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catagory: Mechanics question: A man and a bicycle have a total mass of 100 kg. He is cycling at a constant 8m/s up a hill that makes a 4 degree angle with the horizontal direction. What power must the rider expend against gravitational forces?

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The idea here is to utilize the formula P = F*v where P is the power output, F is the force, v is the velocity and * is the so called "dot" or "inner product" of the vectors F and v. In other words (1) P = |F||v|cos(a) Where a is the angle between F and v. In this case the angle is 94 degrees because F is down (gravity force) and the incline is 4 degrees above horizontal. OK so let plug all this stuff in. We get P = |mg||v| cos(94) =100kg X 9.8m/s^2 X 8m/s X cos(94) = -546.9 J/s Note: The minus sign means that energy is being expended by the cyclist. *********************** * * * P = -546.9 W * * * *********************** P.S. I traveled in N.Z. in 1981 and loved every minute of it! A great country and I was treated wonderfully by the citizens! :-)