Tag Archives: Problem Solving

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:

Answer

(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:

Answer

(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 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

Commentary:

Answer

(6) This is a two-principle problem. Again, student response is
not as important as discussing what clues there are for deciding what
principles are needed.

A2L Item 155

Goal: Problem solving

Source: UMPERG-ctqpe84

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?

  1. -4 N-s
  2. -2 N-s
  3. 0 N-s
  4. 2 N-s
  5. 4 N-s
  6. none of the above
  7. cannot be determined.

Commentary:

Answer

(2) This problem requires students to put together the concepts
of kinetic and potential energy, and change of momentum. Some may be
tempted to resort to the definition of impulse and try to determine the
force due to the spring.

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

Commentary:

Answer

(3) Balancing torques about the center of the disk determines that the
friction force points up and is equal to the tension in the string. (The
other forces, gravity and normal pass through the point and contribute
no torques.) Balancing torques about the contact point determines the
tension readily.

A2L Item 095

Goal: Problem Solving

Source: UMPERG-ctqpe164

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

  1. Mg
  2. Mg/2
  3. 2Mg/5
  4. Mg/4
  5. None of the above
  6. Cannot be determined

Commentary:

Answer

(4) This problem can be solved a variety of ways. The simplest method is
to balance torques about the contact point. This situation is an
excellent one for discussing the advantages of thinking about preferred
points about which to write the rotational dynamics equation.

A2L Item 088

Goal: Problem solving

Source: UMPERG

A quantity of gas is confined to a cylinder. The cylinder is vertical
and capped by a moveable piston of mass 2 kg and area 0.1 m2.
The gas is heated until the piston rises 20 cm. The amount of work done
by the gas is most nearly

  1. 4 J
  2. 1 J
  3. -20 J
  4. 0.4 J
  5. None of the above
  6. Cannot be determined

Commentary:

Answer

(1) This problem helps interrelate concepts from mechanics and
thermodynamics. The work can be determined from the work done against
the gravitational force.

A2L Item 081

Goal: Develop a strategic approach to problem solving.

Source: UMPERG

A bug walks on a rotating disk. Given: Mbug,
Idisk, Rdisk, and ωo when the bug
is at r1. The bug crawls to r2. Find
ωfinal for the system.

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 theorem
  6. Not enough information given

Commentary:

Answer

(5) This problem helps students develop a principle-based approach to
problems. Many students may think correctly that this is a conservation
of angular momentum problem and not recognize that the general principle
is the angular impulse – angular momentum theorem.

A2L Item 069

Goal: Problem solving.

Source: UMPERG-ctqpe146

A
child having mass 32kg is standing at the rim of a rotating disk of
radius 1.5m. The disk is free to rotate without friction. The disk has
moment of inertia I = 125kg-m2 and is initially at rest. The
child throws a rock of mass 4kg in the forward tangential direction as
shown in the figure with a speed of 5m/s. The final angular speed of
the disk is most nearly

  1. 0.10 rad/s
  2. -0.25 rad/s
  3. 0.41 rad/s
  4. 1.5 rad/s
  5. -1.0 rad/s
  6. 0.50 rad/s
  7. -0.15 rad/s
  8. None of the above
  9. Cannot be determined

Commentary:

Answer

(7) is the most appropriate response. Initially there is no angular
momentum in the system. The child and disk must rotate clockwise to
balance the angular momentum of the rock. Some students may forget to
add the moment of inertia of child to that of the disk.

Background

Throwing the rock tangentially gives the rock angular momentum relative
to the fixed center of the disk. The disk-child system must have an
angular momentum which is the negative of that of the rock. Thus, it is
possible to find the angular velocity. The angular velocity is
negative, i,e, into the page.

Questions to Reveal Student Reasoning

Does the total system have angular momentum just before the rock is
thrown? just after it is thrown?

Does the rock have angular momentum just before it is thrown? just
after it is thrown?

What happens to the child upon throwing the rock? Does the child move?
How?

Suggestions

Have students relate their answer to this question to items 67 and 68.

A2L Item 038

Goal: Reason qualitatively. Consider alternate solution paths.

Source: UMPERG

Two blocks, M2 > M1, having the same speed move
from a frictionless surface onto a surface having friction coefficient
μk as shown below.

Which block stops in the shorter time?

  1. M1
  2. M2
  3. Both blocks stop in the same time.

Commentary:

Answer

(3); both blocks have the same acceleration and the same initial
velocity, so they must stop in the same length of time.

Background

This problem can be reasoned through without the use of equations.
However, the problem can be solved easy enough algebraically. The item
provides an opportunity for students to reflect on different approaches
for solving problems.

Questions to Reveal Student Reasoning

Which block experiences the largest net force?

Which block experiences the largest acceleration?

What determines which block stops first?

Suggestions

Ask students to consider the following questions, and to determine if
their answer to the problem is inconsistent with their answers to these
questions:

If two blocks enter the rough region side by side and have the same
mass, which one will stop first?

If the blocks are connected by a rope, will the time it takes for the
blocks to stop change? Would the time it takes to stop change if the
blocks were glued together?