You devise a wind-up car powered by a spring for trips to the grocery store. The

Question

You devise a wind-up car powered by a spring for trips to the grocery store. The car has an inertia of500kg and is 4.9m long. It should be able to accelerate from rest to 26m/s at least 50 times before the spring needs winding. The spring runs the length of the car, and a full winding compresses it to half this length.

Part A

In order to meet the acceleration requirement, what must the value of the spring constant be?

Express your answer to two significant digits and include the appropriate units.

Explanation / Answer

The energy needed = 0.5*m*v^2 per trip

hence

the total energy = 50 *0.5*m*v^2

This is supplied by the spring where E = 0.5*k*x^2

x is half the length of the car = 2.45 m
so 50 *0.5*500*26^2 < 0.5*k*2.45^2
so

k > 2.815*10^6

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