Question

A 1.90 kg solid, uniform ball of radius 0.200 m is released from rest at point A in the figure below, its center of gravity a distance of 1.90 m above the ground. The ball rolls without slipping to the bottom of an incline and back up to point B where it is launched vertically into the air. The ball then rises to its maximum height h_max at point C.

a) At point B, find the ball's translational speed v_B (in m/s).

= 0 1.90 m max 0.300 m

b) At point B, find the ball's rotational speed ω_B (in rad/s).

c) At point C, find the ball's rotational speed ω_C (in rad/s).

d) At point C, find the maximum height h_max of the ball's center of gravity (in m).

Answer 1

Kerst = 1 2 3 w 2 - 1 2 ( MR?) (m² = 4 m2 KE trang - 12 m2 = 2 m 2 ke / mv ² + 1 2 = 72 m2 = 0.7 m2 & PEA + KE = PEA + KEA Mgha + 0 = mghat 0.7 mu? 9.8% (1.90 -0.30) = 0.70 TV = 4.83 m/s egy yo - 9:24 = 29.7 redle 3 we = cp = 23.7 sadle (no torque) 0.2 Now might + 12 mu? = mghn to only translational ke will convert into PE] hom = (0-8) + (4.7² ) Thank = 1.44m