Problem 7.77 Bumper guards. You are asked to design spring bumpers for the walls

Question

Problem 7.77 Bumper guards. You are asked to design spring bumpers for the walls of a parking garage. A freely rolling 1200 kg car moving at 0.750 m/s is to compress the spring no more than 7.00 cm before stopping.

Part A What should be the force constant of the spring?

Part B What is the maximum amount of energy that gets stored in it?

Part C If the springs that are actually delivered have the proper force constant but can become compressed by only 5.00 cm , what is the maximum speed of the given car for which they will provide adequate protection?

Explanation / Answer

A.  use the conservation law of energy:
All kinetic energy transfer to potential energy of the spring

KEi + Ui = KEf + Uf

KEf = 0, Ui = 0
0.5*m*v^2 = 0.5*k*x^2

with x =< 7.00*10^-2
k = m*v^2/x^2 = 1200*0.75^2/0.07^2

k >= 137755.102 N/m

B. Maximum amount of energy stored when KEf = 0 and all the energy will be potential energy.

U = 0.5*k*x^2 = 0.5*137755.102*0.07^2 = 337.5 J

C. now max compression is = 0.05 m

max speed will be

0.5*k*x^2 = 0.5*m*v^2

v = (137755.102*0.05^2/1200)^0.5

v = 0.535 m/sec

Please comment below if you have any doubt.

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