Question

Tarzan spies a 36.0 kg chimpanzee in severe danger, so he swings to the rescue. He adjusts his strong, but very light, vine so that he will first come to rest 4.20 s after beginning his swing, at which time his vine makes a 11.0 ∘ angle with the vertical.

Part A How long is Tarzan's vine, assuming that he swings at the bottom end of it?

Part B What is the frequency of Tarzan's swing?

Part C What is the amplitude (in degrees) of Tarzan's swing?

Part DJust as he passes through the lowest point in his swing, Tarzan nabs the chimp from the ground and sweeps him out of the jaws of danger. If Tarzan's mass is 65.0 kg , find the frequency of the swing with Tarzan holding onto the grateful chimp.

Part E Find the amplitude (in degrees) of the swing with Tarzan holding onto the grateful chimp.

Answer 1

a)

The total period of a pendulum is T = 2*π*√lL/g]. The first "rest" comes at half the period (period is a full back and forth swing). So

T = π*√lL/g]

L = T²g/π² = 4.2^2*9.81 / 3.14^2 = 17.55 m

b)

Frequency is 1/period, period is 17.55/2 = 8.77 s, so F = 1/ 8.77 = 0.1139 Hz

c)

Amplitude is 11.0º

d)

The frequency does not depend on mass.

e)

The energy at max amplitude is E = L*(1 - cosθ)*m*g

The energy without the chimp was E = L*(1 - cos11º)*mT*g
The enery with the chimp is E = L*(1 - cosθ)*(mT+mC)*g

Since no energy was added or taken by grabbing the chimp, these must be equal:

L*(1 - cos11º)*mT*g = L*(1 - cosθ)*(mT+mC)*g

(1 - cos11º)*mT = (1 - cosθ)*(mT+mC)

(1 - cosθ) = (1 - cos11º)*mT/(mT+mC)

cosθ = 1 - (1 - cos11º)*mT/(mT+mC)

cosθ = 1- ( 0.0183* 65/ (65+36))

θ = 8.819 degrees