7) On a meter stick, there are masses hanging. On the left are masses of 3 g at 0.20 m and 10 g at 0.40 m from the center. On the right is a 6 g mass at 0.50 m from the center. Where would a 4 g mass have to be hung to make the meter stick balance at the center (so that CM is at center)? Setx=0 at CM m3x3m10x10 +M6x6 + m 4x4 + MMS XMS XCM 0.2m ? 0.4m 0.5m m3 +m10 +m6 +m+mMs 3(-0.3)+10(-0.1)+6(0)+4x + ms (0) MS 0 = 3+10+6+4+MMS 4g 0=-0.9-1+4x4 3g 6g 10g x = 0.48m Center of mass worksheet 8) Two masses are hanging from the ends of a 1 m bar. Where is the balance point (center of mass) of the system? m is 1 kg, m2 is 3 kg. Ignore the mass of the bar between the two masses. XCM 4XCM mx +m2x2 1(0)+3(1) m +m 4 = 3 XCM = 0.75m Setx=0 m m1 9) Same as the previous question, but m is 20 kg and m2 is 50 kg and the masses are each 1 cm in from the ends of the bar, so they're 0.98 m apart. mx +m2x2 XCM == m + m 70xCM = 49.7 XCM = 0.71m 20(0.01)+50(0.99) 70 Setx=0 at CM 10) A person is standing on the very end of a 2 m long board that is level and balanced. The balance point is 0.20 m from the end the person is on. The board has a mass of 20 kg. a) What is the mass of the person? XCM mboard board m board 20(-0.8)+mp +mpx p +m. p +m, (0.2) 0 = 20+mp mp = 80kg b) How much does the person weigh? 784N CM of board in center -0.8 0.2m