what is the answer for these 3 questions ? The string in the Figure is L=119.0 c

Question

what is the answer for these 3 questions ?

The string in the Figure is L=119.0 cm long and the distance d to the fixed P is 96.4 cm. When the ball is released from rest in the position shown, it will swing along the dashed are. How fast will it be going when it reaches the lowest point in its swing? How fast will it be going when it reaches the highest point in its swing (after encounters the peg)? In a rope competition, a 66.4 kg athlete climbs a vertical distance of 4.88 m in 8.40 s. What minimum power output was used to accomplish this feat?

Explanation / Answer

As the string reaches its lowest point, its original potential energy = mgL (measured relative to the lowest point) is converted into kinetic energy. Thus,

mgL = 1/2 mv2 which gives v = (sqrt)2gL = (sqrt)[2x9.8x1.19] = 4.829 m/s

hence v = 4.829 m/s at the lowest point

At the heighest point, the total mechanical energy is shared between kinetic 1 /2mvb2 and potential mgyb. We note that yb = 2r where r = L - d = 0.226m. Energy conservation leads to

mgL = 1 /2mvb2 + mgyb whcih givesvb = sqrt[2gL - 2g(2r)],

r is not visble in the figue so put the value yourself in the last equation and get the result

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