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 0.7 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?
12.25 J

b.) Find the maximum height the pinball rolls to (above its initial location.)
12.5m

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

Given Data Mass of the sphere, m = 0.1 kg Radius of the sphere, r = 0.2 m Spring compression, x = 0.7 m The ball is at a height of , h = 2.5 m Moment of inertia of solid sphere, I = 2/5 m r2                                                          Solution: By law of conservation of energy m g h = 1/2 mv2 + 1/2 I2 m gh = 1/2  mv2 + 1/2 (2/5 m r2) (v/r)2 m gh = 7 /10 m v2 (9.8 m/s2 ) (2.5 m) = 7 / 10 v2 v = 5.92 m/s is the linear speed -------------------------------------------------------------------------------- Angular speed , = v /r                              = (5.92 m/s) / 0.2 m                              = 29.6 rad/s m gh = 7 /10 m v2 (9.8 m/s2 ) (2.5 m) = 7 / 10 v2 v = 5.92 m/s is the linear speed -------------------------------------------------------------------------------- Angular speed , = v /r                              = (5.92 m/s) / 0.2 m                              = 29.6 rad/s

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