You are watching people on a new carnival ride. The ride begins with a car and a

Question

You are watching people on a new carnival ride. The ride begins with a car and a rider (150 kg combined) at the top of a curved track. At the bottom of the track is a strong but lightweight horizontal spring whose other end is fixed in a concrete wall. The car slides down the track on a very good lightweight rollers ending up moving horizontally when it crashes into the spring, sticks to it, and oscillates at a rate of 1 repetition every T=2.0 seconds. Just after the collision, you notice that the spring's maximum compression is d=12 ft . You decide to calculate the starting height of the car based on your observations.

Please answer in ft, thank you!

Explanation / Answer

m = 150 Kg
Max compression, d = 12 ft = 3.66 m
Let the starting height of the car = h
f = 1/2 Hz
w = 2**f
w = sqrt(k/m)
Substituing Values,
2**(1/2) = sqrt(k/150)
k = 1479 N/m

Initial PotentialEnergy = Spring Potential Energy at max compression.

Using Energy Conservation,
m*g*h = 1/2*kx^2
150 * 9.8 * h = 1/2 * 1479 * 3.66^2
h = 6.74 m
h = 22.11 ft

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