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=0.2 m) is cocked back 0.8 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) energy stored in the spring is U = 0.5*k*x^2 = 0.5*50*0.8*0.8 = 16 J

B) using conservation of energy

0.5*k*x^2 = m*g*H = 16

H = 16/(m*g) = 16/(0.1*9.81) = 16.3 m

C) using conservation of energy

energy stored in spring = total energy at the 2.5 m

0.5*k*x^2 = 0.5*m*v^2 +m*g*h

16 = 0.5*0.1*v^2 + (0.1*9.81*2.5)

then linear speed is v = 16.46 m/s

angular speed is w = v/r = 16.46/0.2 = 82.3 rad/s

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