Question

A pinball (solid sphere of mass=0.2 kg, outer radius=0.3 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

Answer 1

energy stored = 0.5 * k * x^2

energy stored = 0.5 * 50 * 0.8^2

energy stored = 16 J

by conservation of energy

initial energy = final energy

0.5 * kx^2 = mgh

16 = 0.2 * 9.8 * h

maximum height = 8.163 m

when height is 2.5 m

16 = 0.2 * 9.8 * 2.5 + 0.5 * mv^2 + 0.5 * (2/5) * m * r^2 * (v/r)^2

16 = 0.2 * 9.8 * 2.5 + 0.5 * mv^2 + 0.5 * (2/5) * m * v^2

16 = 0.2 * 9.8 * 2.5 + 0.5 * 0.2 * v^2 + 0.5 * (2/5) * 0.2 * v^2

v = 8.9042 m/s

angular speed = linear speed / radius

angular speed = 8.9042 / 0.3

angular speed = 29.68 rad/sec