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