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Calculating Power and Work Done Against Gravity, Slides of Physics
Formulas and calculations for determining the work done by gravity and the power expended by a hiker climbing a hill. Topics include the relationship between mass, gravity, distance, and work, as well as the concept of power and its measurement in watts.
Typology: Slides
2012/2013
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Power
Uphill
You (
m
= 60 kg) hike up a 30° hill with a net height
increase (
h
= 50 m). What work is done by gravity?
-^
Distance
d
h
/ sin
^
= (50 m) / sin 30° = 100 m
-^
Work done by gravity
W
mg d
sin
^
^
(60 kg)(9.8 m/s2)(50 m) =
30 kJ Gravity doesnegative workon the hiker
d^
= 100 m
-mg
The Watt
The rate of work is called power.
The SI unit of power is the watt (W).
-^
1 watt = 1 J/s = 1 N m/s = 1 kg m
2
/ s
(^3)
Energy can be measured in watt-seconds = joules.
W^ t
P
t P
E
Average Power
The walker had an averagepower output based on thework compared to the time.^ •
P
W
/^
t
•^
P
= 30 kJ / 100 s = 300 W
The runner generated thesame work in one quarter ofthe time.•
P
= 30 kJ / 25 s = 1200 W
When running seems harder,it isn’t work, it’s power.
Power Plants
Electrical power is measuredin watts.•
60 W light bulb
-^
1000 MW power plant
Energy used is measured inpower times time.
If electricity costs $ 0.083 perkWh, how much does it costto leave a 1500 W floodlampon all year?•
Energy used is
W
Pt
(1500 W)(3.2 x 10
7 s) =
4.8 x 10
10
J
•^
Cost is
(4.8 x 10
10
W s) *
(1 kW / 1000 W) (1 h / 3600 s)(0.083 / kWh)= $1,
Force and Velocity
Power is work per time.•
Work is force acting over adistance
-^
Distance per time is velocity
Power is force times velocity.
r^ t
F
t
r
F
W t
P
next
v
F
P
^
F
v