Tag Archives: Mechanics

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:

Answer

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 178

Goal: Problem solving with rotational dynamics

Source: UMPERG-ctqpe140

A disk
on a horizontal surface sits against a curb. A string wound around the
disk is attached to a mass as shown. If R=5 cm and h=2 cm, the largest
m for which the disk will not move is

  1. Less than 2M
  2. 2M
  3. 3M
  4. 4M
  5. 5M
  6. Greater than 5M
  7. Cannot be determined.

Commentary:

Answer

(4) When m = 4M the torques about the contact point between the disk and
curb balance. Students find this problem very difficult although rather
simple. Many have the most difficulty with the simple geometry needed to
find the moment arms.

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:

Answer

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

A2L Item 177

Goal: Problem solving with rotational dynamics

Source: UMPERG-ctqpe135.5

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 angular acceleration of the disk about its
center?

  1. 0
  2. 64 rad/s2
  3. 8 rad/s2
  4. 4 rad/s2
  5. 12 rad/s2
  6. None of the above.
  7. Cannot be determined

Commentary:

Answer

(6) The correct value of αcm is 16 rad/s2. Students have the erroneous
concept of ‘conservation of force’. Many think that since the disk
moves, the full force cannot contribute to the torque about the center
of the disk.

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:

Answer

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

A2L Item 172

Goal: Hone the concept of torque

Source: UMPERG-ctqpe130

Given
F1 = 6N, and F2 = 8N, what is the total torque
about point A?

  1. 1.0 N-m, out
  2. 0.7 N-m, in
  3. 7.0 N-m, out
  4. 1.0 N-m, in
  5. 6.0 N-m, out
  6. None of the above.

Commentary:

Answer

(6) Many students use the origin rather than the point A. This provides
the opportunity to stress that torque is found with respect to a
specified point. Students using the right hand rule incorrectly may
answer #2.

A2L Item 173

Goal: Hone the concept of angular momentum

Source: UMPERG-ctqpe132

Which situation has the least (magnitude) angular momentum about the
origin?

  1. A 2 kg mass travels along the line y = 3m with speed
    1.5 m/s.
  2. A 1 kg mass travels in a circle of r = 4.5 m about the
    origin with speed 2 m/s.
  3. A disk with I = 3 kg-m2
    rotates about its center (on origin) with ω = 3 rad/s.
  1. A
  2. B
  3. C
  4. Both A and B
  5. Both A and C
  6. Both B and C
  7. All have the same magnitude angular momentum

Commentary:

Answer

(7) Students frequently think that objects traveling in a straight line
have no angular momentum. An interesting follow up question is to ask
how students would answer if the disk in situation were rotating about
the point (1,0).

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:

Answer

(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 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:

Answer

(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 167

Goal: Problem solving

Source: UMPERG-ctqpe118

A mass
m slides down a frictionless track of radius R=0.5m. As the mass
reaches the bottom, relative to the center of curvature, its angular
velocity is most nearly:

  1. 6 rad/sec
  2. 8 rad/sec
  3. 12 rad/sec
  4. 15 rad/sec
  5. 20 rad/sec
  6. Cannot be determined

Commentary:

Answer

(1) The velocity near the bottom can be found using energy
conservation.