Tag Archives: Friction

A2L Item 035

Goal: Interpreting strobe diagrams in conjunction with verbal information.

Source: UMPERG

Below is shown a strobe diagram indicating the position of four objects
at successive time intervals. The objects move from left to right.

Each of the objects shown experiences a constant friction force as they
slide across the floor. Which of the objects definitely experiences a
force in addition to sliding friction?

Object A only
Object B only
Object C only
Object D only
Objects A and B
Objects B and C
Objects A and C
None of the above
Cannot be determined

Commentary:

Answers

(8); Object (C) slows down and this could be due to a sliding friction force acting to the left. Given that there is a friction force, the objects moving with constant velocity (B and D) must have an additional force. Likewise (A), which accelerates duting the first part of its motion, must have an additional force to the right.

A2L Item 031

Goal: Hone the vector nature of force and interrelate model and procedure forces.

Source: UMPERG

A marble rolls on to a piece of felt and slows down.

Indicate the direction that most nearly corresponds to the direction of
the force that the marble exerts on the felt. If none of the directions
are appropriate, or if the answer cannot be determined, respond (9).

Commentary:

Answer

(3) The force the felt exerts on the marble is up (normal force) and to
the left (friction force). Newton’s third law tells us that the force
the marble exerts on the felt must be down and to the right. Students
may focus on the normal force alone (4) or the friction force alone (2).
These are not two forces, but the components of a single force.
Students also find it difficult to extract some information from the
dynamical statement “slows down” and integrate this with the familiar
normal force.

Background

This presents an interesting twist to students. The friction force is
usually formulated in terms of a moving object and a fixed surface.
Students may not know for sure whether there is a friction force on the
felt – the felt is not moving. The analysis on the marble is reasonably
straightforward. Newton’s third law can be used to determine the force
on the felt if the force cannot be determined from the situation
directly.

Questions to Reveal Student Reasoning

Question students about how they got their answer. Did they use the
force laws that they learned previously? Did they use Newton’s second
or third laws?

Suggestions

Instead of a marble consider a sliding block and see if students think
differently – some students will have difficulty thinking about friction
with a rolling object.

A2L Item 029

Goal: Analyze the role of internal and external forces and the difference between static and kinetic friction.

Source: UMPERG

A person sits in an office chair with small wheels that swivel. The
person claims she can move the chair across the room without touching
anything but the chair, simply by kicking her legs outward. This claim:

Is consistent with Newton’s laws and can be done.
Is consistent with Newton’s laws but cannot be done.
Is not consistent with Newton’s laws and, therefore, cannot be done.
Is not consistent with Newton’s laws but nevertheless can be done.
It is not possible to determine the correctness of the claim.

Commentary:

Answer

(1); the process is possible because sudden impulse due to internal
forces can exceed the static friction limit. By rapidly extending legs,
alternated by slow retraction, the chair can be moved. Students are
often aware of this but find it difficult to explain in terms of forces
and dynamics.

A2L Item 028

Goal: Reasoning using the 2nd law.

Source: UMPERG

A tow truck (2,000kg) pushing a car (1000kg) experiences an average
friction force of 13,000N while accelerating from rest to a final
velocity of 36 mi/hr (16 m/s). The air and the road exert an average
resistive force of 1,000N on the car. What force does the car exert on
the tow truck?

1,000N
2,000N
4,000N
5,000N
6,000N
12,000N
14,000N
None of the above
Cannot be determined

Commentary:

Answer

(4) The net force on the car and tow truck is 12,000N (13,000N –
1,000N). The acceleration is 4m/s2. The magnitude of the force between
the two vehicles is 5,000N.

Background

Answers are not as important as approach. What did students do to
understand the physical situation? Did they draw pictures. Did they
draw a free-body diagram.

Questions to Reveal Student Reasoning

Ask a couple of students to describe how they approached the problem.
Ask them to describe the steps they took without getting into
mathematical details. For example, did they draw a free-body diagram?
What forces did they consider? What system did they analyze?

Suggestions

After a couple of descriptions of how to approach solving the problem,
work through the problem with help from the class.

A2L Item 024

Goal: Reason and evaluate statements about a real-world situation.

Source: UMPERG

At the scene of an accident the car causing the crash left skid marks of
a length D. The accident reconstruction team did a test and found that a
police cruiser traveling at the speed limit produces skid marks of
length d < D. Which of the following statements is valid?

Since D > d the car must have been traveling over the speed limit.
One cannot conclude that the car was speeding because the test failed
to take reaction time into account.
One cannot conclude that the car was speeding because the test failed
to take the mass of the car into account.
One cannot conclude that the car was speeding because the test failed
to take into account possible differences in the coefficient of friction
for different tires.
Two of the above statements are valid.
None of the above statements is valid.
It cannot be determined if any of the statements is valid.

