CK-12-Physics - Intermediate

http://www.ck12.org Chapter 6. Work and Energy

energyandpotential energy. The three on the left represent types of kinetic energy, where the word “kinetic”

means related to motion.

• lightning→moving electrical charge→electrical energy


• campfire→moving molecules→thermal energy or heat


• bullet→moving object→mechanical kinetic energy or just “kinetic energy”

The three on the right represent less obvious forms of energy, known as potential energy.

• battery→can release electrical energy→chemical potential energy


• log→can release thermal energy→chemical potential energy


• rock on hill→can release kinetic energy→gravitational potential energy

Kinetic Energy

The simplest result of work is kinetic energy. If you have a stationary object and you push it with some force over

a distance, then it is moving and thus has kinetic energy. Suppose you push a baseball of massmwith forceFover

distanced. The work done would beF×d. We know from our previous mechanics thatF=ma. If it started from

rest and accelerated from only this force, then the distance it went isd=^12 at^2 and its final velocity isv=at. This

tells us that the work done is:

W=F×d= (ma)(^12 at^2 ) =^12 m(at)^2 =^12 mv^2

This expression is true for all kinetic energy, regardless of how it was accelerated. Kinetic energy is abbreviatedKE

and is found by the standard formula:

KE=

1

2

mv^2

The units of energy are the same as for work, the Joule. 1 Joule is 1 Newton×1 meter, or more fully, since 1

Newton is kgs· 2 m, a Joule iskg·m

2

s^2.

Example 1

a. Aroldis Chapman of the Cincinnati Reds is credited with throwing the fastest baseball during a game. The ball

had a speed of 46.95 m/s and a mass of 145.0 g. What was the kinetic energy of the ball?

Answer: KE=^12 mv^2 ,KE=^12 ( 0 .145 kg)( 46 .95 m/s)^2 = 159 .8 J

b. How would the kinetic energy compare for a ball with half the mass thrown with the same speed?

Answer:The kinetic energy would be^12 as great.

c. How would the kinetic energy compare for a ball thrown with half the speed but the same mass?

Answer:The kinetic energy would be^14 as great.

Example 2

a. A race car of mass 900 kg is at rest on the starting line, then uniformly accelerates at 5 m/s^2 over a distance of

60m67.1 m. What was its change in kinetic energy?

Answer:We can solve the change in velocity from the kinematic equation:vf^2 =vi^2 + 2 a∆x.