A makeshift swing is constructed by making a loop in one end of a rope and tying

Question

A makeshift swing is constructed by making a loop in one end of a rope and tying the other end to a tree limb. A child is sitting in the loop with the rope hanging vertically when the child's father pulls on the child with a horizontal force and displaces the child to one side. Just before the child is released from rest, the rope makes an angle of 17o with the vertical and the tension in the rope is 220 N. (a) How much does the child weigh? (b) What is the magnitude of the (horizontal) force of the father on the child just before the child is released? (c) If the maximum horizontal force the father can exert on the child is 81 N, what is the maximum angle with the vertical the rope can make while the father is pulling horizontally?

Explanation / Answer

a) = 21.44 kg

Hyp: 220 N
Opp: 64.32 N
Adj: 210.38 N

Theta: 17°
Right: 90°
Opposite: 73°

210.38 N = Ft [when child is vertical...]

Ft = m*g
m = 210.38/9.81
m = 21.44 kg

b) horizontal force =64.32N

c) Max angle = 16.061°

Opp: 81
Hyp: 220
Adj: 211.41

Theta: 16.061°
Right: 90°
Opposite: 73.939°

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