Answer to Question #175409 in Physics for Caynat

Question

A person is crossing a canyon by swinging on a vine, as shown in the given figure. The person has a mass of 90kg and the vine he is using is 15m long from where it connects to the tree to the person's center of mass. At the instant he is at the lowest point of the swing, so the vine is going straight up from his hands, the person is moving at 10m/s. At that instant, what is the tension force in the vine?

Answer 1

Find the weight of the person:

$$W=mg$$

Find the centripetal force:

$$F_c=m\frac{v^2}{R}$$

Find the tension:

$$T=m\bigg(g+\frac{v^2}{R}\bigg)=1482\text{ N}.$$