A car of mass 2000 kg tows another car of mass 1000 kg along a level road. The r

Question

A car of mass 2000 kg tows another car of mass 1000 kg along a level road. The resistance to motion of the cars is 0-5 N per kg. If the maximum speed of the cars is 72 kmh-1 show that the power output of the towing car is 30kW. The cars travel up a hill of sin , find their maximum speed. Find the tension in the tow rope at the instant when the speed is 5 ms-1 and the power output of the towing car is unchanged. If the tow rope breaks, when travelling at 36 kmh-1 up the hill, how far will the towed car travel before it stops without the use of brakes.

Explanation / Answer

vel = 72 km/hr = 20 m/s total resistance applied = 0.5*(2000+1000) = 1500N power required to overcome the resistance is = F.Vel = 1500 * 20 = 30 kW ? = sin-1 (1/20) = 2.86deg force to overcome gravity is mg sin? = 3000(1/12) =250 N the new resistance will be 1500*cos? = 1498.12N net force = 1498.12 + 250 = 1748.5 N Power = F.vel vel = 30000/1748.5 = 17.16m/s = 61.76 km/hr

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