Conservation of Energy

What Is Energy?• Energy makes change

possible.

• Science definition: Energy is the ability to do work

• Measured in Joules, J. Just like work

• There are multiple different kinds of energy.

Types of Energy

Mechanical

Nonmechanical

Kinetic

Potential

Gravitational

Elastic

Energy

Kinetic Energy

• Kinetic Energy: the energy of an object due to its motion

• Kine in Greek means "to move" so all objects with kinetic energy are in motion

• Symbol KE

• Equation: mv2

Problems

1.A 7.00 kg bowling ball moves at 3.00 m/s. How much kinetic energy does the bowling ball have?

2.How fast must a 2.45 x 10-3 kg ping pong ball move in order to have the same amount of energy as the bowling ball?

Gravitational Potential Energy• Gravitational Potential Energy

is energy stored into the object's position.

• It is the object's potential to move due to gravity.

• As an object falls its energy is transferred from gravitational energy to kinetic energy.

• Symbol GPE

• GPE= mgh

Problems

3.A 70.0 kg stunt man is about to bungee jump off of a 50.0 m high bridge. What is his gravitational potential energy?

4.A 0.500 kg Jenga block has 3.00 J of gravitational potential energy stored. How high up is the Jenga block?

Elastic Potential Energy• Elastic Potential Energy is

energy stored in a spring that is compressed or stretched.

• Its the potential for that spring to return to its neutral position.

• Symbol: EPE

• 2

• k is the spring constant and is different for each individual spring. It's measured in N/m.

• x is the distance the spring is stretched or compressed.

Problems5.A spring with a spring constant of 5.2

N/m has a relaxed length of 2.45 m. It is stretched to a length of 3.57 m. What is the energy stored in the spring?

6.The staples inside a stapler are kept in place by a spring with a relaxed length of 0.115 m. If the spring constant is 51.0 N/m, how much elastic potential energy is stored in the stapler spring when it's length is 0.150 m?

Energy Transformations

7.What energy transformations occur on a roller coaster?

8.What energy transformations occur with a child swinging?

Conservation of Energy• As energy is transferred it is also conserved,

meaning that the energy before the transformation is the energy after.

• Initial Mechanical Energy = Final Mechanical Energy

• Energy is always conserved between KE, GPE, and EPE unless there is friction. Then energy is still conserved, but some of it turns to heat (thermal energy) due to friction.

Problems9.Starting from rest, a 25.0 kg child zooms

down a frictionless slide from an initial height of 3.00 m. What is her speed at the bottom of the slide?

10.A 76 kg diver drops from a board 10.0 m above the water. Find the diver's speed at 5.00 m and right when the diver hits the water.

Work- Energy Theorem

•The net work done on an object is equal to the change of the object's kinetic energy.

•Work = Change in Kinetic Energy

•W = ∆KE

Problems11.A student wearing frictionless ice skates on

a horizontal surface is pushed by a friend with a constant force of 45 N. How far must the student be pushed, starting from rest, so that her final kinetic energy is 352 J?

12.A 75 kg bobsled is pushed along a horizontal surface by two athletes. After the bobsled is pushed a distance of 4.5 m starting from rest, its speed is 6.0 m/s. Find the magnitude of the net force on the bobsled.