Work IN, Work OUT

The Work/Energy Principle

Kinetic Energy

• KE depends on mass and velocity

• Work done on an object will change KE

2

2

1mvKE

if KEKEW

Example• A 2 kilogram toy car starts from rest and

attains a velocity of 3 meters per second as it travels a distance of 4.5 meters.

– What is the car’s initial KE?0 Joules

– What is the car’s final KE?9 Joules

– How much work was done on the car?9 Joules

– What was the average force on the car?2 Newtons

Example• A 2 kilogram toy car changes its speed from 5

meters per second to 2 meters per second within 7 meters of travel.

– What is the car’s initial KE?25 Joules

– What is the car’s final KE?4 Joules

– How much work was done on the car?-21 Joules

– What was the average force on the car?-3 Newtons (friction force)

Gravitational Potential Energy

• How much energy does an object in a gravitational field have?– Strength of the field (g)– Mass of object (m)– Height in the field (h)

• GPE can be changed by changing “h”– Increase height Increases GPE– Decrease height Decrease GPE

mghPE

Example

• An model aircraft with a mass of 2.0 kilograms is flying at an altitude of 15 meters. – What is its gravitational potential energy?

294.3 Joules

– How much work needed to be done against gravity for the aircraft to reach this altitude?

294.3 Joules

Elastic (Spring) Potential Energy (PES)

• How much energy can be stored in an elastic object?

– Strength of the spring (spring constant - k)– Distance of stretch/compression (x)

2

2

1kxPES

Example• The spring in a toy dart gun has a spring constant of 50

newtons per meter. When a dart is loaded into the gun, the spring compresses 0.05 meters.

– What amount of energy is stored in the spring when it is compressed?

0.063 JoulesThe amount of work needed to compress the

spring is the SAME as the energy stored.

This is also the same amount of KE that the dart will gain when fired.

Work/Energy Principle SummaryWork/Energy Principle Summary

• Work in a mechanical system (horizontal)– Becomes KE (if speed increases)

• Work in a gravitational field (vertical)– Becomes PEg if moving upward– PEg becomes KE if allowed to fall

• Work in a spring system (horizontal or vertical)– Becomes PES if spring is stretched/compressed– PES becomes KE when the spring is released