Please show me your work for the question below. You should get an answer of 192

Question

Please show me your work for the question below. You should get an answer of 192 N/M but I am unsure how to do it. We normally do a chart which I also showed below for reference. I do not remember the equations exactly and am trying to prepare for a test. Please Help!

- A Pinball Plunger is pulled back 0.20 meters, to launch a ball with a mass of 0.050 KG. At the instant the plunger is 3/4 released (still 0.05m compressed), the ball has already reached a speed of 12m/s. What is the spring constant of the plunger?

Height -0.2 M -0.05 X? 0.2? 0.05? Velocity ______ 12m/s Potential Energy Kinetic Energy Spring Energy Total

Explanation / Answer

Potential energy of the spring, PE = (1/2)*k*x^2 = 0.5*k*0.0.20^2

Now, kinetic energy of the ball, KE = (1/2)*m*v^2 = 0.5*0.050*12^2

Now, apply energy conservation -

PE = KE

=> 0.5*k*0.0.20^2 = 0.5*0.050*12^2

=> k = (0.050*12^2) / (0.20^2) = 180 N/m

So, according the calculations, spring constant of the spring, k = 180 N/m

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