Gigantic pinball machine: A pinball (solid sphere of mass= 0.2 kg, outer radius=

Question

Gigantic pinball machine:
A pinball (solid sphere of mass=0.2 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.

only need solution for part c.

c.) When the pinball is 2.5 m above its initial location (on the way up), find its linear and angular speeds.
A pinball (solid sphere of mass=0.2 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.

Explanation / Answer

a)the initial energy stored in the spring is

E = (1/2)kd^2

where k = 50 N/m and d = 0.8 m

b)let h be the maximum height

we know that

(1/2)kd^2 = m x g x h

or E = m x g x h

or h = (E/m x g)

where m = 0.2 kg and g = 9.8 m/s^2

c)the speed of the ball is

v1 = (2gh1)^1/2

where h1 = 2.5 m

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