Question

A solid sphere of uniform density starts from rest and rolls without slipping a distance of d = 2 m down a θ = 20° incline. The sphere has a mass  M = 5.8 kg and a radius R = 0.28 m.

1. Of the total kinetic energy of the sphere, what fraction is translational?

KE _tran/KE_total

2)What is the translational kinetic energy of the sphere when it reaches the bottom of the incline?

KE _tran =

3. What is the translational speed of the sphere as it reaches the bottom of the ramp?

v =

Answer 1

ouro o) M = mass of sphere =5.8kg d=am TT o = 20° R = 0.28m i) condition for co rolling vewr Refiline K. E total = £mv²t 21 w2 = £mv² + ².2 m R² w²= {mv²t & mu? 1/2 mu? kºrea amua k Frotal = po kilt 2) 큽me F KE frons T E to feel From lon sesvalion of energy MIRIS M.Ef mg (dsino) = 2mv²t 2 I w2 = 7 mu? 3) 5.8x9.81X3 819 20 = (4mu?) - Translational kE=k. Etrans = 5 x 5.8 X 9181 X2 Sincron) = 27.87 ASS 3) 4 mv?= 27.8 5v5 2x27.5 = 312m/s 5.8