Question

Use the law of the conservation of energy and the formulas for one-dimensional projectile motion, gravitational potential energy. and kinetic energy to solve the problems below. Neglect friction. air resistance, and other dissipative forces in all problems.

Use g = 9.8 m/s.

1. A metal ball bearing with mass 5.0 g falls out of a factory machine and drops to the concrete floor 3.0 m below. It bounces back up to its starting point. Find the changes in the bearing's potential and kinetic energies as it a) travels from the machine down to the floor, and b) travels up from the floor back to its starting point.

Answer 1

First, let’s convert the mass of the ball bearing from grams to kilograms: 5.0 g = 0.005 kg.

a)

As the ball bearing falls from the machine to the floor, its gravitational potential energy is converted into kinetic energy. The change in potential energy can be calculated using the formula for gravitational potential energy: PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object above some reference point.

In this case, the change in potential energy is ΔPE = mgh = (0.005 kg)(9.8 m/s²)(3.0 m) = 0.147 J.

Since energy is conserved, this means that the change in kinetic energy is equal to the change in potential energy: ΔKE = ΔPE = 0.147 J.

b)

As the ball bearing bounces back up from the floor to its starting point, its kinetic energy is converted back into potential energy. Since energy is conserved and there are no dissipative forces, the changes in potential and kinetic energies are the same as in part a): ΔPE = 0.147 J and ΔKE = 0.147 J