1. The point masses m and 2m lie along the x-axis, with m at the origin and 2m at x = L. A third point mass Mis moved along the x-axis. At what point is the net gravitational force on M due to the other two masses equal to zero? (4 points) (Hint: Fgren Gimm ) m 2m XO XL
2. We wrap a light, non stretching cable around a solid cylinder with radius R = 2m and moment of inertia 1 =4 kg m². The cylinder rotates with negligible friction about a stationary horizontal axis. We tie the free end of the cable to a block of mass m=1kg and release the block from rest at a distance h=1.6 m above the floor. As the block falls, the cable unwinds without stretching or slipping. (4 points) m h a) Find the speed of the falling block as the block strikes the floor. (Free fall acceleration is g=10m/s) (1 point)
b) What's the linear acceleration of the block m before it strikes the floor. (1 point)
c) What's the tension in the cable? (1 points) d) What's the net torque applied to the cylinder about the center axis?