A machine part consists of a thin 40.0-cm-long bar with small 1.15-kg masses fastened by screws to its ends. The screws can support a maximum force of 75.0 N without pulling out. This bar rotates about an axis perpendicular to it at its center. (a) As the bar is turning at a constant rate on a horizontal, frictionless surface, what is the maximum speed the masses can have without pulling out the screws? (b) Suppose the machine is redesigned so that the bar turns at a constant rate in a vertical circle. Will one of the screws be more likely to pull out when the mass is at the top of the circle or at the bottom? Use a free-body diagram to see why. (c) Using the result of part (b), what is the greatest speed the masses can have without pulling a screw?
Solution 43E Step 1 of 4: v2 The mass moves circular path,so the acceleration israd= R ,directed toward the centre of path Step 2 of 4: a) F xma x 2 F=ma rad=m R =75 N FR v = m v = (75)(0.2) 1.15 =3.61 m/s Step 3 of 4: b) At the top F yma y So F=ma rad- mg At the bottom F xma x So F=ma rad+mg The value of F required is larger at the bottom of the path