# 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 279

Goal: Unspecified.

Source: Unspecified.

An applied force FA pushes a block of mass m up a rough incline having coefficient of kinetic friction μk. The friction force on the block is:

1. mgcosθ
2. mgsinθ
3. μkmgsinθ
4. μkmgcosθ
5. μkmgtanθ
6. μkmgsinθcosθ
7. None of the above.
8. Can’t be determined.

None provided.

# A2L Item 189

Goal: Problem solving with dynamics

Source: UMPERG-ctqpe168

A
uniform disk with mass M and radius R rolls without slipping down an
incline 30° to the horizontal. The friction force acting through
the contact point is

1. 0
2. Mg/3
3. Mg/4
4. Mg/6
5. none of the above

### Commentary:

(4) This problem requires students to use the 2nd law written in
terms of the CM acceleration and the rotational dynamic relation written
about the CM or the contact point. In either case they also need the
geometric constraint for rolling. This is a difficult problem for
students requiring a lot of additional knowledge, such as the moment of
inertia for a disk and, depending upon solution method, the Parallel
Axis Theorem.

Having gone to the trouble of solving the problem it is best to make
sure that the students glean as much as they can. A good followup
question is which would have a larger friction force, a hoop, a disk or
a sphere. They may try to reason from the acceleration of these objects
that the larger the acceleration, the smaller the friction force. The
friction force depends upon the mass, however, and the question cannot
be answered without knowledge of the masses.

# A2L Item 142

Goal: Reasoning with forces and kinematics

Source: UMPERG-ctqpe60 variant

Two
blocks, M2 = M1 but of different sizes, having the
same speed, move from a frictionless surface onto a surface having
friction coefficient μk.

Which stops in the shorter time?

1. M1
2. M2
3. Both stop in the same time
4. Cannot be determined

### Commentary:

(3) Both blocks will experience the same acceleration. If they
have the same initial velocity, they will stop in the same time.

# A2L Item 138

Goal: Problem solving with momentum

Source: UMPERG-ctqpe46

A
block slides along a frictionless surface and onto a slab with a rough
surface. The plot on the right shows the velocity of the blue slab as a
function of time. The slab has mass of 4kg and the block has mass of
2kg. If the block remains on top of the slab, what was its initial
speed?

1. 2 m/s
2. 4 m/s
3. 6 m/s
4. 8 m/s
5. 12 m/s
6. None of the above
7. Cannot be determined

### Commentary:

(6) The block initially has velocity 3 m/s. This problem is
difficult for students. They generally have difficulty obtaining
relevant information from a diagram. In this case they must use the plot
to tell that the final velocity is 1 m/s.

# A2L Item 137

Goal: Problem solving

Source: UMPERG-ctqpe44-46

A
block slides along a frictionless surface and onto a slab with a rough
surface. The plot on the right shows the velocity of the blue slab as a
function of time. The slab has mass of 4kg and the block has mass of
2kg. What is the friction force on the small block at t = 1 second?

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

### Commentary:

(5) The acceleration of the slab can be found from the plot. The
only force on the slab in the horizontal direction is the friction force
so it must be responsible for the acceleration. The force on the block
can then be found using the 3rd law.

# A2L Item 131

Goal: Reasoning with dynamics

Source: UMPERG-ctqpe30

A
block of mass m, when placed on a rough inclined plane and moved, moves
down the plane with constant speed. If a block of mass 2m were placed
on the same incline and moved, it would …

2. accelerate until the speed is half.
3. move with some constant speed.
4. None of the above.
5. Cannot be determined

### Commentary:

The block will have the same motion. Both the gravitational force
and the friction force scale with the mass so there is no net force in
either case.

# A2L Item 128

Goal: Hone the concept of static friction

Source: UMPERG-ctqpe27

A mass of 5 kg sits at rest on an incline making an angle of 30° to
the horizontal.

If μs = 0.7 the friction force on the block is

1. 43.3N, down the incline
2. 25N, up the incline
3. 10N, down the incline
4. 30.3N, up the incline
5. none of the above
6. cannot be determined

### Commentary:

(2) this is all that is needed to hold the block at rest. Some
students will give #4 as the answer having calculated the maximum static
friction force.

It helps to classify forces as model forces obtainable from a formula,
and procedure forces. Static friction is an example of a procedure
force, one that cannot be determined without application of the 2nd law.

# A2L Item 100

Goal: Reasoning about work and energy.

Source: UMPERG-ctqpe72

Consider the two situations shown above. The springs are identical and
are compressed the same amount, but the masses are different with M > m.
The surfaces they sit on have the same non-zero coefficient of friction.
Both start from rest. Which mass has the largest speed when the spring
reaches its relaxed length?

1. m
2. M
3. Both have the same speed.

### Commentary:

(1) Friction is only a confounding element. The lighter mass will have
the greater speed whether or not there is friction.

Students may correctly reason that the friction force will be less on m
and less of the potential energy stored in the spring will be dissipated
as the spring returns to its relaxed length. While true this is not
relevant for the question.

This is an instance where it is important to elicit student reasoning.
It is a case where students can use wrong reasoning to get the correct

# A2L Item 096

Goal: Problem solving

Source: UMPERG-ctqpe166

A uniform disk with mass M and radius R sits at rest on an incline
30° to the horizontal. A string is wound around disk and attached
to top of incline as shown. The string is parallel to incline. The
friction force acting at the contact point is:

1. Mg/2, down the incline
2. Mg/2, up the incline
3. Mg/4, up the incline
4. Mg/0.86, down the incline
5. None of the above
6. Cannot be determined