# Category Archives: Middle School

Items appropriate for use in a middle-school physics or physical science course.

# A2L Item 280

Goal: Unspecified.

Source: Unspecified.

A student suggests that an unknown mass can be measured by placing a known mass on a frictionless incline and measuring the acceleration. Then place the unknown mass on the same incline and measure the acceleration. From this information you can find the value of the new mass. Will this work? Be prepared to explain.

1. Yes
2. No

None provided.

# A2L Item 263

Goal: Reason regarding interactions

Source: CT151.2S02-43

A
cart of mass 2m collides and sticks to a cart of mass m that is
initially at rest. Which cart exerts the larger force on the other?

1. m
2. 2m
3. Both exert the same force
4. Cannot be determined

### Commentary:

(3) Yet another instance of Newton’s Third Law. Some students still
stumble because they the question considers the object exerting the
larger force as opposed to the one having the larger force applied to
it.

# A2L Item 258

Goal: Hone the concept of average velocity

Source: CTtil2;12;02

While traveling from Boston to Hartford, Person A drives at a constant
speed of 55 mph for the entire trip. Person B drives at 65 mph for half
the trip and then drives 45 mph for the second half of the trip. When
would B arrive in Hartford relative to A?

1. B arrives before A.
2. B arrives at the same time as A.
3. B arrives after A.
4. Not enough information.

### Commentary:

(3) Many students are inclined to average the speeds and conclude that
they arrive at the same time. It is often useful to compare this
situation to the one in which time is halved.

# 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 169

Goal: Link acceleration to the slope of a velocity/time graph

Source: CT151.2-6

An
object’s motion is described by the graph above. The instantaneous
acceleration at t=10 sec is most nearly…

1. 0 m/s2
2. -2 m/s2
3. 3 m/s2
4. -4 m/s2
5. 5 m/s2
6. Other

### Commentary:

(1) Useful follow-up questions include; when does the object have
positive acceleration, when negative acceleration; does the object ever
stop?; when is it farthest from the origin?

# A2L Item 168

Goal: Interpreting graphs

Source: CT151.2-5

An
object’s motion is described by the graph above. The average
acceleration during the first 10 s is most nearly…

1. 0 m/s2
2. 20 m/s2
3. 30 m/s2
4. 40 m/s2
5. 50 m/s2
6. Other

### Commentary:

(3) Students may have difficulty understanding what they are
asked. Recasting the problem in terms of areas helps. The only
contenders should be #2 or #3. Counting blocks should make it clear that
the result is much closer to #3.

# A2L Item 058

Goal: Perceiving acceleration from description of motion.

Source: UMPERG Core A.4

How many of the objects below are NOT accelerating?
(A) A race car going around a circular track at 150 MPH
(B) A sky diver falling at a constant speed
(C) A heavy box sliding across the floor, after being released
(D) A bowling ball colliding with a pin
(E) A vibrating guitar string
(F) A baseball flying through the air
(G) A child swinging on a swing

1. 1
2. 2
3. 3
4. 4
5. 5
6. 6
7. 7

### Commentary:

(1) Only the skydiver, who has reached terminal velocity, has zero
acceleration. In each of the other situations either the speed or
direction of motion is changing.

#### Background

Students may use a variety of factors in deciding whether an object
accelerates.

The goal is to focus students more narrowly on changes in the speed
and/or direction of an object’s motion.

#### Questions to Reveal Student Reasoning

How do you know whether an object is accelerating? What are some
examples of objects undergoing an acceleration?

#### Suggestions

Play a “challenge game” with the class where two teams of students take
turns challenging each other with situations in which an object
undergoes some motion, and the other team needs to determine whether or
not the object is accelerating.

Have students write out how they determine whether an object is
accelerating. After listening to the different method students use,
have students vote on which method they think is best.

002

# A2L Item 055

Goal: Classify forces and hone the concept of contact force.

Source: UMPERG

A person throws a ball straight up in the air. The ball rises to a
maximum height and falls back down so that the person catches it. What
forces are being exerted on the ball when it is half way to the maximum
height? Ignore air resistance.

1. The gravitational force only.
2. The force of the person’s hand only.
3. Both the gravitational force and the force of the person’s hand.
4. The gravitational force, the force of the person’s hand, and a third
force.
5. None of the above
6. Cannot be determined

### Commentary:

(1); nothing is in contact with the ball (we ignore forces due to the
air), and so the earth’s gravitational force is the only
“action-at-a-distance” force present.

#### 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 hand” that propels the ball up during flight.

#### Questions to Reveal Student Reasoning

Ask students to state what forces are acting 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 and why.

Do you have any control over the force of the hand on the ball while the
ball is in the air? Can you make it larger or smaller or change its
direction once you release the ball?

#### Suggestions

Have students brainstorm situations in which two objects interact
without touching each other. Use as the criteria for an interaction
that an object move or change shape. Have students divide their
situations into two groups: those for which the objects interact
directly, and those for which the objects interact through some other
object (e.g., two blocks “interact” through a spring placed between
them).

Eventually raise the point that in physics the term force refers to
direct interactions only and that most objects interact only when placed
in contact. Demonstrate electric and magnetic forces as examples of
“action-at-a-distance” forces.

# 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 047

Goal: Hone the concept of force, recognize the presence of force.

Source: UMPERG

A water balloon is shown at rest in three different situations. In each
case the water balloon is in contact with a system that supports it.

Which system exerts the largest force on the balloon?

1. Spring support in A
2. Cardboard and blocks in B
3. Table in C
4. None of the systems exert a force
5. None of the above
6. Cannot be determined

### Commentary:

(5). Each system exerts the same magnitude force on the balloon. The
size of the force equals the weight of the balloon.

#### Background

Context for Use: Give to students before they receive a formal
introduction to interactions.

Assessment Issues: (1) What are students’ naive views about
interactions? (2) Can students perceive when an interaction is
occurring? (3) What factors do students attend to when determining
whether a force is present? (4) What factors do students use to compare
the relative magnitude of two forces?

#### Questions to Reveal Student Reasoning

Which systems exert a force on the balloon? How did you decide whether
the system exerts a force on the balloon? In each case how did the
force affect the balloon? How did the interaction between the balloon
and system affect the system? When comparing two forces, how can you
tell which force is larger?

#### Suggestions

Recognizing the presence of an interaction is a difficult problem for