Question

A 300 kg piano needs to be moved to the other side of the room. The maximum static frictional force is equal to 90 N and the kinetic frictional force is equal to 70 N. Calculate the acceleration of the piano for an applied force of 100 N.

Answer 1

Answer:

a = 0.1 m/s²

Explanation:

• If the maximum static frictional force is 90 N, this means that any applied force that will overcome this force, will cause the piano to slide, so kinetic frictional force applies.
• Under these conditions, the net force in the horizontal direction is just the difference between the applied force (which is larger that the static friction force) and the kinetic frictional force, as follows:

       $F_{net} = F_{app} -F_{frk} = 100 N - 70 N = 30 N (1)$

• By the same token, according Newton's 2nd Law, this force is just equal to the product of the mass of the piano, times the acceleration, as follows:

       $F_{net} = m* a = 300 Kg * a = 30 N (2)$

• Solving for a:

        $a = \frac{F_{net}}{m} = \frac{30 N}{300kg} = 0.1 m/s2 (3)$