Tag Archives: Vectors

A2L Item 210

Goal: Relate representations

Source: 283-342 Graph Ex(x)

We have a charge configuration
(shown at the right). Which graph is the plot of Ex(x), the
x component of the electric field, as you move along the
x-axis?

Commentary:

Answer

(6) Students should recognize that the field goes singular at the
charges. The only graphs doing that, #1 and #4, are eliminated because
the x-component of the field must be negative everywhere between the two
charges. Have students sketch the graph.

A2L Item 202

Goal: Reason regarding electric fields

Source: 283-11, E at origin due to charged rods

For which of the configuration(s) below does the total electric field
vector at the origin have non-zero components in both the x and y
directions?

  1. 2 only
  2. 1 and 3 only
  3. 5 only
  4. 4 only
  5. 1 and 5 only
  6. None of the above

Commentary:

Answer

(6) Only situation 3 meets the condition. A good exercise is to have
students draw the contribution to the field at the origin due to each
rod. The contributions should have the correct relative size and
direction.

A2L Item 203

Goal: Reason regarding electric fields

Source: 283 –

Charge, Q, is at the origin. Points A-E are positions where other
charges may be present. Etotal at point F is non-zero and
points in the +i direction. Which of the following situations
could account for this?

  1. Another charge is present at position
    A.
  2. Two other charges are present at C & D.
  3. Two other
    charges are present at D & B.
  4. Two other charges are present at
    E & A.
  1. A only
  2. B only
  3. C only
  4. D only
  5. A and B
  6. A, C and D
  7. A, B, and D
  8. A, B, C, and D

Commentary:

Answer

(2) Only a charge at C can counter the y component of the field of Q at
F. A charge at B or D can then create a field at F that points in the i
direction.

A2L Item 201

Goal: Reason regarding electric fields

Source: 283-10, E at origin due to charged rods

All of the configurations shown below consist of charged rods of the
same length L. The magnitude of the total charge is also the same for
each rod. The total charge in each rod is distributed uniformly.

For which
configuration(s) is the electric field vector at the origin in the
positive x direction?

  1. 2 only
  2. 1 and 3 only
  3. 5 only
  4. 4 only
  5. 1 and 5 only
  6. None of the above

Commentary:

Answer

(4) Because they are given lots of examples involving point charges,
spheres and rings, students often miss the fact that there are many
situations for which the direction of the field can be deduced even
though determining the value or formal expression for the field is way
beyond them.

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 104

Goal: Hone the concept of torque

Source: UMPERG-ctqpe131

Which of the following statements is true about this situation?

  1. There are no points having zero total torque.
  2. There is one point having zero total torque.
  3. There are many points having zero total torque.

Commentary:

Answer

(3) Many students realize that there is at least one point, the
intersection of the lines of action of the two forces, having zero
torque. A drawing is usually sufficient to convince students that there
is an entire line along which the torque is zero.

A2L Item 066

Goal: Hone the vector nature of velocity.

Source: UMPERG-ctqpe142

A
child is standing at the rim of a rotating disk holding a rock. The
disk rotates without friction. The rock is thrown in the RADIAL
direction at the instant shown, which of the indicated paths most nearly
represents the path of the rock as seen from above the disk?

  1. path (1)
  2. path (2)
  3. path (3)
  4. path (4)
  5. path (5)
  6. cannot be determined

Commentary:

Answer

(4) is the correct path if the rock is thrown radially.

Background

Once thrown the components of the velocity of the rock lying in a
horizontal plane are constant so the rock will have a path which is a
straight line.

Questions to Reveal Student Reasoning

Identify a coordinate frame. What are the components of the velocity
vector immediately after the rock is thrown?

What is the radial component of the velocity if the rock follows path
(2)?

Is it possible to throw the rock in such a way that the rock follows
path (5)?

Suggestions

This item should be compared to 63.

A2L Item 063

Goal: Understanding the first law.

Source: UMPERG-ctqpe120

A
child is standing at the rim of a rotating disk holding a rock. The
disk rotates without friction. If the rock is dropped at the instant
shown, which of the indicated paths most nearly represents the path of
the rock as seen from above the disk?

  1. path (1)
  2. path (2)
  3. path (3)
  4. path (4)
  5. path (5)
  6. cannot be determined

Commentary:

Answer

(2) is the correct path if the rock is simply dropped. Some students
selecting answer (3) may be viewing the rock from the child’s
perspective. Some students indicating choice (5) may interpret this
path as ‘straight down’.

Background

This question is similar to others which seek to reveal student
perceptions about path persistence. It is a slightly different context
from the purely horizontal case of a ball rolling on a horizontal
surface around an semicircular section of hoop.

Questions to Reveal Student Reasoning

What path would the child see?

What is the velocity of the rock just before it is dropped? just after?

What would the path of the rock have been if the child continued to hold
it?

Suggestions

There are a variety of demonstrations that can be done as followup to
this question. It is important that students perceive the similarity
between the demonstration context and the problem situation.

A2L Item 060

Goal: Hone the vector nature of force and identify all the forces.

Source: UMPERG

A small ball is released from rest at position A and rolls down a
vertical circular track under the influence of gravity as depicted
below.

When the ball reaches position B, which of the indicated directions most
nearly corresponds to the direction of the net force on the ball?

Enter (9) if the direction cannot be determined.

Commentary:

Answer

(9) The net force is the sum of the forces acting on the ball. If the
ball rolls along the track there is a normal force, a friction force and
a gravitational force being exerted on the ball. Although a best answer
can be determined it would require a good understanding of dynamics,
energy, and circular motion to achieve and we assume the student is
addressing this question before all these elements are in place. [The
actual answer is (2) but few students are able to appreciate that
without much thought.]

Background

To become adept at identifying forces, students should consider a wide
array of situations, even if the situations are too complex for them to
fully analyze. To determine the direction of the net force students
need to be able to judge the relative sizes of forces.

Questions to Reveal Student Reasoning

What forces are being exerted on the ball? What are the directions of
these forces? What are the relative sizes of the different forces?

Suggestions

Consider a block sliding down an incline at 450? How does
the block on an incline compare to the ball on the curved track? What
are some similarities and differences?