# A2L Item 270

Goal: Unspecified.

Source: Unspecified.

A person throws a ball straight up. The ball rises to a maximum height
and falls back down so that the person catches it. When is the
acceleration of the ball at its MAXIMUM?

1. Just after it leaves the person’s hand.
2. At its maximum height.
3. Just before the person catches it.
4. Both 1 and 3.
5. None of the above.

None provided.

# A2L Item 182

Goal: Distinguish between mass, gravitational force and weight.

Source: CT151.2S02-21

An astronaut floats inside an orbiting spacestation. Which of the
following are true?

1. No forces act on the astronaut.
2. The astronaut has no mass.
3. The astronaut has no
weight.
1. A only
2. B only
3. C only
4. A and B
5. A and C
6. B and C
7. all are true
8. none are true

### Commentary:

The only possible answers are #3 and #8. The issue turns on the
definition of weight. At the surface of the earth weight and the
gravitational force are often considered equivalent. Further, since the
gravitational force depends upon the mass, mass and weight are
proportional and mass units are sometimes used as a measure of weight.
In orbit bodies still experience a gravitational force but are said to
have no weight. Is it any wonder that students are confused? Invoking
scale readings as weight is not a solution either as one’s weight would
change in an elevator. The best solution to this is to sensitize
students to these issues and charge them with the responsibilty of
determining how to interpret these quantities in context.

# A2L Item 136

Goal: Reasoning with dynamics

Source: UMPERG-ctqpe43

Block
m1 sits on block m2 and both sit on the floor of
an elevator at rest. When the elevator starts to move down, the normal
force on the upper block will …

1. increase.
2. remain the same.
3. decrease.
4. Cannot be determined

### Commentary:

(3) As it starts the elevator must accelerate downward and so
will the upper block. The only forces on the block are gravity and the
normal force. The normal force must diminish so gravity can provide the
downward acceleration.

Students answering #2 may have interpreted the question to mean ‘as the
elevator moves’ and think that the elevator moves with constant velocity.

# A2L Item 007

Goal: Linking acceleration to changes in velocity.

Source: UMPERG

A marble rolls onto a piece of felt that is 30 cm in length. At 20 cm
the speed of the marble is half of its initial value. Which of the
following is true? Assume that the acceleration is constant on the felt.

1. The marble will come to rest on the felt.
2. The marble will go past the end of the felt.
3. What will happen cannot be determined.

### Commentary:

(1) The marble will come to rest on the felt. A graph of velocity vs. time is helpful for analyzing this problem. The distance traveled while slowing down to half its initial speed (i.e., the first 20 cm) is three times the additional distance (i.e., the distance beyond 20 cm) the marble will roll before coming to rest. This can be seen by comparing the areas for
these two different time periods. The marble will come to rest at approximately 26.7 cm.

#### Background

Students should have some experience using the concept of acceleration to solve kinematics problems and analyze graphs. The answer is less important than how students represent the problem and how they approach solving the problem.

Issues to consider:
(1) Do students only solve the problem using algebraic methods? (2) To what extent do students use other approaches? (3) Do students use graphical methods involving areas? (4) Do theycompare average speeds for the two periods (i.e., the period covering the first 20 cm and the remaining period of time before the marble comes to rest)? (5) Do they compare the actual speeds of the marble at each instant of time for the two time periods (the ratio is usually greater than or equal to 2/1 at each corresponding time, as shown in the accompanying graph). (6) Even if the students use algebraic methods, do they employ a strategy or do they do so mindlessly?

#### Questions to Reveal Student Thinking

Ask students to consider the following context (which they are familiar with and is algebraically simple): an object is dropped from rest. How fast is it moving after one second? … after two seconds? …after three seconds? How far has it traveled after one second? …after two seconds?…after three seconds? What is the relationship between velocity and position? Why is the relationship not linear?

#### Suggestions

If students do not use a graph to solve the problem, ask them to draw a velocity vs. time graph for the situation and then use the graph to solve the problem.

A demonstration is possible.