Question

A cup of coffee on a horizontal board of a car slides forward when the driver decelerates from 45km/h to rest in 3.5s or less. However, it does not slip if it decelerates in a longer time. What is the coefficient of static friction between the cup and the board? Suppose the path and the board are horizontal.

Answer 1

Answer on Question #72158-Physics-Other

A cup of coffee on a horizontal board of a car slides forward when the driver decelerates from 45km/h to rest in 3.5s or less. However, it does not slip if it decelerates in a longer time. What is the coefficient of static friction between the cup and the board? Suppose the path and the board are horizontal.

Solution

It does not slip if the friction force is greater or equal to the pushing force:

$$F_{fr} \leq m a.$$ $$\mu m g \leq m a.$$ $$\mu g \leq a.$$

The minimum coefficient of static friction between the cup and the board is

$$\mu = \frac{a}{g} = \frac{v}{g t}$$ $$\mu = \frac{\frac{45}{3.6}}{9.8 \cdot 3.5} = 0.36.$$

Answer: 0.36.

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