fessor drives off with his car (mass 840 kg), but forgot to take his coffee mug (mass 0.41 kg) off the roof. The coefficient of static friction between the mug and the roof is 1.1, and the coefficient of kinetic friction is 0.4. What is the maximum acceleration of the car, so the mug does not slide off

Acceleration = 4.42m/s^2

Explanation:

As the mug is not sliding on the car roof, there must be static friction between the car and the mug. The maximum limit of static friction that can act is given by:

Kmg

Where I is coefficient of static friction between car roof and mug

m = mass of mug

g = acceleration due to gravity

Acceleration of the car = Kmg

Acceleration = 1.1 * 0.41 * 9.8 = 4.42m/s

10.791 m/s^2

Explanation:

Solution:

- 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 = k*m*g

- Where, 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,

(m*a = k*m*g)

a = k*g

- Therefore max. a = 1.1*g = 1.1*9.81 = 10.791 m/s^2