# A stunt man whose mass is 70 kg swings from the end ofa 4.0 m long rope along thearc of a vertical circle. Assuming that he starts from rest whenthe rope is horizontal, find the tensions in the rope that are required to make him follow his circular path at each of the following points. (a) at the beginning of his motion N (b) at a height of 1.5 m above the bottom of the circular arc N (c) at the bottom of the arc N

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A stunt man whose mass is 70 kg swings from the end ofa 4.0 m long rope along thearc of a vertical circle. Assuming that he starts from rest whenthe rope is horizontal, find the tensions in the rope that are required to make him follow his circular path at each of the following points.
(a) at the beginning of his motion N
(b) at a height of 1.5 m above the bottom of the circular arc N
(c) at the bottom of the arc N

2021-04-27
m = 70 kg, L = 4.0 m,
(a) at the beginning of his motion T=0
b) h = 1.5 m
$$\displaystyle{m}{g}{L}={m}{g}{h}+{m}\frac{{v}^{{2}}}{{2}}$$
so $$\displaystyle{m}{v}^{{2}}={2}{m}{g{{\left({L}-{h}\right)}}}$$
$$\displaystyle{T}-{m}{g}{\cos{\theta}}={\frac{{{m}{v}^{{2}}}}{{{L}}}}$$ where $$\displaystyle{\cos{\theta}}={\frac{{{L}-{h}}}{{{L}}}}$$
$$\displaystyle\therefore{T}={m}{g}{\frac{{{L}-{h}}}{{{L}}}}+{2}{m}{g}{\frac{{{L}-{h}}}{{{L}}}}={3}{m}{g}{\frac{{{1}-{h}}}{{{L}}}}={1286}\ {N}$$
c) let h=0 in $$\displaystyle{T}={3}{m}{g}{\frac{{{1}-{h}}}{{{L}}}}$$
So T=3mg=2058 N

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