QUIZ 8

  1. Three balls of mass m1 = 5kg, m2 = 2kg, and m3 = 4kg, locate at the three corners of a square 20cm on a side, and are connected by light cords as shown. Find the center of mass of the system.
    2. Solution.

    Choose the coordinate system as shown with m3 as the origin.

    We find the center of mass from

                xCM = (m1x1 + m2x2 + m3x3)/(m1 + m2+ m3)

                        = [(5kg)(-20cm) + (2kg)(0) + (4kg)(0)]/(5kg + 2kg + 4kg)

                        = -9.1cm

                yCM = (m1y1 + m2y2 + m3y3)/(m1 + m2+ m3)

                        = [(5kg)(20cm) + (2kg)(20cm) + (4kg)(0)]/(5kg + 2kg + 4kg)

                       = 12.7cm

    The center of mass of the system is at -9.1cm to the left and 12.7cm above m3.

    		  
  2. A wheel rotates about its center from rest to 200 revolutions in 2.5minutes. Assume uniform acceleration. What is its angular acceleration in rad/s2?

          Solution.

          We find the angular acceleration from

                           q = q0 + w0t + 1/2at2;

                           2p(200rev)(rad/rev) = 0 + 0 + 1/2a[(2.5min)(60s/min)]2,

          which gives a = 0.11rad/s2.