19.4.10 Evaluate the solution The problem: You are helping design a stopping sys

Question

19.4.10 Evaluate the solution The problem: You are helping design a stopping system for Soapbox Derby race cars. The proposed stopper is a padded cushion that catches the car at the end of the race. The far end of the cushion, opposite the car, is attached to a spring that compresses at collision. The car's mass with driver is 60 kg, and it is traveling at 12 m/s when it first contacts the stopper; the mass of the stopper is 20 kg. The car is to stop in 2.0 m after contacting the stopper. What is the spring constant of the spring needed for this system? Proposed solution: The initial kinetic energy of the car is converted into elastic potential energy of the compressed spring when the car tops. Thus. a. Identify any errors in the solution to this problem. b. Provide a corrected solution if there are errors.

Explanation / Answer

apply KE   = Elastic potential enrgy

as   0.5 mv^2 = 0.5 kx^2

K = mv^2/x^2

where m is mass of the car

v is speed

x is distance

so

K = 60 * 12*12/2*2

K =2160 N/m

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