A person places a cup of coffee on the roof of her car while she dashes back into the house for a forgotten item. When she returns to the car, she hops in and takes off with the coffee cup still on the roof. You may want to review (Pages 156 - 163). Part A 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

The car can have a maximum acceleration of 2.55 m/s² without causing the cup to slide.

Explanation:

When the car is in motion, there are two forces acting on the cup. First force is exerted by the car on the cup in its direction of motion and it is given by newton's second law of motion:

F = ma

The second force is the force of friction between the surface of car and the cup. It is given by the formula:

f = μR

where,

R = Normal reaction = weight of cup = W = mg

Therefore,

f = μmg

So, for the cup not to slide, both these forces must be equal or the frictional force must be greater than the car's force. In the last limiting case of equal forces:

F = f

ma = μmg

a = μg

where,

a = maximum possible acceleration of the car for cup not to slide

μ = coefficient of static friction = 0.26

g = acceleration due to gravity = 9.8 m/s²

Therefore,

a = (0.26) (9.8 m/s²)

a = 2.55 m/s²