Please show every step of the solution for this one question: You and your bicyc

Question

Please show every step of the solution for this one question:

You and your bicycle have combined mass 80.0 kg. When you reach the base of a bridge, you are traveling along the road at 5.00 m/s (Fig. P6.78). At the top of the bridge, you have climbed a vertical distance of 5.20 m and have slowed to 1.50 m/s. You can ignore work done by friction and any inefficiency in the bike or your legs. (a) What is the total work done on you and your bicycle when you go from the base to the top of the bridge? (b) Flow much work have you done with the force you apply to the pedals?

Explanation / Answer

(a) W= K2 -K1 = 1/2 m vf 2 - 1/2 m vi 2 = (0.5)(80)(1.52) - (0.5)(80)(52) = -910J


(b)PE = mgh = (80)(9.8)(5.20) = 4076.8 J


W = PE + KE = (4076.8 J) + (-910 J) = 3166.8 J

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