A person places a cup of coffee on the roof of her car while shedashes back into

Question

A person places a cup of coffee on the roof of her car while shedashes back into the house for a forgotten item. When she returnsto the car, she hops in and takes off with the coffee cup still onthe roof. (a) If the coefficient of static frictionbetween the coffee cup and the roof of the car is 0.22, what is the maximum acceleration the car canhave without causing the cup to slide? Ignore the effects of airresistance.
1 m/s2
(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?
2 s (a) If the coefficient of static frictionbetween the coffee cup and the roof of the car is 0.22, what is the maximum acceleration the car canhave without causing the cup to slide? Ignore the effects of airresistance.
1 m/s2
(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?
2 s

Explanation / Answer

Draw the force diagram. Since there is no acceleration in the y direction, N=m*g There is acceleration in the x direction. fs=ma fs=us*N=us*m*g So, us*m*g=m*a us*g=a a=.22*9.8=2.156 m/s^2 b) Given a=2.156 m/s^2, v0=0, vf=13 m/s, find t Use vf=v0+a*t 13=0+2.156*t t=6.0297 s

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