Question

A person places a cup of coffee on the roof of his car while he dashes back into the house for a forgotten item. When he returns to the car, he hops in and takes off with the coffee cup still on the roof.

(a) If the coefficient of static friction between the coffee cup and the roof of the car is 0.24, what is the maximum acceleration the car can have without causing the cup to slide?
(b) What is the smallest amount of time in which the person canaccelerate the car from rest to 13 m/s andstill keep the coffee cup on the roof?

Answer 1

(a) The acceleration is 2.35 m/s^2.

(b) The time is 5.53 s.

Step-by-step explanation:

coefficient of friction = 0.24

(a) The acceleration of the car is

`a =\mu g\\\\a = 0.24 *9.8\\\\a = 2.35 m/s^2`

(b) initial velocity, u =0, final velocity, v = 13 m/s

Let the time is t.

Use first equation of motion

v = u + a t

13 = 0 + 2.35 x t

t = 5.53 seconds