A) what is the maximum tension in the rope? B) what is the maximum acceleration

Question

A) what is the maximum tension in the rope?

B) what is the maximum acceleration of the man?

C) what is the maximum energy stored in the rope?

A man attached to a rope jumps from a bridge. The bridge is 180 m above the water level. The natural length of the rope is 30 m, the mass of the man is 90kg. The spring constant of the rope is 1200 N/m, and the maximum elongation of the rope is delta=7.419 m. A) what is the maximum tension in the rope? B) what is the maximum acceleration of the man? C) what is the maximum energy stored in the rope?

Explanation / Answer

max elongation = 7.419 m

max tension in the rope = spring constant of the rope*max elongation

= 1200*7.419 = 8902.8

max accleration of man will be attained at lowest point of his trajectory

means at max elongation point

net force on man = T-mg

= 8902.8 - 90*9.8 = 8020.8 N

max acc = 8020.8/90 = 89.12 m/s2

max energy stored in the rope = 0.5kx2

= 0.5*1200*7.4192

= 33024.9 J

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