Question

Find the speed of a disk degreef mass M= 0 8 kg and radius R= 0.03m when it reaches the of an inclined plane. The disk starts at rest at a vertical height H= 1.2m and rolls without slipping. Find the speed for a solid sphere of the same mass and radius that slides down a frictionless plane without rotating.

Answer 1

a) Initial PE = mgh = 9.408 J
Final KE = rotational KE + translational KE = 0.5*mv^2 + 0.5*Iw^2 = 0.5*mv^2 + 0.5*0.5*mr^2*(v/r)^2 = mv^2[0.5 + 0.25] = 0.75mv^2
Final KE = Initial PE ( conservation of energy)
v = 3.9597 m/s
b) Initial PE = mgh = 9.408 J
Final KE = 0.5mv^2
v = 4.8497 m/s