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Chapter 5 Work, Power, and Energy

5.1 Objectives

- Understand the concept of work.
- Be able to perform work calculations.

Work

work a force applied through a distance (not

a displacement!)

Work is a scalar.

force (F)

f

distance (d)

W (Fcosf)d

James Joule studied the relationship

between work and thermal energy

units Nm J (joules)

Work

- positive () work is done if f lt 90o
- zero (0) work if f 90o
- negative (-) work if f gt 90o
- net work SW (SFcosf)d

Work Problem

A 107 N golf bag is dragged 125 meters (at

constant speed) with a force of 8.5 N. The

force is oriented 32o above the horizontal. How

much work is done by the golfer? By friction?

By gravity? By the normal force?

W Fcosfd

5.4 Power

power the rate at which work is done (work

time)

units J/s W (watts)

W in an equation is work W as units are Watts 746

W 1 hp

James Watt inventor of the steam engine

Power Problem

A weightlifter lifts a 275 kg mass from the floor

to a height of 1.92 m in only 1.48 seconds. How

much work is done by the weightlifter? How much

power is used?

5.2 Objectives

- Understand the concept of kinetic energy (KE) and

the closely-related work-energy theorem - Solve KE and work-energy theorem problems.

Kinetic Energy

A moving object is capable of doing work if it

runs into something elseit has stored energy.

kinetic energy the energy held by a moving

object (due to relative motion)

F ma

KE ½mv2

Fd mad

Why?

W mad

force

W ma½at2

distance

W ½ma2t2

W ½mv2

KE Problem

- A major league baseball has a mass of 0.145 kg.

How much KE does a baseball have if it is thrown

at 44.4 m/s (100 mph)?

Work-Energy Theorem

If the sum of all the work done on an object (by

all the forces) is calculated, then the SW will

equal the change in kinetic energy of the object.

SW SF d DKE KEf - KEi

SW SF d ½ mDv2 therefore, d Dv2

Work-Energy Theorem Problem

- Brakes apply FFK ( SF)
- How much SW is done to stop a 1450 kg car

traveling at 20 m/s and 40 m/s? 45 mph 80 mph - What is the stopping distance in each case if the

brakes apply 7.5 kN of force?

Stopping Distance Chart

5.2 Objectives

- Understand the concept of potential energy,

particularly gravitational potential energy

(GPE). - Be able to solve gravitational potential energy

problems.

Potential Energy

Something is required to do work. That

something is called energy.

potential energy stored energy (due to the

presence of a force)

gravitational potential energy (GPE)

W Fdcos f

W FWhcos(0o) FWh

height (h)

W mgh

GPE mgh

units Nm J

GPE Problem

A 43 kg television is moved from the bottom to

the top of a flight of stairs that is 2.62 m

high. The stairs angle upward at 45o. How much

work is done? How much GPE does the TV have at

the top of the stairs?

5.3 Objectives

- Understand the law of conservation of energy.
- Use the law of conservation of energy to solve

assorted dynamics problems.

Conservation of Energy

Mechanical energy (ME) is the sum of KE and all

PE.

law of conservation of energy energy is

conserved when converted from one form to another

(the total ME remains constant).

SPEi SKEi SPEf SKEf

Why?

vf2 vi2 2ad

vf2 2gh

GPE

KE ½mv2

KE ½m2gh

height (h)

KE mgh

( GPE mgh)

KE ?

Conservation of Energy Problem

With what speed must a ball be thrown

directly upward to reach a final height of 28

meters?

Conservation of Energy Problem

A roller coaster traveling at 16 m/s drops down a

steep incline that is 25 meters high and then

moves up another incline. What is the height of

the second incline if the roller coaster is

moving at 12 m/s at its crest? Assume the effect

of friction is negligible.

website

Bullseye Lab

h1

razor

h2

What is the equation to find the range? dx ? It

is an extremely simple equation!

dx ?

Objectives

- Be able to identify simple machines.
- Be able to explain how simple machines make doing

work easier. - Be able to calculate the ideal mechanical

advantage (IMA), actual mechanical (AMA)

advantage, input work (WI), output work (WO), and

efficiency (e) of a simple machine.

Simple Machines

4 kinds lever, inclined plane, pulley, wheel and

axle

Simple machines generally make doing work easier

by reducing applied force (but distance is

increased).

input work WA FAdA

output work WO FOdO

If no friction WA WO If friction is present

WA gt WO

Simple Machines

mechanical advantage (MA) factor by which input

force is multiplied by the machine

ideal

actual

efficiency ratio of output work to input work

(indicates amount of friction in machine)