A professor drives off with his car (mass 870 kg), but forgot to take his coffee mug (mass 0.37 kg) off the roof

kinetic-friction

#1

A professor drives off with his car (mass 870 kg), but forgot to take his coffee mug (mass 0.37 kg) off the roof. The coefficient of static friction between the mug and the roof is 0.9, and the coefficient of kinetic friction is 0.5. What is the maximum acceleration of the car, so the mug does not slide off?

Answer:

As the mug is not sliding on the car roof , there will be static friction between car and mug.
The maximum limit of static friction that can act is given by = kmg
here, k = coefficient of static friction between the mug and the roof
m = mass of mug
g = acc. due to gravity

So the maximum acc. of car ,a = kg (ma = kmg)
Therefore max. a = 0.9g