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Learning Introductory Physics with Activities

Paul J. Emigh, Rebecka Tumblin, Kathryn Hadley, Danielle Skinner

Section 3.10 A*R*C*S

A*R*C*S 3.10.1. The Brick against the Rail.

A small brick of mass \(0.8 \mathrm{~kg}\) is positioned against a horizontal wooden railing. You pull on the rope at the \(60^o\) angle shown so that the acceleration of the brick is \(2 \mathrm{~m/s^2}\) to the left. Find the magnitudes of all forces on the brick.
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Top-down view: a brick against a horizontal railing, connected to a rope that runs down and to the left at an angle of sixty degrees.
Figure 3.10.1. A brick is pulled against a wooden railing.
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1. Analyze and Represent
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  1. Identify known and unknown quantities with both a symbol and a number.
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  2. Identify and justify any assumptions.
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  3. Choose an appropriate system and draw a-free-body diagram for the system.
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2. Calculate
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  1. Represent physics principles that will help you solve for the unknown quantities.
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  2. Determine a symbolic equation for each force in terms of known variables.
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  3. Plug numbers into your symbolic answer.
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3. Sensemake
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  1. Check the units of your symbolic answer.
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  2. Compare your numerical answers to other numerical forces with which you are familiar.
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  3. Use covariational reasoning: how should your symbolic equations depend on \(m\text{,}\) \(a\text{,}\) and \(\theta\text{?}\)
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A*R*C*S 3.10.2. The Coach vs. the Student-Athletes.

The figure below shows a top-down view of a tug-of-war between a coach (in red on the left) and two teams of “student-athletes”. The coach can pull with a force of \(1500 \mathrm{~N}\text{,}\) and the two teams together are just able to keep the rock connected to the ropes from beginning to accelerate. Determine the magnitude of the tension force provided by each of the two teams.
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Top-down view: a boulder pulled by three ropes: a leftward rope pulled by a single coach; an up and to the right rope pulled by three orange atheletes; and a down and to the right rope pulled by two blue athletes
Figure 3.10.2. A tug of war between a coach (left) and two teams of student-athletes (right).
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Hint 1.
Analyze and Represent: Sketch a free-body diagram for the situation. Think carefully about what reference frame you want to choose and break each force into components.
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Hint 2.
Calculate: Remember that your answer and work should be primarily symbolic. Choosing good symbols for both known and unknown quantities (including the angles!) can help support both your algebra and your sensemaking.
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Hint 3.
Sensemake: As part of your symbolic sensemaking (part 3c), try covariational reasoning for at least one of the three known quantities.
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References References

[1]
Tug of War image inspired by teamwork by Lucas Helle from Noun Project (CC BY 3.0)
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