# 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 186

Goal: Problem solve with rotational dynamics

Source: UMPERG-ctqpe156

A
uniform rod is hinged to a wall and held at a 30° angle by a thin
string that is attached to the ceiling and makes a 90° angle to rod.
The tension in the string is 10N. The weight of the rod is about

1. 13N
2. 18N
3. 20N
4. 23N
5. 40N
6. none of the above

### Commentary:

(4) Some students will use the wrong trigometric function and
conclude that the weight is 40N.

An interesting follow up question is to ask what is the hinge force.
Students often forget that both the sum of the forces and the sum of the
torques must be zero for static equilibrium.

# A2L Item 185

Goal: Reasoning and hone the concept of torque.

Source: UMPERG-ctqpe152

A
uniform rod of length 4L, mass M, is suspended by two thin strings,
lengths L and 2L as shown. What is net torque about the left end of the
rod?

1. 0
2. 4MgL
3. 8MgL
4. 12MgL
5. None of the above

### Commentary:

(1) Since the rod does not rotate the total torque must be zero
about any point. Many students overworry this problem not realizing
that, independent of the angle of the rod, the other string is twice as
far as the center of mass of the rod.

# A2L Item 175

Goal: Problem solving

Source: UMPERG-ctqpe135.1

A
disk, having radius R and mass M, is free to rotate about an axis
through its center. A massless string is wound around disk and attached
to mass m. The moment of inertia for a disk given by is
1/2(MR2). If M=4m what is the acceleration of mass m?

1. 0
2. g/2
3. g/8
4. g/5
5. g/3
6. None of the above
7. Cannot be determined

### Commentary:

(5) Students answering #2 are likely making the common mistake of
thinking that the tension in the string is mg.

# A2L Item 106

Goal: Hone rotational dynamics

Source: UMPERG-ctqpe1246

A system consisting of two masses on a string is rotating with angular
velocity ω on a frictionless horizontal surface. The center of
rotation is the left-hand side of the string (nailed to the table).

The ratio of the tension in the inner string to that in the outer string
is

1. 0.25
2. 0.5
3. 1.5
4. 2.0
5. 3.0
6. None of the above

### Commentary:

(3) Many students think the ratio is determined just by the string
lengths and give as an answer either (2) or (4). They fail to draw a
free body diagram for the inner mass and, consequently, fail to realize
that it is the net force on the inner mass that must maintain the
circular motion of the inner mass.

# A2L Item 099

Goal: Reasoning about forces and torques.

Source: UMPERG-ctqpe158

A uniform rod is hinged to a wall and held at a 30° angle by a thin
string that is attached to the ceiling and makes a 90° angle to rod.
Which statement must be true?

1. The hinge force is purely vertical.
2. The hinge force is purely horizontal.
3. The string tension equals the hinge force.
4. The string tension is less than the rod’s weight

### Commentary:

(4) This is easily determined by considering torques about the hinge.
The hinge force cannot be purely vertical because there is a horizontal
component to the tension that must be balanced. Also the hinge force
cannot be purely horizontal or the rod would rotate counterclockwise
about its center. Since the hinge force must have a horizontal component
in the opposite direction as the horizontal component of the tension,
(3) cannot be true either.

# A2L Item 097

Goal: Hone the concept of torque.

Source: UMPERG-ctqpe150

A uniform rod of length L, mass M, is suspended by two thin strings.
Which of the following statements is true regarding the tensions in the
strings?

1. T2 = T1
2. T2 = 2.5T1
3. T2 = 0.6T1
4. T2 = 0.8T1
5. None of the above

### Commentary:

(3) The ratio is most easily found by considering torques about the
center of the bar. The distances of the strings to the center of the
bar need to be determined visually from the figure.

# A2L Item 098

Goal: Reasoning with forces

Source: UMPERG-ctqpe154

A uniform rod of length 4L, mass M, is suspended by two thin strings,
lengths L and 2L as shown. What is the tension in the string at the
left end of the rod?

1. Mg
2. Mg/2
3. Mg/3
4. Mg/4
5. None of the above

### Commentary:

(2) For many this is straightforward but a few students are confused
about the effect of the unequal lengths of string.

# A2L Item 070

Goal: Recognizing the presence of forces.

Source: UMPERG

A block having mass m moves along an incline having friction as shown in
the diagram above. As the block moves a small distance along the
incline, how many forces act on the block?

1. One force
2. Two forces
3. Three forces
4. Four forces
5. Five forces
6. Six forces
7. Seven forces
8. None of the above
9. Cannot be determined

### Commentary:

(5) Five forces act on the block: gravitation, rope, spring, kinetic
friction (because you are told the block moves), and normal due to the
incline. Many student errors are due to the failure to identify all of
the forces acting on a body.

#### Background

It is helpful to classify forces into action-at-a-distance forces, such
as gravity and electromagnetism, and contact forces. Students can then
employ a strategy for identifying all the forces since every object
touching a body will give rise to a force. The only exceptions are the
fundamental forces, which is an easily exhausted list.

#### Questions to Reveal Student Reasoning

Does it matter if the block is moving up the plane or down? If the block
is at rest, how many forces MUST be acting on the block? How many forces
may be acting but you can’t be sure?

#### Suggestions

Set up some situations with blocks, springs and ropes and let students
practice identifying all the forces. This is a good activity to do in
conjunction with drawing free body diagrams.