Power and Efficiency
6.4 p 262
Power is the rate at which work is done or the rate at which energy is transferred.
Note:
P = power (W) … 1 W = 1 J/s
E = energy transferred (J)
W = work done (J)
Δt = time interval ﴾s﴿
1 hp = 745.7 W
Model Problem p 263
1. A crane is capable of doing 1.50 x 105 J of work in 10.0 s. What is the power of the crane in watts?
P = ?
W = 1.50 x 105 J
Δt = 10.0 s
2. A cyclist and her mountain bike have a combined mass of 60.0 kg. She is able to cycle up a hill that changes her altitude by 4.00 x 102 m in 1.00 min. (Assume that friction is negligible.)
a. How much work does she do against gravity in climbing the hill?
b. How much power is she able to generate?
W = ΔEg
W = Eg2 – Eg1 Eg1 = 0
W = mgΔh
W = (60.0 kg)(9.81 m/s2)(4.00 x 102 m)
W = 2.35 x 105 J
Complete Practice Problems
‐ p 266 #41‐43
Efficiency
p 268
Transforming energy from one form to another always involves some “loss” of useful energy. Often the lost energy is transformed in to heat. The efficiency of a machine or device describes the extent to which it converts input energy or work into the intended type of output energy or work.
Efficiency is the ratio of useful energy or work output to the total energy or work input.
Model Problem p 269
A model rocket engine contains explosives storing 3.50 x 103 J of chemical potential energy. The stored chemical energy is transformed into gravitational potential energy at the top of the rocket’s flight path. Calculate how efficiently the rocket transforms stored chemical energy into gravitational potential energy if the 0.500 kg rocket is propelled to a height of 1.00 x 102 m.
Ei = 3.50 x 103 J
Eo = Eg = mgΔh
m = 0.500 kg
g = 9.81 m/s2
Δh = 1.00 x 102 m
Eg = mgΔh = ﴾0.500 kg﴿﴾9.81 m/s2)( 1.00 x 102 m)
Eg = 490.5 J
Complete Practice Problems
‐ p 270 #44‐50