commentary:

(3) The big mass has kinetic energy mv2 and the small mass
has energy 2mv2. Some students may answer (6) because they
have confused M and m. It is important to determine the reasons that
any student might select (7). They might be unwilling to assume that
the system is initially at rest. Students taking this perspective
should not be disconfirmed but congratulated for making a critical
interpretation of the wording.

# A2L Item 091

Goal: Hone the concept of internal energy and heat.

Source: UMPERG-ctqpe180

Body A has a higher temperature than body B. Which of the following
statements is true?

1. Body A will feel hotter than body B.
2. Body A contains more energy than body B.
3. If placed in contact with each other, energy will flow from body A to
body B.
4. If placed in contact with a third body having temperature greater
than body A, body B will absorb more heat than A.
5. More than one statement is true.