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 q = (50 m) / sin 30 ° = 100 m Work done by gravity W = - mg d sin q = - (60 kg)(9.8 m/s2)(50 m) = - 30 kJ. d = 100 m.
d = 100 m
Gravity does negative work on the hiker
You (60 kg) walk up a 30° hill with a net height increase of 50 m at 1 m/s.
t = (50 m)/sin30°/(1/ms) =100 s
W = 30 kJ
You run up the same 30° hill with a net height increase of 50 m at 4 m/s.
t = 25 s, W = 30 kJ
But, running is harder!
The rate of work has increased by 4 times by running.
Hiker does positive work to overcome gravity
d = 100 m
The walker had an average power output based on the work compared to the time.
P = W / t
P = 30 kJ / 100 s = 300 W
The runner generated the same work in one quarter of the time.
P = 30 kJ / 25 s = 1200 W
When running seems harder, it isn’t work, it’s power.
Electrical power is measured in watts.
60 W light bulb
1000 MW power plant
Energy used is measured in power times time.
If electricity costs $ 0.083 per kWh, how much does it cost to leave a 1500 W floodlamp on all year?
Energy used is W = Pt = (1500 W)(3.2 x 107 s) = 4.8 x 1010 J
Cost is (4.8 x 1010 W s) * (1 kW / 1000 W) * (1 h / 3600 s)*(0.083 / kWh) = $1,100
Power is work per time.
Work is force acting over a distance
Distance per time is velocity
Power is force times velocity.