Ch 6. Work and Energy

FsW J joule 1 mN 1

sFW cos

Example 1 Suitcase-on-Wheels

Find work done if force is 45.0-N, angle is 50.0 degrees, and displacement is 75.0 m.

m 0.750.50cosN 0.45

sFW cos

J 2170

2

6.1 Work Done by a Constant Force

Example 3 Accelerating a Crate

A truck accelerating at +1.50 m/s2. Massof crate is 120-kg. Displacement is 65 m. What is total work done on crate by all the forces acting on it?

Angle between displacement and normal force is 90 degrees.

Angle between displacement and weight is 90 degrees.

090cos sFWAngle between displacement and friction force is 0 degrees.

J102.1m 650cosN180 4W N180sm5.1kg 120 2 maf s

s

F

When multiple forces are acting:

smasFW

3

Work-Energy Theorem & Kinetic Energy

2212

2122

21

ofof mvmvvvmasmW

axvv of 222 2221

of vvax

KINETIC ENERGY

Kinetic energy KE of mass m traveling with speed v

221KE mv

WORK-ENERGY THEOREM

When a net external force does work on an object, the kinetic energy of the object changes according to

2212

f21

of KEKE omvmvW

4

Work-Energy Theorem & Kinetic EnergyExample 4 Deep Space 1

Mass of space probe is 474-kg and initial velocity is 275 m/s. A 56.0-mN force acts on the probe through a displacement of 2.42×109m, what is its final speed?

2212

f21W omvmv sF cosW

m1042.20cosN105.60 9-2

2212

f21 sm275kg 474kg 474 v

sm805fv kfmgF 25sinnet force

Example: Down-hill Skier

s

5

6.3 Gravitational Potential Energy

sFW cos

fo hhmgW gravity

Example 7 Gymnast on a Trampoline

Gymnast leaves trampoline at initial height of 1.20-m; reaches max height of 4.80 m. What was the initial speed of the gymnast?

2212

f21W omvmv

fo hhmgW gravity 221

ofo mvhhmg

foo hhgv 2

sm40.8m 80.4m 20.1sm80.92 2 ov

DEFINITION OF GRAVITATIONAL POTENTIAL ENERGY

mghPE J joule 1 mN 1 Units

6

Conservative Forcework done independent of path between initial & final positions

no work done moving in a closed path

fo hhmgW gravity

fo hh fo hhmgW gravity

7

Nonconservative Force

Example = Friction

sfsfsFW kk 180coscos

Total work = conservative (Wc) + Nonconservative (Wnc)

ncc WWW

KEKEKE of WPEPEPE fogravity foc mghmghWW

ncc WWW

ncW PEKE

WORK-ENERGY THEOREM

PEKE ncW

Conservation of Mechanical Energy

initalfinal EE

Mechanical Energy E = KE + PE

If there is NO non-conservative force

0 PEKE ncW

8

Conservation of Mechanical Energy

Example 8 Daredevil Motorcyclist

Motorcyclist leaps across canyon drives horizontally at 38.0 m/s. Find the speed with which the cycle strikes the ground on the other side.

of EE

2212

21

ooff mvmghmvmgh

2212

21

ooff vghvgh

22 ofof vhhgv

22 sm0.38m0.35sm8.92 fv

sm2.46

9

WORK-ENERGY THEOREM

of EE ncW 2

212

21

ooffnc mvmghmvmghW

Example 11 Fireworks

The nonconservative force generated by the burning propellant does 425 J of work. What is the final speed of the 200gm rocket.

2212

21

ofofnc mvmvmghmghW

2

21

2

kg 20.0

m 0.29sm80.9kg 20.0J 425

fv

221

fofnc mvhhmgW

sm61fv

10

6.7 PowerPower = rate at which work is done

tWP

TimeWork

(W)watt sjoule

Timeenergyin Change

P

watts745.7 secondpoundsfoot 550 horsepower 1

vFP

6.8 Conservation of Energy

Energy can neither be created not destroyed. Only converted from one form to another.

6.9 Work Done by a Variable Force

sFW cosConstant Force

Variable Force

2211 coscos sFsFW