Coffee Mug on Car Roof A professor drives off with his car (mass 870 kg), but forgot to take his coffee mug (mass 0.47 kg) off the roof. The coefficient of static friction between the mug and the roof is 0.7, and the coefficient of kinetic friction is 0.5. What is the maximum acceleration of the car, so the mug does not slide off?

maximum acceleration is 6.86 m / s²

Explanation:

We use Newton's second law for each axis

X axis

Fr = ma

Axis y

N-W = O

N = mg

The equation for the force of friction is

fr = μ N

The maximum value of the friction force occurs with the static coefficient

fr = 0.7 0.47 9.8

fr = 3,224 N

a = fr / m

a = 3,224 / 0.47

a = 6.86 m / s²

If the vehicle exceeds this acceleration the cup begins to slide and the friction force is reduced because its efficient changes to dynamic