A2L Item 050

Goal: Hone the vector nature of force.

Source: UMPERG

A thin wire is stretched horizontally between two walls. If a weight, W,
is hung on the wire, what is true about the tension, T, in the wire?

1. T < W
2. T = W
3. T > W
4. The relationship between T and W cannot be determined.

Commentary:

Answers

(3); The vertical component of the tension force exerted on the weight
must equal half the gravitational force. For a nearly horizontal wire
this means the tension must exceed the weight.

Background

The intent is to get students to use their intuitive notions of
balancing force to reason how directions of forces change the value of
forces.

Questions to Reveal Student Reasoning

How do you determine the tension force? What direction does the tension
force point? In (A) what does the tension force equal? Does it matter
what angle the strings point? Explain.

Suggestions

Have some students try to lift an object with strings straight up and at
an angle. Which is easier.

Set up a demonstration with spring scales.

A2L Item 046

Goal: Recognize appropriate free body diagram.

Source: UMPERG

A
block of mass 2 kg is at rest on the surface of a wedge that makes an
angle of 30° with the horizontal as shown. The coefficient of
static friction is 0.64 and of kinetic friction is 0.42.

Which figure below best represents the free-body diagram for the block?

6. None of the above
7. Cannot determine the free-body diagram

Commentary:

Answer

(1). The component of the gravitational force parallel to the incline
will balance the frictional force in this situation. The component of
the gravitational force perpendicular to the incline must balance the
normal force.

Background

Even in static situations students can be confused about the relative
sizes of forces.

Questions to Reveal Student Reasoning

What forces are present? What determines how big the gravitational
force is? … the normal force is? … the gravitational force is?

A2L Item 023

Goal: Develop good problem solving practices. Determining the value of procedure forces, those requiring use of the 2nd law.

Source: UMPERG

A child is walking along the sidewalk at a constant speed of 1 m/s while
pulling his dog sitting in a wagon. The dog has a mass of 30kg and the
wagon weighs 50N. If the child pulls the wagon with a force of 60N at an
angle of 30°, what is the frictional force exerted by the wagon on
the dog?

1. 0N
2. 2N
3. 5N
4. 10N
5. 15N
6. 20N
7. 32N
8. None of the above
9. Cannot be determined

Commentary:

Answer

(1) The dog is moving at a constant speed, presumably in a straight
line. The net force on the dog must be zero. Since there are no other
possible horizontal forces (if we ignore air resistance) other than the
friction force, the friction force must be zero.

Background

This problem provides students with a lot of information. The challenge
of the problem (and most real problems) is to come to an understanding
of the situation independent of the specific details. Then based on an
understanding of the situation one can attempt to address specific
questions and make use of detailed information.

Questions to Reveal Student Reasoning

Ask students to describe the situation. Ask them to describe how they
approached the problem. Did you describe all the forces? Did you draw
any free-body diagrams?

Suggestions

Have students draw a free-body diagram (drawing all possible forces) for
the dog. Have them describe the motion for the dog. Ask them to
re-answer the question.
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