Tag Archives: Mechanics

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.

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 161

Goal: Problem solving with kinematics

Source: CT151.2-4

Ann is running with a constant speed of 3 m/s on a straight track. Deb
is also running with constant speed but is initially 10 m behind Ann. If
Deb catches up to Ann after Deb has traveled 55 m, how fast is Deb
running?

  1. 3.2 m/s
  2. 3.55 m/s
  3. 3.75 m/s
  4. 4.15 m/s
  5. More than 4.2 m/s
  6. none of the above
  7. cannot be determined

Commentary:

Answer

(6) The correct speed is 3.67 m/s. Students indicating #2 or #3
are likely making an arithmetic error. Have students graph the position
vs. time graphs for each runner.

A2L Item 160

Goal: Developing a strategic approach to problem solving

Source: CT151.2S02-44 spinoff

A cart
of mass 2m collides and sticks to a cart of mass m that is initially at
rest. The combination of the two then moves together. Which of the
following principles would be the most efficient way to find the final
speed of the combination?

  1. The Work/Energy Theorem
  2. Newton’s Laws and the basic equations of motion
  3. Conservation of Energy
  4. Conservation of Momentum
  5. Conservation of Angular Momentum
  6. A different principle entirely.
  7. Two (or more) of them would be equally efficient.
  8. Need more information.

Commentary:

Answer

(4) It is valuable to always associate conservation of momentum
with the third law. In addition, it is worthwhile to distinguish totally
inelastic collisions from typical inelastic collisions.

A2L Item 159

Goal: Explore momentum concepts

Source: CT151.2S02-44

A cart
of mass 2m collides and sticks to a cart of mass m that is initially at
rest. What is the speed of the combination after the collision?

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

Commentary:

Answer

(2) This question is useful for probing pre-existing ideas about
momentum, and also for distinguishing momentum ideas from kinetic
energy. It should be used just after, or even before, covering momentum
concepts.

Usually students starting momentum already have had some energy, and
kinetic energy in particular. If appropriate, they can be asked if
energy is lost in the collision. Is more or less energy lost if the
carts do not stick together?

A2L Item 157

Goal: Hone the concept of impulse

Source: UMPERG-ctqpe86

The
two blocks shown below are identical. In case A the block sits on a
horizontal surface and in case B the block is in free fall. Which
statement is correct regarding the impulse delivered to the block by the
gravitational force during a time interval Δt?

  1. In case A the impulse is zero.
  2. In case B the impulse depends upon v.
  3. The impulse is larger in case B than A.
  4. None of the above
  5. Cannot be determined

Commentary:

Answer

(4) Even students who understand forces and would respond
correctly to this question if asked in terms of forces have difficulty
with this question. Many think that motion matters, or answer the
question as if it was about the net impulse.

A2L Item 158

Goal: Hone the concept of displacement

Source: CT151.2-2

Bekki walks 3 m to the right, 4 m to the left, 5 m to the right, and 2 m
to the left. What is her displacement?

  1. 0 m
  2. 2 m
  3. 2 m (to the right)
  4. 2 m (to the left)
  5. 14 m (to the right)
  6. 8 m to the right and 6 m to the left
  7. impossible to determine
  8. none of the above

Commentary:

Answer

(3) Students need to distinguish between distance and
displacement. Questions such as this are good introductions to vectors.

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 154

Goal: Distinguish distance traveled from displacement

Source: CT151.2-1

Andy has the following series of displacements: 3 m to the right; 4 m to
the left; 5 m to the right; and 2 m to the left. What is his distance
traveled?

  1. 0
  2. 2 m
  3. 2 m (to the right)
  4. 2 m (to the left)
  5. 14 m (to the right)
  6. 8 m (to the right)
  7. Impossible to determine
  8. None of the above

Commentary:

Answer

(8) Students just learning about vectors and displacements are
inclined to over specify quantities. Before they knew anything about
vectors they used distance as a scalar but can become confused and give
it the direction of the total displacement.