Conservation of Energy Review

A 60 kg boulder (on Earth) falls 50 m to the ground below.

Tip: Draw a diagram with the ME, PE, KE, height, and velocity at all relevant locations.

A 60 kg boulder (on Earth) falls 50 m to the ground below.

What is its gravitational potential energy just before it falls?

GPE = mgh = (60 kg)(9.8 m/s²)(50 m) = 29,400 J

A 60 kg boulder (on Earth) falls 50 m to the ground below.

What is its kinetic energy just before it falls?

Before it falls its velocity is 0 m/s, which means its KE = 0 J.

A 60 kg boulder (on Earth) falls 50 m to the ground below.

What is its mechanical energy just before it falls?

GPE = 29,400 J

KE = 0 J

ME = PE + KE = 29,400 J + 0 J = 29,400 J

A 60 kg boulder (on Earth) falls 50 m to the ground below.

What is its mechanical energy just as it hits the ground?

Mechanical Energy is the same at every point on this boulder's journey, so ME = 29,400 J.

A 60 kg boulder (on Earth) falls 50 m to the ground below.

What is its gravitational potential energy just as it hits the ground?

At ground level, the height is zero, which means GPE = 0 J

A 60 kg boulder (on Earth) falls 50 m to the ground below.

What is its kinetic energy just as it hits the ground?

ME = 29,000 J

PE = 0 J

KE = ME - PE = 29,400 J - 0 J = 29,400 J

A 60 kg boulder (on Earth) falls 50 m to the ground below.

What is its velocity just as it hits the ground?

Rearrange the KE formula:  $KE=\frac{1}{2}mv^2$  becomes  $v=\sqrt{\frac{2KE}{m}}$  

A 60 kg boulder (on Earth) falls 50 m to the ground below.

What is its gravitational potential energy when it has fallen to a height of 30 meters above the ground?

GPE = mgh = (60 kg)(9.8 m/s²)(30 m) = 17,640 J

A 60 kg boulder (on Earth) falls 50 m to the ground below.

What is its kinetic energy when it has fallen to a height of 30 meters above the ground?

ME = 29,400 J

PE = 17,640 J

KE = ME - PE = 29,400 J - 17,640 J = 11,760 J

A 60 kg boulder (on Earth) falls 50 m to the ground below.

What is its kinetic energy when its traveling at a velocity of 28 m/s?

A 60 kg boulder (on Earth) falls 50 m to the ground below.

What is its potential energy when its traveling at a velocity of 28 m/s?

ME = 29,400 J

KE = 23,520 J

PE = ME - KE = 29,400 J - 23,520 J = 5,880 J