ENGR 215 ~ Dynamics
Sections 14.4
Power
• Power is the flow of energy per unit time
P
dU
dt
• Units
– Light Bulb: 100W
• 1 W = 1 Nm/s
– Car Engine: 250 Hp
• 1 Hp = 0.707 Btu/sec = 550 ft lb / sec = 746 W
Lecture Example 1: How much power can a 20
amp circuit at 120 volts supply in your home at
66% of full load? How many horsepower is that
equivalent to?
More on Power
P
dU
dt
dU  F  dr
P
dU
dt
 F
dr
dt
 Fv
v , velo city a t th e p o in t w h ich is a cted
o n b y th e fo rce, F
Efficiency
• Efficiency = Power Output / Power Input
Lecture Example 2: Determine the average
power (kW) required to accelerate a 1300-kg car
from 0 to 100 km/h in 10 seconds. Assume a
constant acceleration and the zero frictional
losses.
Also, determine the maximum power required.
Lecture Example 3: Determine power (kW)
required for a 2500-kg Ford F-250 pickup truck
to tow a 2000-kg trailer up a hill with 50 m rise
for every 1000 m of road at 60 km/h.
Also calculate your answer in horsepower.
Lecture Example 4: Trevor who weighs 150 lb
challenges your instructor who weighs 180 lb to
a bike race up a 1 km long hill with a rise of
100m for every 1000 m of road (5.74% grade).
Both your instructor and Trevor are capable of
generating 250W of power. By what distance
does you instructor lose the race? Assume the
bike weighs 22 lb and that air resistance is
negligible.
Lecture Example 4.1: How much difference in
time does a make if Trevor carries a full water
bottle (500ml = 0.5 kg) up the hill in comparison to
if he had dumped his water at the bottom of the
hill.
Lecture Example 5: A river flowing steadily at a rate of
240 m3/s is considered for hydroelectric power generation.
It is determined that a dam can be built to collect water and
release it from an elevation difference of 50 m to generate
power. Determine how much power (MW) can be
generated from this river water after the dam is built.
Lecture Example 6: The material hoist
and load have a total mass of 800 kg and
the counterweight has a mass of 150 kg.
If the upward speed of the hoist
increases uniformly from 0.5 m/s to 1.5
m/s in 1.5 s, determine the average
power generated by the motor during this
time. The motor operated with and
efficiency equal to 80%.
Solve using P=Fv.
Solve using P =ΔE/ Δ t