A road slopes upward so that it climbs 1.0m for each 12m ofdistance along the ro

Question

A road slopes upward so that it climbs 1.0m for each 12m ofdistance along the road. A car whose weight is 10kN moves upthe road at a constant speed of 24m/s. Find the minimum powerrequired by the engine to maintain this speed up the incline. Thank you A road slopes upward so that it climbs 1.0m for each 12m ofdistance along the road. A car whose weight is 10kN moves upthe road at a constant speed of 24m/s. Find the minimum powerrequired by the engine to maintain this speed up the incline. Thank you

Explanation / Answer

The angle made by the slope is
tan = (1/12) or = tan-1(1/12) = 4.7o The forces acting on the car in the x and y directionsare Fx = w * sin ------------(1) and Fy = n + (-w * cos) =0 or n = w * cos ------------(2) From equation (1) we get m * ax = mg * sin or ax = g * sin where g = 9.8 m/s2 The time required for the car to climb up the slope is t = (v/ax) = (v/g * sin) The kinetic energy of the car as it climbs up the slopeis K = (1/2)mv2 where m = (w/g),w = 10 kN = 10 * 103 N The minimum power required by the engine to maintain thisspeed up the incline is P = (K/t) Thank you where m = (w/g),w = 10 kN = 10 * 103 N The minimum power required by the engine to maintain thisspeed up the incline is P = (K/t) Thank you

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