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Tarzan, who weighs 688 N, swings from a cliff at the end of a vine 18 m long (Fig. 8-38). From the top of the cliff to the bottom of the swing, he descends by 3.2 m. The vine will break if the force on it exceeds 950 N. (a) Does the vine break? (b) If no, what is the greatest force on it during the swing?

Respuesta :

Answer:

Part a)

here greatest tension is less than the maximum possible tension so it will not break

Part b)

So the greatest tension in the string is given as

[tex]T = 932.6 N[/tex]

Explanation:

Part a)

When Tarzen reached to the bottom of the path then the force on the vine is maximum

so at that position we can write the force equation as

[tex]T - mg = \frac{mv^2}{L}[/tex]

now we can fine the speed of Tarzen by energy conservation

[tex]\frac{1}{2}mv^2 = mgh[/tex]

so we will have

[tex]v^2 = 2gh[/tex]

Now the tension force in the vine at this position is given as

[tex]T = mg + \frac{mv^2}{L}[/tex]

Now plug in all values in it

[tex]T = mg + \frac{m(2gh)}{L}[/tex]

[tex]T = 688 + \frac{2(3.2)}{18}(688)[/tex]

[tex]T = 932.6 N[/tex]

So here this is less than the maximum possible tension so it will not break

Part b)

So the greatest tension in the string is given as

[tex]T = 932.6 N[/tex]

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