Problem 6.73 You are asked to design spring bumpers for the walls of a parking g

Question

Problem 6.73

You are asked to design spring bumpers for the walls of a parking garage. A freely rolling 1200 kgcar moving at 0.62 m/s is to compress the spring no more than 7.5×102 m before stopping.

Part A

What should be the force constant of the spring? Assume that the spring has negligible mass.

Express your answer using two significant figures.

It is not 8.2*10^5 and must be in N/m

Problem 6.73

You are asked to design spring bumpers for the walls of a parking garage. A freely rolling 1200 kgcar moving at 0.62 m/s is to compress the spring no more than 7.5×102 m before stopping.

Part A

What should be the force constant of the spring? Assume that the spring has negligible mass.

Express your answer using two significant figures.

Explanation / Answer

m = 1200 kg
v = 0.62 m/s
x = 7.5 * 10^-2 m
All the kinetic energy of the car need to be converted to spring potential energy to stop the car effectively,
So,
Using Energy conservation,
Initial Kinetic Energy = Final Spring potential Energy
1/2 * m * v^2 = 1/2 * k * x^2
1200 * 0.62^2 = k * (7.5 * 10^-2)^2
K = 82005.33N/m

In two sig fig,
K = 8.2 * 10^4 N/m

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