Question

tarzan plans to cross a gorge by swinging in an arc from a hanging vine. if his arms are capable of exerting a force of 1400N on nthe vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80kg, and the vine is 5.5m long

Answer 1

To solve this problem it is necessary to use three key concepts. The first of these is the Centripetal Force which is in the upward direction and would be described as

$F_c = \frac{mv^2}{r}$

Where,

m= mass

v= Velocity

r = Radius

The second is the voltage generated which is given by 1400N. Finally the third is the force generated by the weight and that would be described by Newton's second law as

F =mg

Where,

m = Mass

g = Acceleration gravity

F = 80*9.8

F = 784N

For balance to exist, the sum of Force must be equal to the Centripetal Force, therefore

$\sum F = F_c$

$T - mg = \frac{mv^2}{r}$

Replacing we have

$1400 - 784 = \frac{(80kg)v^2}{5,5}$

$v^2 = \frac{ 616*5.5}{80}$

$v = \sqrt{42.35}$

$v=6.5m/s$

Therefore the maximum speed he can tolerate at the lowest point of his swing is 6.5m/s