Work and Energy

© 2007

The Ninja, a roller coaster at Six Flags over Georgia, has a height of 122 ft and a speed of 52 mi/h. The potential energy due to its height changes into kinetic energy of motion.

Objectives: After completing this module, you should be able to:

Define kinetic energy and potential energy, along with the appropriate units in each system.

Describe the relationship between work and kinetic energy, and apply the WORK-ENERGY THEOREM.

Define and apply the concept of POWER, along with the appropriate units.

EnergyEnergy

EnergyEnergy is anything that can be is anything that can be converted into work; i.e., anything converted into work; i.e., anything that can exert a force through a that can exert a force through a distancedistance.

Energy is the capability for doing Energy is the capability for doing work; the ability to cause change.work; the ability to cause change.

Potential Energy

Potential Energy:Potential Energy: Ability to do work Ability to do work by virtue of position or conditionby virtue of position or condition.

A stretched bowA stretched bowA suspended weightA suspended weight

Example Problem: What is the potential energy of a 50-kg person in a skyscraper if he is 480 m above the street below?

Gravitational Potential Gravitational Potential EnergyEnergy

What is the P.E. of a 50-kg person at a height of 480 m?

PE = mgh = (50 kg)(9.8 m/s2)(480 m)

PE = 235 kJPE = 235 kJ

Kinetic Energy

Kinetic Energy: Ability to do work Kinetic Energy: Ability to do work by virtue of motion. (Mass with by virtue of motion. (Mass with velocity)velocity)

KE = ½ mvKE = ½ mv22

Examples of Kinetic EnergyWhat is the kinetic energy of a 5-g What is the kinetic energy of a 5-g

bullet traveling at 200 m/s?bullet traveling at 200 m/s?

What is the kinetic energy of a What is the kinetic energy of a 1000-kg car traveling at 14.1 m/s? 1000-kg car traveling at 14.1 m/s?

5 g5 g

200 200 m/sm/s

KE = 100 JKE = 100 J

KE = 99405 J

KE = 99405 J

2 21 12 2 (1000 kg)(14.1 m/s)K mv

Work and Kinetic EnergyA resultant force changes the velocity A resultant force changes the velocity

of an object and does work on that of an object and does work on that object.object.

m

vo

m

vfx

F F

( ) ;Work Fx ma x

2 21 102 2fWork mv mv

a = vf2 – vi

2

2x

Note: “x” = Δd

The Work-Energy TheoremWork is Work is equal to the equal to the change in change in ½mv½mv22

If we define kinetic energy as ½mvIf we define kinetic energy as ½mv22 then we can state a very important then we can state a very important

physical principle:physical principle:

The Work-Energy Theorem: The work The Work-Energy Theorem: The work done by a resultant force is equal to done by a resultant force is equal to the change in kinetic energy that it the change in kinetic energy that it produces.produces.

2 21 102 2fWork mv mv

Example 1: A 20-g projectile strikes a mud bank, penetrating a distance of 6 cm before stopping. Find the stopping force F if the entrance velocity is 80 m/s.

x

F = ?F = ?

80 80 m/sm/s

6 cm6 cmWork = ½Work = ½ mvmvff

2 2 - ½- ½ mvmvoo

22

0

F x = - F x = - ½½ mvmvoo22

FF (0.06 m) cos 180 (0.06 m) cos 18000 = - = - ½½ (0.02 kg)(80 (0.02 kg)(80 m/s)m/s)22

FF (0.06 m)(-1) = -64 J (0.06 m)(-1) = -64 J F = 1067 NF = 1067 N

Work to stop bullet = change in K.E. for Work to stop bullet = change in K.E. for bulletbullet

Example 2: A bus slams on brakes to avoid an accident. The tread marks of the tires are 80 m long. If k = 0.7, what was the speed before applying brakes?

8080 mm ff

Work = KE

Example 3: A 100-kg cheetah moves from rest to 30 m/s in 4 s. What is the power?

WorkP

t2 21 1

02 2fWork mv mv

2 21 12 2 (100 kg)(30 m/s)

4 sfmv

Pt

m = 100 kg

Power Consumed: P = 1.22 kW

Power Consumed: P = 1.22 kW