Tarzan (m =40 kg) tries to cross a river by swinging from a vine. The vine is 10 m long, and he know that the vine has a breaking strength of 1140 N. What is the maximum speed?

Question

Tarzan (m =40 kg) tries to cross a river by swinging from a vine. The vine is 10 m long, and he knows that the vine has a breaking strength of 1140 N. What is the maximum speed that will be obtained at the bottom of the swing?

Answer 1

We can use conservation of energy to determine the maximum speed Tarzan can reach without breaking the vine.

At the highest point of the swing, all of Tarzan's gravitational potential energy is converted to kinetic energy, so we have:

mgh = (1/2)mv^2

where m is Tarzan's mass, g is the acceleration due to gravity, h is the maximum height Tarzan reaches, and v is his maximum speed.

The maximum height Tarzan reaches is half the length of the vine, or 5 m. The breaking strength of the vine is given by:

F = mg + T

where F is the breaking strength, T is the tension in the vine, and g is the acceleration due to gravity. At the bottom of the swing, the tension in the vine is equal to the centripetal force, which is given by:

T = mv^2 / r

where r is the length of the vine.

Substituting for T in the equation for the breaking strength and solving for v, we get:

F = mg + mv^2 / r

v = sqrt((Fr - mgr) / m)

Substituting the given values, we get:

v = sqrt((1140 N * 10 m - 40 kg * 9.81 m/s^2 * 5 m) / 40 kg) = 5.95 m/s

Therefore, the maximum speed Tarzan can reach without breaking the vine is 5.95 m/s.