A Pinball, Spring and Conservation of Energy Problem

[omgpuppylol]

A pinball (solid sphere of mass=0.2 kg, outer radius=0.3 m) is cocked back 0.7 m on a spring (k= 50 N/m), and fired onto the pinball machine surface, which is tilted.



c) When the pinball is 2.5 m above its initial location (on the way up), find its linear and angular speeds.



I got the answers to parts a through c as the following: a) 12.25 J of energy is initially stored in the spring
b) 6.24363 is the maximum height the pinball rolls to (above its initial location.) However, I'm having trouble tackling part c..not really sure where to begin.

Anything will help. Thank you so much!

 

[Poley]

I'll have a go.

When the ball is 2.5 metres above its initial position, it has acquired $mg_{0}h$ joules of potential energy.

The mechanical energy of the ball (which was calculated in part A) is equal to the sum of its kinetic energy and potential energy. Thus,

$mg_{0}h+\frac{1}{2}mv^{2}=12.25J$

The linear speed can now be calculated from this equation.

To convert from linear speed to angular speed, I believe the linear speed is divided by the circumference (I find it can help to think about the units: metres per second divided by metres per revolution yields revolutions per second).

Hope this helps!