Question

Elvis and Noah want to move the piano in their living room. Elvis pushes from behind with a force of 400 N, and Noah pulls from the front using a rope with a force of 150 N. The piano has a mass of 225 kg, and the friction force of the floor and the piano is 100 N.

a. Determine the acceleration of the piano.
b. Find the net force acting on the piano.
c. Calculate the frictional force opposing the motion.

Answer 1

The net force acting on the piano is 450 N, resulting in an acceleration of 2 m/s². The frictional force opposing the motion is 100 N.

Determining the Acceleration and Net Force on a Piano

Elvis and Noah are trying to move a piano. To determine the acceleration of the piano, we must first calculate the net force. The net force (Fnet) is the sum of all forces acting on the piano. Elvis pushes with a force of 400 N, Noah pulls with 150 N, and the frictional force opposes the motion with 100 N.

To find the net force, we sum the forces in the direction of motion: Fnet = FElvis + FNoah - Ffriction. Substituting the given values gives us Fnet = 400 N + 150 N - 100 N = 450 N.

Now, using Newton's second law Fnet = m × a, where m is the mass of the piano and a is the acceleration, then a = Fnet / m = 450 N / 225 kg = 2 m/s2.

The frictional force opposing the motion is already provided and is 100 N.