Question

A bell hanging at the top of a tower has 8,550 J of gravitational potential energy. It has a mass of 20 kg. If the bell falls to the ground so that all of its potential energy gets converted to kinetic energy, what will it's final velocity be?​

Answer 1

The gravitational potential energy (PE) of an object is given by the formula:

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 bell has a PE of 8,550 J and a mass of 20 kg. We can rearrange the above formula to solve for the height h:

h = PE/(mg)

Substituting the given values, we get:

h = 8,550 J / (20 kg x 9.81 m/s^2) ≈ 43.4 meters

This is the height from which the bell falls. When the bell falls to the ground, all of its PE is converted to kinetic energy (KE). The formula for KE is:

KE = (1/2)mv^2

where m is the mass of the object and v is its velocity.

Setting the PE equal to the KE, we get:

PE = KE

mgh = (1/2)mv^2

Simplifying and solving for v, we get:

v = √(2gh)

Substituting the values for g and h, we get:

v = √(2 x 9.81 m/s^2 x 43.4 m) ≈ 29.4 m/s

Therefore, the final velocity of the bell when it hits the ground is approximately 29.4 m/s.