moments of inertia (1 Viewer)

[clicker]

A solid sphere of radius 0.05 m and mass 1.00 kg rolls on a horizontal surface with a velocity of 15 ms-1 and then rolls up an incline at an angle of 20o.If friction forces can be neglected , to what height above the horizontal surface will the sphere rise before it comes to rest?
(the moment of inertia of a sphere is given by 0.4Mr2).

 

[wogboy]

let initial total kinetic energy = K,
K = translational kinetic energy + rotational kinetic energy
= 1/2*mv^2 + 1/2*Iw^2
= 1/2*mv^2 + 1/2*0.4*mr^2*w^2
= 1/2*mv^2 + 1/2*0.4*mv^2 (assuming v = rw, i.e. no wheel slipping against the ground)
= 0.7*mv^2

Gravitational potential energy increase = initial total kinetic energy (conservation law of energy, assuming no friction)
mgh = K
h = K/(mg)
= 0.7*mv^2 / (mg)
= 0.7*(v^2)/g
= 16.07 m

Note that most of the information (mass, radius, incline angle) given is quite useless as far as this problem is concerned (unless there are extra parts to this question). All you needed to know was it's initial velocity, and it's shape (solid sphere).