# A2L Item 159

Goal: Explore momentum concepts

Source: CT151.2S02-44

A cart
of mass 2m collides and sticks to a cart of mass m that is initially at
rest. What is the speed of the combination after the collision?

1. v
2. 2v/3
3. v/3
4. 0
5. None of the above.
6. Cannot be determined.

### Commentary:

(2) This question is useful for probing pre-existing ideas about
momentum, and also for distinguishing momentum ideas from kinetic
energy. It should be used just after, or even before, covering momentum
concepts.

Usually students starting momentum already have had some energy, and
kinetic energy in particular. If appropriate, they can be asked if
energy is lost in the collision. Is more or less energy lost if the
carts do not stick together?

# A2L Item 065

Goal: Recognize physical conditions under which conservation principles hold.

Source: UMPERG-ctqpe134

A
child is standing at the rim of a rotating disk holding a rock. The
disk rotates without friction. The rock is dropped at the instant
shown. What quantities are conserved during this process.

1. Only angular momentum is conserved.
2. Only mechanical energy is conserved.
3. Both angular momentum and mechanical energy are conserved.
4. Neither is conserved.
5. cannot be determined.

### Commentary:

(3) is the correct response if the rock is simply dropped. Some
students may fail to include the rock as part of the system after it is
dropped.

#### Background

Objects traveling in a straight line do have angular momentum with
respect to any origin that is not on the path of the object. The rock
does not cease to have angular momentum with respect to the center of
the disk when it is dropped. Although the angular momentum and energy of
the rock will change as the rock falls, its angular momentum and energy
just after it is dropped are the same as just before.

#### Questions to Reveal Student Reasoning

Does the rock have angular momentum (or energy) just before it is
dropped? just after it is dropped?

If energy (angular momentum) is lost, what happens to it?

Changes in angular momentum are caused by a net torque. What torques
act on the system?

#### Suggestions

Have students relate their answer to this question to the previous one.

# A2L Item 062

Goal: Interlink several dynamical concepts and associate with a physical process.

Source: UMPERG-ctqpe98

Mass M1 is traveling along a smooth horizontal surface and
collides with a mass M2 (stationary) which has a spring
attached as shown below.

The spring between the blocks is most compressed when

1. all the energy in the system is potential energy stored in the spring.
2. the net momentum of the system is zero.
3. the velocity of the center of mass has its smallest value.
4. mass M1 is no longer delivering an impulse to Mass M2.
5. the only kinetic energy in the system is that of the center of mass.
6. none of the above
7. cannot be determined

### Commentary:

5: When the spring is maximally compressed, both masses have the same
velocity which is the velocity of the center of mass.

#### Background

The total energy of an isolated system can be decomposed into three
categories; kinetic energy associated with center of mass motion,
kinetic energy of bodies in the center of mass coordinate frame and
potential energy associated with the interaction of bodies comprising
the system.

#### Questions to Reveal Student Reasoning

Is M2 ever traveling faster than M1?

Do the masses ever have the same velocity?

How would you find Pcm, the momentum of the center of
mass?

How is the kinetic energy of the center of mass related to its
momentum?

#### Suggestions

A
sketch of the velocities of the two masses over time would look
something like the graph at the right. [Note that the velocity of
M1 can be negative after the collision if it is less massive
than M2.] Such a graph helps make the relationships between
Vcm, the relative velocity of the masses and the spring
compression clear.

# A2L Item 049

Goal: Recognize the presence of a force.

Source: UMPERG

A monkey hangs on a rope. What forces act on the monkey? (Ignore
forces due to the air.)

1. Friction, Gravitation
2. Tension, Gravitation
3. Friction, Tension, Gravitation
4. Normal, Friction, Gravitation
5. More than one answer is true
6. None of the above
7. Cannot be determined

### Commentary:

(1); Assuming the monkey hangs from a vertical rope
the only forces can be gravity and friction. Students should realize
that there is only one action-at-a-distance force in this case, that of
gravity, and that there must be some contact force(s) to balance that.

# A2L Item 048

Goal: Hone the concept of force, classify forces as contact and action-at-a-distance.

Source: UMPERG

A baseball is struck by a bat. While the ball is in the air, what
objects exert forces on the ball?

1. Earth
2. Bat
3. Air
4. Bat, Air
5. Earth, Bat
6. Earth, Air
7. Earth, Bat, Air
8. There are no forces on the ball.
9. None of the above

### Commentary:

(6); the earth’s gravitational force (an “action-at-a-distance” force),
and air resistance (a contact force) are the only two forces being
exerted on the ball while in the air.

