Question

A solid steel ball with mass = 1.0 kg and radius 0.25 m is held at rest on top of a ramp at height h = 2.0 m. The moment of inertia, I = (2/5)mR² for a solid sphere. What is the final velocity of its center of mass, v_cm, when it gets to the bottom of the ramp?

Answer 1

Mass of the ball m = ing Radius R = 0.25 m hei of ramp h = 2 m eight .. Initial potential energy v= mgh at the bottom the potential energy is zero so from 1 energy we can write conservation that, at Bottom linear kinetic Rotational kinetic energy (Initial potential energy energy .. } mum + 1/2 I wr migh Com= relocity ball - لا of center of mass (linear) angular relocity of moment of inertia 2/3 mar 11 I and U= WXR cm ler mum t 1 x 2 / 3 xm x R x Pr = mgh v Cem + Com 5 56cm't 2 en = gh gh 10 2 to gh 10 X 9.8 x 2 ucm = 7 7 clem = 5•29 mis :. Velocity of center of mass um = 5.29 m/s