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?
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 spring = k x^2 / 2 = 50 x 0.7^2 / 2 = 12.25 J

b) using energy conservation, '

initially it had only spring PE and finally it had only gravitational PE

using energy conservation ,

kx^2 /2 = m gh

12.25 = 0.1 x 9.81 x h

h = 12.49 m

c) at 2.5 m suppose it have linear speed v and it is rolling without slipping,

at that point KE = mv^2 /2 + Iw^2 /2

= mv^2 /2   +    (2 m r^2 /5) v^2 /2    = 7mv^2 /10

using energy conservation,

0 + 12.25 = (0.1 x 9.81 x 2.5) +   0.7mv^2

0.7 x 0.1 x v^2 = 9.80

v = 11.83 m/s

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