# A2L Item 276

Goal: Unspecified.

Source: Unspecified.

A pendulum is released from rest at position A and swings toward the
vertical under the influence of gravity as depicted below.

When at position B, which direction most nearly corresponds to the
direction of the acceleration?

Enter (9) if the direction cannot be determined.

None provided.

# A2L Item 275

Goal: Unspecified.

Source: Unspecified.

Two cars have a race. Car A drives with constant speed of 20 m/s. Car B
drives with speed 10 m/s for 3 s, then accelerates uniformly to a speed
of 25 m/s during the next 3 s. Car B maintains the speed of 25 m/s for
the rest of the race.

What is the minimum length of race if Car B is to overtake car A?

None provided.

# A2L Item 273

Goal: Unspecified.

Source: Unspecified.

Jane is riding in a hot air balloon that is rising vertically at a
constant speed of 3 m/s over a lake. She reaches out and drops a rock
from the balloon when the distance from the rock to the water is 50 m.
Use g=10 m/s2, and let the up direction be positive. About
how long after Jane drops the rock will it splash into the water?

1. 2.0 sec
2. 2.6 sec
3. 3.5 sec
4. 5.0 sec
5. 6.8 sec
6. 8 sec

None provided.

# A2L Item 271

Goal: Unspecified.

Source: Unspecified.

Jane is riding in a hot air balloon that is rising vertically at a
constant speed of 3 m/s over a lake. She drops a rock from the balloon
when the distance from the rock to the water is 50 m. Use g=10
m/s2, and let up be the positive direction. What is the
initial velocity of the rock?

1. 3 m/s
2. -3 m/s
3. 0
4. Cannot be determined.
5. None of the above.

None provided.

# A2L Item 272

Goal: Unspecified.

Source: Unspecified.

Jane is riding in a hot air balloon that is rising vertically at a
constant speed of 3 m/s over a lake. She drops a rock from the balloon
when the distance from the rock to the water is 50 m. Use g=10
m/s2, and let up be the positive direction. Assume the origin
is on the surface of the water, what is the initial position of the
rock?

1. 0
2. 50 m
3. -50 m
4. None of the above.

None provided.

# A2L Item 183

Goal: Reason with impulse and energy

Source: CT151.2S02-46

Two
blocks are connected to the ends of a spring as shown. Assume that the
mass is proportional to the size of the block. The spring is compressed
(same amount) and released suddenly. In which orientation will the
system achieve the largest height?

1. A
2. B
3. both go to the same height
4. cannot be determined

### Commentary:

(2) This is a very rich problem for reasoning. It IS possible for
students to reason to the correct solution if they consider appropriate
concepts. To help them along suggest the following: Draw free body
diagrams for each of the masses separately. Combine them to get a valid
free body diagram for the system. Such a process reveals that the normal
force is responsible for the impulse causing the system to jump. The
spring force is internal to the system and does not appear on the
system’s free body diagram.

Students can deduce the answer using analogy or experience. Pogo sticks
or even the human body are analogous systems.

# A2L Item 176

Goal: Problem solving with dynamics

Source: UMPERG-ctqpe135.3

A
disk, with radius 0.25 m and mass 4 kg, lies on a smooth
horizontal table. A string wound about the disk is pulled with a
force of 8N. What is the acceleration of the disk?

1. 0
2. 0.5 m/s2
3. 1 m/s2
4. 2 m/s2
5. 4 m/s2
6. None of the above.
7. Cannot be determined

### Commentary:

(4) Students find it difficult to grasp that the angular dynamic
relationship does not replace, but rather augments, the 2nd law.

# A2L Item 163

Goal: Problem solving and developing strategic knowledge

Source: UMPERG-ctqpe101

You are given this problem:

A
block sits on a frictionless incline. Given the angle of incline, the
distance along incline, and the mass of block, find the acceleration
after traveling a distance d.

What principle would you use to solve the problem MOST EFFICIENTLY?

1. Kinematics only
2. F = ma or Newton’s laws
3. Work-Energy theorem
4. Impulse-Momentum theorem
5. Angular Impulse-Ang. Momentum
6. More than one of the above
7. Not enough information given

### Commentary:

(2) The 2nd law is needed to find the acceleration. Students who
answer that only kinematics is needed are relying on memory.

# A2L Item 152

Goal: Reason with kinematics

Source: UMPERG-ctqpe76

Two identical steel balls are released from rest from the same height,
and travel along tracks as shown and labeled below.

Which reaches the end of its track first?

1. Ball on track A
2. Ball on track B
3. They reach the end at the same time
4. Not enough information

### Commentary:

(2) The ball on track B accelerates down the second slope. A component
of this acceleration is in the x-direction. This means that the x
component of ball B’s velocity is never smaller than that of ball A.
Since the tracks have the same x-dimension, ball B gets there first.

A large majority of students choose answer C incorrectly thinking that
since the balls return to the same height, they have the same speed and,
therefore, arrive at the same time.

# A2L Item 151

Goal: Reason with kinematics

Source: UMPERG-ctqpe75

Two identical steel balls are released from rest from the same height,
and travel along tracks as shown and labeled below.

Which ball reaches the end of its track first?

1. ball on track A
2. ball on track B
3. they reach the end at the same time
4. not enough information