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.

Answer 1

In question we need application of conservation of linear momentum and SHM.Here we have a spring system which is struck by a mass of 150 kg.

Let it be following from height H

It strikes spring with velocity V.

Spring undergo SHM of

amplitude=12 ft

time period =2 sec

so V will be given by.    V=Acoswt

                                     where w is natural frequency of vibration given by w=2 (pie)/T

                                                                                                                        =2(pie)/2

                                                                                                                        =(pie)

  V=Acoswt

     = 12cos(pie)*2  

    =12*1

    =12 ft/sec

This velocity is as a result of K.E. gain because of loss of potential energy

              so,

              = (1\2)*m*v

              KE. =PE.

            1/2*m*v ^2​ =​m​*g*h

            1/2*v^2​ =g*h     take g = 32.174 ft/m^2​

             h= ​2.23 feet.

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