C. Oscillating wheel hanging on a tree Spare wheel (5 kg) is found oscillating o

Question

C. Oscillating wheel hanging on a tree Spare wheel (5 kg) is found oscillating on a tree vine. Wheel's total displacement from top to bottom of the oscillation is 3 m. C-1. The spare wheel's equilibrium position is 0.125 m from the vine's initial position. Find the vine's spring constant. Answer: N/m C-2. What is the amplitude of the oscillation? Answer: C-3. What is the period of the oscillation? Answer: sec C-4. What is the speed of the wheel when net acceleration is zero? Answer: C-5. Astronaut is making a simple pendulum clock to track time on the planet. pendulum. Astronaut wants to have the pendulum tick-tock' with a period of 1.0 m/s Using the gravitational acceleration on the planet of 5.0 m/s, find the length of the second. Answer: Inm

Explanation / Answer

given m = 5 kg

total displacement from top to bottom of osscilation , h = 3 m

C1. equilibrium position, lo = 0.125 m

let spring constant of the wine be k

then from force balance

klo = mg

k = mg/lo = 392.4 N/m

C2. amplitude of osscilation = h/2 = 1.5 m

C3. Period of osscialtion, T = 2*pi*sqroot(m/k) = 0.7092516 s

C4. speed of wheel when net acceleration is 0 is v

form conservation of energy

0.5*k*(h/2)^2 = 0.5*m*v^2

v = 13.28834 m/s

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