Commentary:

Answer

(4) is valid assuming that the usual kinetic friction model is
applicable. Some students may think that (3) is valid and indicate (3)
or (5). All of the others are definitely invalid. Since (1) is
invalid, (7) is also invalid.

Background

This question seeks to encourage students to reason and analyze the
situation. It offers the opportunity to engage the students in a
discussion of the meaning of validity as well as the physics underlying
the various assertions.

Questions to Reveal Student Reasoning

How would reaction time influence the skid marks?

Suppose the car had several people inside. Would that have affected the
skid marks?

Suppose the test had been made with the same model car as the one in the
accident. Would that make the test more valid?

Suggestions

Allow students to form small groups according to their views and let
them present their arguments to the class. Have student ‘consultants’
suggest appropriate tests to determine if the car was speeding.

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?

0N
2N
5N
10N
15N
20N
32N
None of the above
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.

A2L Item 009

Goal: Relate friction, velocity, and time.

Source: UMPERG

A cart rolls across a table two meters in length. Half of the length of
the table is covered with felt which slows the cart at a constant rate.
Where should the felt be placed so that the cart crosses the table in
the least amount of time?

On the first half of the table
Centered on the table
On the second half of the table
It doesn’t matter where the felt is placed
None of the above
Cannot be determined

Commentary:

Answer

The
felt should be placed on the second half of the table. After the cart
rolls across the felt it will travel at a lower speed. To minimize the
time to cross the table one must minimize the time the cart spends at
the lower speed. The graph to the right illustrates the point for the
two extreme cases: felt on first half (gray curve) and felt on second
half (black curve). The velocity vs. time graph for the case where the
felt is on the second half of the table is above the velocity vs. time
graph for all other possibilities. Answer (3) is the best choice.

Background

Students should have some experience using the concepts of velocity and
acceleration to solve kinematics problems and analyze graphs. The
question students need to answer is what configuration will permit the
cart to travel at a higher speed for the longest period of time (or the
lowest speed for the shortest period of time). A graph provides support
for a conceptual argument.

Issues to consider: (1) Can students reason and analyze a situation
involving constant acceleration. (2) Do students try to solve the
problem using algebraic methods? (2) Can students use graphical methods
and conceptual reasoning? (3) Can students verbalize the central idea —
an object will travel a certain distance in less time if its speed is
higher?

Questions to Reveal Student Thinking

Where is the cart moving the fastest? … the slowest?

What does a graph of the velocity vs. time look like?

How do you determine when the cart has reached the end of the table from
a graph of velocity vs. time?

Suggestions

Try some limiting cases. If the piece of felt were small (say 10 cm)
but slowed the cart from 1 to .8 m/s on a 3m table. Approximately how
long would the trip take if the felt were placed at the beginning of the
table?…at the end of the table?

A2L Item 007

Goal: Linking acceleration to changes in velocity.

Source: UMPERG

A marble rolls onto a piece of felt that is 30 cm in length. At 20 cm
the speed of the marble is half of its initial value. Which of the
following is true? Assume that the acceleration is constant on the felt.

The marble will come to rest on the felt.
The marble will go past the end of the felt.
What will happen cannot be determined.

Commentary:

Answer

(1) The marble will come to rest on the felt. A graph of velocity vs. time is helpful for analyzing this problem. The distance traveled while slowing down to half its initial speed (i.e., the first 20 cm) is three times the additional distance (i.e., the distance beyond 20 cm) the marble will roll before coming to rest. This can be seen by comparing the areas for
these two different time periods. The marble will come to rest at approximately 26.7 cm.

Background

Students should have some experience using the concept of acceleration to solve kinematics problems and analyze graphs. The answer is less important than how students represent the problem and how they approach solving the problem.

Issues to consider:
(1) Do students only solve the problem using algebraic methods? (2) To what extent do students use other approaches? (3) Do students use graphical methods involving areas? (4) Do theycompare average speeds for the two periods (i.e., the period covering the first 20 cm and the remaining period of time before the marble comes to rest)? (5) Do they compare the actual speeds of the marble at each instant of time for the two time periods (the ratio is usually greater than or equal to 2/1 at each corresponding time, as shown in the accompanying graph). (6) Even if the students use algebraic methods, do they employ a strategy or do they do so mindlessly?

Questions to Reveal Student Thinking

Ask students to consider the following context (which they are familiar with and is algebraically simple): an object is dropped from rest. How fast is it moving after one second? … after two seconds? …after three seconds? How far has it traveled after one second? …after two seconds?…after three seconds? What is the relationship between velocity and position? Why is the relationship not linear?

Suggestions

If students do not use a graph to solve the problem, ask them to draw a velocity vs. time graph for the situation and then use the graph to solve the problem.

A demonstration is possible.