A car is moving on an inclined road with friction acting upon it. When it is moving up the road at a speed v the engine is working at power 3P and when it is moving down the road at v the engine is working at a power P. Find the value of P.
Incline is at θ where sin θ = 1/20 and mass of the car is 800kg and v is 12.5 m/s
Up the road: Power = Fv F = R + (800g)/20
Power = (R + 40g)*25/2 = 3P …. P = (R + 40g)*25/6
Down the road: Power = Fv F = R – (800g)/20
Power = (R - 40g)*25/2 = P
Equate the equations:
(R + 40g)*25/6 = (R – 40g)*25/2
25R + 1000g = 75R – 3000g so R = 80g
Therefore P = (80g – 40g)*25/2 = 500g = 4900W
JM
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