Kinetic EnergyKinetic Energy

Origin of WorkOrigin of Work

Work describes a process.Work describes a process. Where does work come from, and go to?Where does work come from, and go to?

The ability to do work can come from our bodies, The ability to do work can come from our bodies, electricity, chemicals, nuclear reactions, and motion.electricity, chemicals, nuclear reactions, and motion.

Energy measures the state of an object, and its ability Energy measures the state of an object, and its ability to do work.to do work.

Energy of MotionEnergy of Motion

Consider the work done on Consider the work done on an object with constant an object with constant acceleration in a straight acceleration in a straight line.line.

The distance is related to the The distance is related to the acceleration.acceleration.

madFdW

22

2

2

1

2

2

mvdd

vmW

d

va

F=ma

d

adv 2

The work done becomes kinetic energy: (1/2) mv2

Changing EnergyChanging Energy

211 )2/1( mvK

The definition of kinetic The definition of kinetic energy applies to all objects.energy applies to all objects.

• If an object speeds up it If an object speeds up it gains kinetic energy.gains kinetic energy.

• If an object slows down it If an object slows down it loses kinetic energy.loses kinetic energy.

This matches the work done This matches the work done on or by an object.on or by an object.

Work done on the ball

v2v1

222 )2/1( mvK

233 )2/1( mvK 2

44 )2/1( mvK

Work done by the ball

v4v3

Work-Energy PrincipleWork-Energy Principle

The change in kinetic energy is due to net work done The change in kinetic energy is due to net work done on the object.on the object.

• WWnetnet = = KK22 – – KK11 = = KK

• The sign of work is positive when energy is addedThe sign of work is positive when energy is added

Using Kinetic EnergyUsing Kinetic Energy

A man lets the 300 kg piano A man lets the 300 kg piano pick up speed from 2.0 m/s pick up speed from 2.0 m/s to 4.0 m/s over 3.0 m. What to 4.0 m/s over 3.0 m. What work is done on the piano?work is done on the piano?

• The initial kinetic energy is The initial kinetic energy is KK11 = (0.5)(300 kg)(2.0 m/s) = (0.5)(300 kg)(2.0 m/s)22

= 600 J.= 600 J.

• The final kinetic energy is The final kinetic energy is KK22 = (0.5)(300 kg)(4.0 m/s) = (0.5)(300 kg)(4.0 m/s)22

= 2400 J.= 2400 J.

• The work done on the piano The work done on the piano is 1800 J.is 1800 J.

mg

v1

v2

x

Limits of Kinetic EnergyLimits of Kinetic Energy

At very high speed the work-energy principle fails.At very high speed the work-energy principle fails.• Nothing goes faster than the speed of lightNothing goes faster than the speed of light• Kinetic energy can continue to increaseKinetic energy can continue to increase• Contradiction – energy increases but not speedContradiction – energy increases but not speed

At speeds close to the speed of light we use At speeds close to the speed of light we use Einstein’s special relativity.Einstein’s special relativity.

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