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Friction

Instructions: Read each question carefully. Choose the answer that best fits the question. Short answer response questions must be responded to in complete sentences. If the question involves calculations, you must show all your math work.

1.
In the diagram shown, calculate the minimum value of friction coefficient $mu$ between the person's feet and the floor required to prevent the person from slipping. Express your answer in terms of the person's mass $M$, any quantities shown on the diagram, and fundamental constants. Assume the ball of mass $m$ is being swung in the horizontal plane.

2.
Use the information in the following scenario to answer the next two questions.

You start pushing a 2 kg sanding block, with coefficients of friction, $mu_s=0.77" and "mu_k=0.70$, against a wooden desk you are sanding. You use a normal force of 91.5N.
A.
Determine the resistive force of friction just before the start of the sanding block's movement.

B.
Once the sanding block starts moving, what is the resistive force of friction?

3.
What is minimum force required to overcome the resistive force of friction and to keep the box moving, when Ashton pushes a 53 kg wooden box up a cement incline at an $ang30deg$? The coefficients of friction of a wooden box against cement are $mu_s=0.42 and mu_k=0.36$.

4.
Use the following information to answer the next six questions.

Coefficient of friction for all-weather tread tire:
Dry road: $mu=0.7$
Wet road: $mu=0.4$
Icy road: $mu=0.1$

Mass of a typical car: 1500kg

Coefficient of friction for NASCAR tread-less tire:
Dry road: $mu=0.9$
Wet road: $mu=0.1$

Mass of a typical NASCAR:1542kg
A.
Calculate the resistive force of friction of a typical car with new tires on a dry road with an incline of $ang23deg$.

B.
Calculate the resistive force of friction of a typical car with new tires on a wet, inclined road. The incline is at $ang23deg$.

C.
Calculate the resistive force of friction of a typical car with new tires being driven up an icy road that has an incline of $23deg$.

D.
Calculate the resistive force of friction of a typical NASCAR car on a dry race track.

E.
Calculate the resistive force of friction of a typical NASCAR car on a wet race track.

F.
Based on what you learned from your calculations, explain why it is important to replace tires on the family car before the tires “go bald,” and why NASCAR races are postponed during wet weather.

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