#### Background

It is common for students to think that motion requires a force; in some
cases this misconception is more specific, namely, that motion requires
a force in the direction of motion. For this assessment item, the
misconception manifests itself in the belief that there is a “force of
the bat” that propels the ball up during flight.

#### Questions to Reveal Student Reasoning

Ask students to state what forces are being exerted on the ball and what
object exerts each force.

How do you know when a force is being exerted by one object on another?

Do the sizes of the forces change? Do the directions of the forces
change? Describe how.

Do you have any control over the force of the bat on the ball? Can you
make it larger or smaller or change its direction once the ball is
flying through the air?

#### Suggestions

Ask students if they have a way of exerting a force on an object without
touching it. Invite them to move an object in the front of the room
without leaving their seats and touching the item.

If Newton’s Second Law has been introduced, attempt to relate the forces
exerted on the ball to the ball’s acceleration. See if students agree
that, if air resistance can be neglected, the ball has a constant
acceleration of 9.8 m/s2 toward the earth during its entire
trajectory. If they agree ask what they can conclude about the net
force on the ball while airborne.

# A2L Item 045

Goal: Reason using 2nd law.

Source: UMPERG-ctqpe24

Consider the two situations presented below. T1 is the tension in the string in case A and T2 is the tension in the string in case B.

Which of the following statements is correct?

1. T1 < T2
2. T1 = T2
3. T1 > T2
4. Cannot be determined

### Commentary:

(2). The force exerted on each block by the attached string must
balance the weight of the block. Since the blocks all weigh the same
amount, the tension in the in the two strings must be equal.

#### Background

This item does not require formal knowledge of Newton’s Second Law. It
can be used after students can identify the tension and gravitational
force, provided they appreciate that for static situations the forces
exerted on each object must balance. Try asking students to answer the
question individually and without discussion, giving their initial
reaction. Then ask students to re-answer the question after discussing
it briefly in small groups.

Students commonly think that T2 is greater than
T1 because the rope in situation 2 “supports” two masses.
This incorrect intuition can even exist in students who are capable of
drawing correct free-body diagrams and who know that the “tension” force
exerted on each block must balance the weight of the block. The
coexistence of conflicting intuition and formal knowledge is common
among novices.

#### Questions to Reveal Student Reasoning

What is tension? How do you measure tension?

For situation (A) consider placing a spring scale between the string and
the block in the vertical region. What force is the spring scale
measuring? For situation (A) consider cutting the string in the middle
of the horizontal region and inserting a spring scale. What force is
this spring scale measuring? How would the readings on the two spring
scales compare?

If spring scales were placed similarly in situation (B), how would their
readings compare to the readings on the spring scales in situation (A)?

#### Suggestions

Consider the original situations and two variations: (a) In (A)
consider a person holding the string in place of the wall; (b) In (B)
consider a person holding the string in place of the block on the left.
In each situation, what force is being exerted on the string so that the
hanging mass at the other end does not move?

Set up the two situations depicted in the item. Insert spring scales at
appropriate points. Discuss the readings on the scales.

# A2L Item 043

Goal: Identifying and classifying forces.

Source: UMPERG

Three blocks are stacked as shown below.

How many forces are acting on the bottom block (m3)?

1. One force
2. Two forces
3. Three forces
4. Four forces
5. Five forces
6. Six forces
7. More than six forces
8. No forces act on the block
9. Cannot be determined

### Commentary:

(3); The gravitational force exerted by the earth, the normal force
exerted by the horizontal surface, and the normal force exerted by the
block with mass m2.

#### Background

Some students have difficulty distinguishing between direct and indirect
interactions. Students may take the view that m1 directly
exerts a force on m3. This view is often verbalized as “the
weight of block m1 is exerted on m3.”

It is helpful to classify forces into action-at-a-distance forces, such
as gravity and electromagnetism, and contact forces. Students can then
employ a strategy for identifying all the forces since every object
touching a body will give rise to a force. The only exceptions are the
fundamental forces, which is an easily exhausted list.

#### Questions to Reveal Student Reasoning

Does m3 exert a force on m1?

What part of m2 interacts with m3? What part of
m1 interacts with m3?

Is weight a force? If so, what object exerts the force?

Can an object interact with another object without touching it? If so,
when? If not, why not?

Is the normal force exerted by m2 on m3 less than,
equal to, or greater than the weight of m2?

#### Suggestions

If one pushes on both sides of a bathroom scale the scale reading will
change. What does the scale measure. How is the reading related to the
forces exerted on the scale?

If bathroom scales are placed between the blocks, what forces would each
scale measure (assuming that the scales themselves have very little mass
compared to the mass of the blocks)?