Question

If the coefficient of static friction between the coffee cup and the roof of the car is 0.20, what is the maximum acceleration the car can have without causing the cup to slide

Answer 1

a = 1.962 m/s²

Step-by-step explanation:

The frictional force applied on the car can be given by the following formula:

`friction = f = \mu R\\`

where,

f = frictional force = ma (according to Newton's Second Law)

μ = coefficient of friction = 0.2

R = Normal Reaction = Weight of car = mg

Therefore, equation becomes:

`ma = \mu mg\\a = \mu g\\`

where,

a = maximum acceleration = ?

μ = coefficient of friction = 0.2

g = acceleration due to gravity = 9.81 m/s²

Therefore,

`a = (0.2)(9.81\ m/s^(2))\\`

a = 1.962 m/s²