Question

If the coefficient of static friction between the coffee cup and the roof of the car is 0.26, what is the maximum acceleration the car can have without causing the cup to slide? Ignore the effects of air resistance.

Answer 1

Answer:

$2.5506 m/s^2$

Explanation:

When the cup slides, the car acceleration would be equal to the acceleration caused by the friction of the roof on the cup, which generated by normal force, which equals to gravity force on the cup.

So the equation of friction force is as the following:

$F_f = \muN = \muP = \mu mg$

where m is the mass of the cup, g = 9.81 m/s2 is the gravitational acceleration, and $\mu = 0.26$ is the friction coefficient

Newton's 2nd law for when the cup slides

$a = F_f/m$

$a = \frac{\mu mg}{m} = \mu g = 0.26 * 9.81 = 2.5506 m/s^2$