Jonathan is riding a bicycle and encounters a hill of height 5.70 m. At the base

Question

Jonathan is riding a bicycle and encounters a hill of height 5.70 m. At the base of the hill, he is traveling at 4.00 m/s. When he reaches the top of the hill, he is traveling at 2.00 m/s. Jonathan and his bicycle together have a mass of 85.6 kg. Ignore friction in the bicycle mechanism and between the bicycle tires and the road. (a) What is the total external work done on the system of Jonathan and the bicycle between the time he starts up the hill and the time he reaches the top? __________J ??? (b) What is the change in potential energy stored in Jonathan's body during this process? __________J ???? (c) How much work does Jonathan do on the bicycle pedals within the Jonathan

Explanation / Answer

(a) there is only one external force - gravitational. And it acts only on "down". So the work done by the gravitational force is: W=F*h=mgh=4781. 6 J (b) change in potential energy is mgh=85.6*9.8*5.7=4781.6 J (c) Jonhatan pushes the peadls to overcome gravitational field.to compute that we need to find a total energy change. at base, he has only kinetic energy of mv^2=85.6*4^2/2=684.8 J at the tom of the hill he ha kinetic and potential energy; mu^2/2+mgh=4952.8 J --> total work is the diff between two energies: W=4952.8-684.8=4268 J

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