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=11 ft . You decide to calculate the starting height of the car based on your observations.

Explanation / Answer

using energy conservation

T = 2 sec

w = 2pi/T

w = sqrt(k/m)

sqrt(k/m) =2pi/T

k/m = 4pi^2/T^2

k = m*4pi^2/T^2

k = 1480.44 N/m

11f = 3.3528m

mgh = kx^2/2

h = kx^2/2mg

h = 5.66 m = 18.56955 ft

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