Why Should the Power Output Be 47.7 Horsepowers?

[davedave]

A 2400 pound car ascends a 10 degree slope at 30 miles per hour. If the overall efficiency is 70 percent, the power output at 70 percent efficiency is 47.7 horsepowers.

By the formula, Power=(force)(velocity) with 1 horsepower=550 ft*lb/s , the power output at 70% efficiency is 23.38 horsepowers.

Can someone explain why it should be 47.7 horsepowers?

 

[Doc Al]

Power = (force)(velocity) will give you the power you need to move the car. You have to find the engine power that will produce the needed power considering that only 70% is useful power. (You took 70% of the power you need, not 70% of the engine power.)

 

[thomate1]

The reason why the power output should be 47.7 horsepowers is because the overall efficiency of the car's engine is taken into consideration. This means that only 70% of the energy produced by the engine is actually being used to move the car up the slope. The remaining 30% is lost due to factors such as friction and heat. Therefore, in order to produce a power output of 23.38 horsepowers at 70% efficiency, the actual power output of the engine would need to be 47.7 horsepowers. This takes into account the energy lost and the fact that only 70% of the engine's power is being used to move the car.