Why Should the Power Output Be 47.7 Horsepowers?

AI Thread Summary
The discussion centers on calculating the necessary power output for a 2400-pound car ascending a 10-degree slope at 30 miles per hour, emphasizing the importance of efficiency. The calculations indicate that to achieve the required power output of 23.38 horsepowers at 70% efficiency, the engine must produce 47.7 horsepowers to account for the loss in efficiency. The formula used is Power = (force)(velocity), with 1 horsepower equating to 550 ft*lb/s. The key point is that the 70% efficiency applies to the engine's output rather than the total power needed. Understanding this distinction is crucial for accurate power calculations in automotive applications.
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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?
 
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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.)
 
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