Question

2. Problem #37 from Chapter 10 3. A ping-pong ball is a hollow sphere that has a radius of 0.100 m and a mass of 0.00270 grams. At one point during a game of table tennis the ball is initially rotating at 100 rad/s counterclockwise (around its center of mass) before being hit by a paddle. The hit from the paddle changes the angular velocity to 60 rad/s clockwise in a time of 0.200 seconds. (a) Through how many radians will the ball turn as the angular velocity changes? (b) The point where the paddle puts a force on the ball, and the direction of this force, are shown. What must be the size of the force? (c) The center of mass of the ball is moving at 3 m/s to the left just before the paddle hits it. What will be the size and direction the velocity of the ball's center of mass after being hit by the paddle? (Note: You can ignore air resistance while the paddle hits the ball) 35° one 4 Problem 47 from Chapter 10, Part a only

Answer 1

a) Wi = 100 rad/s , COF=-60 rad/s, t = 0.2005 Ws = Wit at a = wf-Wi =-60 rad/s -- 100 rod/s - -800 rad/s2 = = c +2a B 0 = (borod/s)? - (+100 rod/32 2 x (-800 rod/s2) 0.200 S 0 - 4 roelians b) Moment of Inestia of ball (hollow sphere) - I = 2 MR² Im=0.00270 gramms = 27X107 kg I = x(27x10*kg) x(0-100 m)? le IR = 0.100m = 1,8810-9 Kg m² torque = RF sin 35° - Ia F = Ia Rsings Fp = (1.8X10-9kg m2) (800 rod ls2 fin magnitude) (onoom) sin 35° Fp = 2.51x10-50 c) acceleration a = Ę = 2.51x10 = 93-0 m/s2 2.7 X10-7 kg due to this acceleration velocity will change in the direction of acceleration AV = at = 93.0 m/s? x 0-200 S = 18.6 m/s at (35° with right up) y = / + sv? 2V; AV Cos35° Vj = 3.0 m/s V = 16.2 mis Direction, ß= fon Av sin3s Vi - AV casso = 139° clockwise with intial direction of ball