EBrion, CIE, CLSSYB
EBrion, CIE, CLSSYB
Power
Average Power is the rate at which work is done , and it is
obtained by dividing the work done by the time required to
perform the work
Power
The SI unit of power is the watt (W), named for the English
inventor James Watt.
The kilowatt-hour is the usual commercial unit of electrical energy.
One kilowatt-hour is the total work done in 1 hour (3600 s) when
the power is 1 kilowatt. The kilowatt-hour is a unit of work or
energy, not power
Power
In the British system, work is expressed in foot-pounds, and the
unit of power is the foot-pound per second. A larger unit called
the horsepower (hp) is used for power.
Power: Example 1
The same amount of work is done in both of these situations, but
the power (the rate at which work is done) is different.
Power
Power alternative formula
Power
Efficiency
Power: example 2
A 40-kg woman runs up a staircase 4m high in 5 s. Find her
minimum power output.
𝑊 = 𝐹𝑠
𝐹 = 𝑊𝑒𝑖𝑔ℎ𝑡 = mg
𝑠=ℎ
𝑊 = 𝑚𝑔ℎ
𝑃=
𝑃=
𝑃=
𝑊
𝑡
𝑚𝑔ℎ
𝑡
𝑚
(40𝑘𝑔)(9.81 2 )(4𝑚)
𝑠
5𝑠
𝑃 = 313.92 𝑊
Power: example 3
Each of the four jet engines on an Airbus A380 airliner develops a
thrust (a forward force on the airliner) of 322,000 N. When the
airplane is flying at 250 m/s, what horsepower does each engine
develop?
𝑃 = 𝐹𝑣
𝑚
250
𝑠
𝑃 = 32000𝑁
𝑃 = 8.05 𝑥 107 𝑊
7
𝑃 = 8.05 𝑥 10 𝑊 𝑥
𝑃 = 107,908.85 ℎ𝑝
1ℎ𝑝
746𝑊
Power: example 4
A hoist powered by a 10-kW motor is used to raise a bucket filled
with concrete and having a total mass of 500kg to a height of
80m. If the efficiency of the hoist is 80 percent, find the time
needed.
𝑃𝑜𝑢𝑡 = Eff × 𝑃𝑖𝑛
𝑃𝑜𝑢𝑡 = 80% × 10000 𝑊
𝑃𝑜𝑢𝑡 = 8,000 𝑊
𝑊
𝑃=
𝑡
𝑊
𝐹𝑠
𝑡= =
𝑃
𝑃
𝑚𝑔ℎ
𝑡=
𝑃
(500)(9.81)(80)
𝑡=
8000
𝑡 = 49.05𝑠