What Is Tarzan's Maximum Tolerable Speed When Swinging on a Vine?

[jordanb23]

i have one question that i need help on

Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (Fig. 5-41). If his arms are capable of exerting a force of 2000 N on the rope, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 70 kg and the vine is 4.8 m long.

i diont know how to start and what formulas to use
can someone please help me

 

[andrevdh]

Welcome to PhysicsForums Jordan. Hope we can help you with some of your physics problems.

Tarzan will swing along a circular path if he hangs onto the vine. His speed will increase towards the bottom and will be a maximum at the lowest point. Motion in a circle requires that a centripetal force be exerted on Tarzan. Now according to Newton's third law if he exerts a 2000 N pulling force on the vine (he needs to pull himself up on the vine) the vine will exert a force of similar magnitude on him. This force is the centripetal force that will help him to swing along a circular path. Do you now how the centripetal force will be related to his speed? Or his centripetal acceleration?

 

[kyle8921]

To start, we can use the equation for centripetal force, which is Fc = mv^2/r, where Fc is the centripetal force, m is the mass of the object, v is the velocity, and r is the radius of the circular motion. In this case, Tarzan's arms are exerting the centripetal force on the vine, so we can set Fc equal to 2000 N. We also know his mass is 70 kg, and the radius of the circular motion is half the length of the vine, so r = 2.4 m.

Plugging in these values, we can rearrange the equation to solve for v: v = √(Fc*r/m). Substituting in our values, we get v = √(2000 N * 2.4 m / 70 kg) = 11.4 m/s. This is the maximum speed Tarzan can tolerate at the lowest point of his swing without losing his grip on the vine.

Remember, this is just the maximum speed. Tarzan can choose to swing at a lower speed, but if he goes any faster than 11.4 m/s, his arms will not be able to hold on to the vine and he will fall. I hope this helps!