Tag Archives: Problem Solving

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

Commentary:

None provided.

A2L Item 274

Goal: Unspecified.

Source: Unspecified.

Two cars have a race. Car A drives with constant speed of 20 m/s. Car B
drives with speed 10 m/s for 3 s, then accelerates uniformly to a speed
of 25 m/s during the next 3 s. Car B maintains the speed of 25 m/s for
the rest of the race.

If the race is very long, can car B ever catch car A?

  1. YES
  2. NO
  3. Not enough information.

Commentary:

None provided.

A2L Item 273

Goal: Unspecified.

Source: Unspecified.

Jane is riding in a hot air balloon that is rising vertically at a
constant speed of 3 m/s over a lake. She reaches out and drops a rock
from the balloon when the distance from the rock to the water is 50 m.
Use g=10 m/s2, and let the up direction be positive. About
how long after Jane drops the rock will it splash into the water?

  1. 2.0 sec
  2. 2.6 sec
  3. 3.5 sec
  4. 5.0 sec
  5. 6.8 sec
  6. 8 sec


Commentary:

None provided.

A2L Item 272

Goal: Unspecified.

Source: Unspecified.

Jane is riding in a hot air balloon that is rising vertically at a
constant speed of 3 m/s over a lake. She drops a rock from the balloon
when the distance from the rock to the water is 50 m. Use g=10
m/s2, and let up be the positive direction. Assume the origin
is on the surface of the water, what is the initial position of the
rock?

  1. 0
  2. 50 m
  3. -50 m
  4. None of the above.

Commentary:

None provided.

A2L Item 271

Goal: Unspecified.

Source: Unspecified.

Jane is riding in a hot air balloon that is rising vertically at a
constant speed of 3 m/s over a lake. She drops a rock from the balloon
when the distance from the rock to the water is 50 m. Use g=10
m/s2, and let up be the positive direction. What is the
initial velocity of the rock?

  1. 3 m/s
  2. -3 m/s
  3. 0
  4. Cannot be determined.
  5. None of the above.

Commentary:

None provided.

A2L Item 270

Goal: Unspecified.

Source: Unspecified.

A person throws a ball straight up. The ball rises to a maximum height
and falls back down so that the person catches it. When is the
acceleration of the ball at its MAXIMUM?

  1. Just after it leaves the person’s hand.
  2. At its maximum height.
  3. Just before the person catches it.
  4. Both 1 and 3.
  5. None of the above.

Commentary:

None provided.

A2L Item 211

Goal: Problem solving with rotational kinematics

Source: CT151.2S02-39

Two masses, attached to the ends of a rigid massless rod, are rotating
about pivot P as shown in the picture below. The mass two meters from P
has speed 0.5m/s. What is the acceleration of the mass one meter from
P?

  1. 0.05 m/s2
  2. 0.0625 m/s2
  3. 0.125 m/s2
  4. 0.250 m/s2
  5. 0.5 m/s2
  6. 1 m/s2
  7. None of the above
  8. Cannot be determined

Commentary:

Answer

(2) Every one of the possible wrong responses indicates a common error
that students make. After the problem has been discussed it is useful to
have students find the acceleration of the mass at 2m and see that the
accelerations are in the same ratio as the velocities. Drawing vector
diagrams showing the Δv for each mass is useful for explaining this
relationship.

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:

Answer

(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 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:

Answer

(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:

Answer

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