The Law of Conservation of Energy states: Conservation of Energy Energy cannot be created or destroyed Energy can be transformed from one form to another.

• The Law of Conservation of Energy states:

Conservation of Energy

• Energy cannot be created or destroyed

• Energy can be transformed from one form to another.

• In other words, the Law of Conservation of Energy states that the amount of energy existing before an event is equivalent to the amount of energy after the event.

• When only gravitational forces are present…


KE1 + PE1 = KE2 + PE2

energy in objectbefore rise/fall

energy in objectafter rise/fall

=

• These equations can be used to solve a variety of problems…

22

212

1 2

1

2

1ygmvmygmvm

• An object with a mass of 15.0 kg is being held at a height of 40.0 meters above the ground. If the object is dropped, how much kinetic energy will it have when it reaches a height of 10.0 meters?


• An object with a mass of 4.00 kg is dropped from the roof of a building. If the object hits the ground with a speed of 16.5 m/s, how tall is the building?


• The Law of Conservation of Energy can also be used to calculate an objects velocity…

If a 3.00 kg rock is thrown downward from a height of 20.0 meters with an initial velocity of 16.0 m/s, how fast will it be traveling when it hits the ground?


• When only spring (elastic) forces are present…


KE1 + PE1 = KE2 + PE2

• These equations can be used to solve a variety of problems…

energy in object and spring while

stretched/compressed

=energy in object and spring after release

22

22

21

21 2

1

2

1

2

1

2

1xkvmxkvm

• A toy dart gun uses a small spring to shoot little plastic darts. The mass of a single dart is 0.100 kg and the spring has a spring constant of 250 N/m. When the dart is loaded into the gun, the spring is compressed 0.06 meters. When the spring is released, the dart is fired. How fast will the dart be traveling when it is fired from the gun?


• Often times the sum of an objects potential energy and kinetic energy is referred to as the object's total mechanical energy.


TME = KE + PE

• Find the TME of a 7.00 kg falling object that is currently 40.0 meters above the ground and is falling at a speed of 15.0 m/s.

• Of course, KE and PE are not the only types of energy in the world, and there are other forces out there doing work that are not related to gravity or springs.


• For example, say you were roller skating at a steady speed when someone came up and pushed you for a short distance so that you were moving faster than before

The force applied to you caused your speed to increase, which gave you more KE (and TME). If we don't consider friction, the amount of work done is equivalent to the energy gained.

• Keeping with the roller skating example…


You decide that you’re moving too fast, so you decide to put on the brakes.

When you put on the brakes, friction does work in the opposite direction that you are moving.

This causes you to slow down and decreases the amount of KE (and TME) that you have.

Where did the energy go?

• The energy was transformed into thermal energy and a little sound energy.


• In fact, the amount of energy that is transformed to thermal energy and sound energy is approximately equal to the amount of work done by friction.

• We’re getting a little ahead of ourselves here…

• In general, the amount of work done by an external forces (other than gravity or elastic/spring) is equal to the amount of TME that is gained or lost.


TME1 + WEXT = TME2

KE1 + PE1 + WEXT = KE2 + PE2

where WEXT is work done by friction, a push, a pull, etc.

• If WEXT is positive, then TME will increase.

• If WEXT is negative, then TME will decrease.

• Examples


1. You are holding a box at shoulder-height. Due to its mass and position, the box has 1500 J of

TME. You then push the box straight up with a force of 1000 N so that it is 0.25 meters higher. What is the box’s new amount of TME?

• Examples


2. A car is traveling along wet pavement with 320,000 J of TME. The car slams on its brakes and slides for 30.0 meters. During the slide, the force of friction was 8,000 N. What was the car’s TME at the end of the slide?

• Examples


3. In another situation, a 1,000 kg car is traveling at a speed of 25.0 m/s. How far will the car travel before coming to a complete stop if the driver applies an average braking force of 7,500 N?

• Examples


4. A child with a mass of 17.0 kg is going down a slide that 3.5 m tall. If the child reaches a speed of 2.50 m/s by the time he/she gets to the bottom, how many Joules of thermal energy were generated?

The Law of Conservation of Energy states: Conservation of Energy Energy cannot be created or destroyed Energy can be transformed from one form to another.

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