How does this work??

A solid sphere of mass 0.604 kg rolls without slipping along a horizontal surface with a translational speed of 5.41 m/s. It comes to an incline that makes an angle of 31.0掳 with the horizontal surface.


(a) What is the total energy of the rolling sphere? Neglect energy losses due to friction.


12.4 J


(b) To what vertical height above the horizontal surface does the sphere rise on the incline?


2.09 m





How do they come up with 12.4J for question a, and 2.09m for question b? I am really confused??How does this work??
you need to know the radius of the sphere too.





No radius given? It must cancel out then -





Moment of Inertia of solid uniform sphere of mass m and radius r about an axis through centre = I_sphere = m*r^2*2/5





kinetic energy of sphere due to rotation = I/2*w^2 where w is angular velocity.





sphere is rotating at 5.41/r radians/sec





so r does cancel - sorry.





KE_sphere is 5.41^2*m/5 add this to 1/2*m*v^2 for translational ke of sphere and you get the 12.4 joules





To work out the height you just equate the total k.e. lost to increase in potential energy due to climbing ( sphere is not rotating when it reaches the highest point).