Abeka Physics Section 11.2 pg. 162 - 163

Question 1

Explain how the power formula is derived

Answer 1

> average acceleration is equal to change in velocity divided by corresponding change in time
physicists say that acceleration is time rate of change in velocity
similar language is used to define power: power is time rate of doing work
since power may vary with time, we often refer to average power when writing formal definition
P = W/t
where P is power (or average power), W is total work, and t is time taken to do the work

Question 2

Define power

Answer 2

> power - the time rate of doing work

Question 3

Give the units of power

Answer 3

> SI unit of power: watt (W)
1 W = 1 J/s
watt is commonly required to operate electric appliance
US customary unit of power: foot-pound per second (ft x lb/s)

Question 4

Describe horsepower

Answer 4

> although it does not belong to any system of units, horsepower (hp) is of great importance historically
before steam engine was developed, horses were used to move heavy loads
these loads ranged from dragging plows in field to pulling wagons over roads to towing barges on canals
James Watt coined term “horsepower” in late 1700s when he patented and sold his steam engines
to provide estimate of engine’s worth, Watt compared engine’s output to strong dray (or “draft”) horses common on farms where he grew up in Scotland
similar method was applied to engines used on steamboats: engine that could drive boat upriver in same time as 2 teams of 2 horses had rating of 4 hp.
although term “horsepower” is based on horse’s power, many people don’t know how horsepower is measured or how it is applied today
for instance many cars have engines with horsepower

Question 5

Describe defining work in terms of power

Answer 5

> P = W/t can be arranged as W = Pt
work (energy transfer) is power multiplied by time
example: measurement of electric energy consumption in terms of kilowatt-hours
kilowatt hour - amount of work done by one kilowatt of power over a time interval of one hour
since 1 kW is 1000 W and 1 hr. is 3600 s,
1 kW x hr. = (1000 W)(3600 s) = 3.6 x 10^6 W x s
= 3.6 x 10^6 J
if force is continuously applied to object so that object is moved at constant velocity, rate of work done on object is described by P = Fv
velocity is distance moved per second; therefore, power describes work being done by force moving some object some distance in a second

Question 6

Solve this: A car is traveling at a speed of 80. ft/s. The thrust of the driving wheels against the road is 650 lb. If power losses in the drive train are neglected, how much horsepower is the engine producing?

Answer 6

In each second, the engine exerts a force of 650 lb. at a constant 80. ft/s. The power is given by equation P = Fv Substitute to obtain
P = (650 lb)(80. ft/s)
P = 52,000 ft x lb/s
Since there are 550 ft x lb/s in 1 hp, convert:
P = 52,000 ft x lb/s ( 1 hp )

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                             550 ft x lb/s