1.) A single-car loop-the-loop ride is launched by means of a giant spring (k=30

Question

1.) A single-car loop-the-loop ride is launched by means of a
giant spring (k=30 kN/m). The car ( 900kg) is
placed at rest against the spring which has been
compressed by a distance, . When released, the spring
propels the car into a frictionless vertical circular track
of radius7.0 m.
a.) Using the methods of Chapter 8, find an algebraic expression (that is without any
numerical values for the quantities) for the smallest that can be if the car is to stay
on the track. (In Section 6-5, your book examines a loop-the-loop bicycle stunt using
Newton

A single-car loop-the-loop ride is launched by means of a giant spring (k=30 kN/m). The car ( 900kg) is placed at rest against the spring which has been compressed by a distance, . When released, the spring propels the car into a frictionless vertical circular track of radius7.0 m. Using the methods of Chapter 8, find an algebraic expression (that is without any numerical values for the quantities) for the smallest that can be if the car is to stay on the track. (In Section 6-5, your book examines a loop-the-loop bicycle stunt using Newton's 2nd Law. You may want to review this example.) b) Find a numerical value for d.

Explanation / Answer

By energy Conservation 1/mu^2=mg2r+1/2mv^2 u=speed of body at lowest point v= speed of body at highest point u^2-v^2=4rg to just complete the circle Normat at higest point must be zero Hence mg=mv^2/r u^2-4rg=rg u^2=5rg Now 1/2kx^2=1/mu^2 x^2=5mrg/k putting the values we get x=3.2m

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