# A2L Item 165

Goal: Problem solving and developing strategic knowledge

Source: UMPERG-ctqpe103

You are given this problem: A
block sits on a frictionless incline. Given the angle of incline, the
distance along the incline, and that the block is initially at rest,
find the speed 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-Angular Momentum
6. 1 and 2
7. 1 and 3
8. 2 and 3
9. None of the above
10. Not enough information given

### Commentary:

(3) The change in gravitational potential can be found directly.
Alternately, the work done by the gravitational force must be equal to
the change in kinetic energy.

# A2L Item 166

Goal: Problem solving and developing strategic knowledge

Source: UMPERG-ctqpe104

You are given this problem: A
block sits on a frictionless incline. Given the mass of the block, the
angle of incline, the distances d1 and d2, and
that the block starts from rest, find the time to travel from
d1 to d2.

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-Angular Momentum
6. 1 & 2
7. 1 & 3
8. 2 & 3
9. None of the above
10. Not enough information given

### Commentary:

(6) Students responding #1 are relying on memory and would have
difficulty if a force other than gravity was involved.

# 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 162

Goal: Problem solving and developing strategic knowledge

Source: UMPERG-ctqpe100

You are given this problem: A
mass m slides down a frictionless track of radius R=0.5m. Relative to
the center of curvature, what is the angular acceleration of the mass as
it reaches the bottom of the track.

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-Angular Momentum
6. 1 & 2
7. 1 & 3
8. 2 & 3
9. none of the above
10. not enough information given

### Commentary:

(7) Students often think this problem requires angular momentum
or angular dynamics. Many cue on anything circular. Some students may
answer #10 thinking that the mass is needed.

# A2L Item 160

Goal: Developing a strategic approach to problem solving

Source: CT151.2S02-44 spinoff A cart
of mass 2m collides and sticks to a cart of mass m that is initially at
rest. The combination of the two then moves together. Which of the
following principles would be the most efficient way to find the final
speed of the combination?

1. The Work/Energy Theorem
2. Newton’s Laws and the basic equations of motion
3. Conservation of Energy
4. Conservation of Momentum
5. Conservation of Angular Momentum
6. A different principle entirely.
7. Two (or more) of them would be equally efficient.

### Commentary:

(4) It is valuable to always associate conservation of momentum
with the third law. In addition, it is worthwhile to distinguish totally
inelastic collisions from typical inelastic collisions.

# A2L Item 156

Goal: Developing strategic knowledge

Source: UMPERG-ctqpe85

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?

Which of the following principles or combination of principles
could be used to solve this problem MOST EFFICIENTLY.

1. Newton’s 2nd law & dynamics
2. Work-Energy theorem
3. Impulse-Momentum theorem
4. 1 and 2
5. 1 and 3
6. 2 and 3
7. Other