Tarzan stands on a branch, petrified with fear as a leopard approaches. Fortunately, Jane is on a branch of the same height in a nearby tree, holding a 25m long vine of negligible mass attached directly above the point midway between her and Tarzan. Jane grasps the vine and steps off her branch with negligible initial velocity. How soon does she reach Tarzan? Find an expression for the maximum tension in the vine in terms of Jane's weight mg and the maximum angle the vine makes with the vertical.
The problem can be modeled as a simple pendulum problem:
The period of this simple harmonic oscillator is:
The time it takes Jane to reach Tarzan is a half a period, therefore:
The tension in the vine is maximum when Jane is at the top bottom position, the force balance there gives:
On the other hand, the speed at this position can be calculated using the energy balance:
Replacing in the expression for Tmax:
Tarzan stands on a branch, petrified with fear as a leopard approaches. Fortunately, Jane is on...
Tarzan stands on a branch, petrified with fear as a leopard approaches. Fortunately, Jane is on a branch of the same height in a nearby tree, holding a 25m long vine of a negligible mass attached directly above the point midway between her and Tarzan. Jane grasps the vine and steps off her branch with a negligible initial velocity. How soon does she reach Tarzan? Find an expression for the maximum tension in the vine in terms of Jane’s weight...
Chapter: Oscillations Some useful equations are: x = Acos (ex+) v = wÅ 4, = 04 E=kł/2 = m = k/m erg/L = gLII ==2x/T 2 1. 4. Two identical mass-springs are displaced different amounts from equilibrium & then released at different times. Which characteristic values are the same for both systems? A. Periods B. Amplitudes C. Phases D. Forces What happens to the period of a pendulum if its mass is doubled? A. Period doubles B. Period is halved...