24 Kg
24 Kg
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A car of mass 1590 kg traveling at 24 m/s is at the foot of a hill that rises 115 m in 3.2 km?
A car of mass 1590 kg traveling at 24 m/s is at the foot of a hill that rises 115 m in 3.2 km. At the top of the hill, the speed of the car is 10 m/s. Find the average power delivered by the car's engine, neglecting any frictional losses.
Please Help!
First, in all questions like this, a drawing is a great help.
Draw a right-angled triangle ABC, angle ABC = 90°
AC = 3.2 km. = 3200 metres; BC = 115 metres.
Let angle CAB = α. Then sin(α) = 115 / 3200. [So α = 2.06° - a shallow rise.]
Now consider the physics.
The car is at the foot of the hill - and on the start of the slope.
The component of the mass of the car that is acting down the slope is m.sin(α),
where m = mass of car.
Therefore, the force acting down the slope = m.g.sin(α), where g = 9.81 m/s²
Now Power = rate of working = Work done per unit time
Work = force X distance.
Therefore, Power = = force X distance ÷ time.
But distance ÷ time = speed.
Therefore, Power = force X speed.
The force that the car has to overcome in climbing the hill,
(neglecting friction and air resistance) = m.g.sin(α).
And we know the speed of the car (we assume that it maintains a constant speed up the hill: no acceleration).
Hence, Power developed = force X speed = m.g.sin(α).v,
where v = speed of car.
End of the Physics. Now put in the numbers:
Power = 1590 X 9.81 X (115 / 3200) X 10 = 5605 Joules / sec
= 5.605 kJ / sec. = 5.605 kW, since 1 watt = 1 Joule / sec.
► Answer: 5.61 kW (to 2 dec. places) ◄
O.K.?