6.4. Power http://www.ck12.org
P=F xt =(mgsintθ)(x)=mg(xtsinθ)=mght =mg
(h
t)
=mgvNote:h=xsinθ,v=ht
The average vertical speed the jogger must have isv=10m16s= 0 .62 m/s and the force required is the jogger’s weight,
mg= ( 65 .0kg)(10m/s^2 ) =650 N, thus,P=mgv=F v= (650N)( 0 .62m/s) =406 W
Horsepower
The term horsepower is often associated with automobiles. It is not uncommon for car salespeople to make a point
of including horsepower rating as a selling point. If they are trying to sell a sport car then horsepower definitely
enters the conversation. For more fuel efficient cars, a sales person is apt to make comments regarding “miles per
gallon” and then add “and it still manages” and then quote some number of horsepower. So what exactly do we
mean by the term “horsepower?”
James Watt (seeFigure6.23) is credited with the invention of the unit of horsepower. Supposedly, he created the
term in order to measure the power output of the steam ships he was marketing. He wanted a unit that anyone during
the early 19thcentury would understand. So Watt chose the given amount of work a horse could do over a given
period of time, settling on the definition that one unit of horsepower was equal to the power output of a horse lifting
550 pounds a height of one foot in one second, that is 1.00 hp = 550ft-pounds/s. In SI units, this is equivalent to 1.00
hp = 746 W.
Illustrative Example 2
The Le Mans car race lasts 24 hours. It is not uncommon during that time for a car to travel at a constant speed of
240 km/h in straight line motion while experiencing a drag force of 4600 N due to air resistance. What power, under
the given conditions above, does a race car engine develop in units of horsepower?
FIGURE 6.25
Answer:
Since the speed of the car is constant and its direction of travel unchanging, the net force on the car must be zero.
The force the engine provides, therefore, must be equal in magnitude to the drag force.
Since power can also be expressed asP=F v, the units of power are also N*m/s. Before we begin, we must
remember to convert 240 km/h to m/s: