Note: Be careful to avoid roundoff errors in this problem. Gigantic pinball mach

Question

Note: Be careful to avoid roundoff errors in this problem.

Gigantic pinball machine:
A pinball (solid sphere of mass=0.1 kg, outer radius=0.3 m) is cocked back 0.7 m on a spring (k= 50 N/m), and fired onto the pinball machine surface, which is tilted.

a.) How much energy is stored in the spring initially?
J

b.) Find the maximum height the pinball rolls to (above its initial location.)
m

c.) When the pinball is 2.5 m above its initial location (on the way up), find its linear and angular speeds.
m/s
rad/s

Explanation / Answer

a) EPE=kx ²/2 = 50 * 0.7 ² / 2 = 12.25 J

b) EPE -> GPE
so 12.25 = mgh = 0.1*9.8*h
So h = 12.5 m

c) It's linear speed, EPE->KE+GPE
12.25 = mv ²/2+mgh
v = sqrt[2(12.25-0.1*9.8*2.5)/0.1] = 14 m/s

For it's angular speed:
v=ωR
so ω = v/R = 14 / 0.3 = 46.7rad/s

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