L/2 x CG Figure P8.47

A solid brass ball of mass 22 g and radius 8.51 mm rolls smoothly along a loop-the-loop track when released from rest from a tall ramp leading to the loop-the-loop. The circular loop has a 17 cm radius. (a) What is the minimum height from which you can release the ball so that it will go around the loop-the-loop without falling off? For part (b), assume that the ball is released from rest at a height of 61.83 cm above the bottom of the loop. (b) What is the magnitude of the horizontal force on ball when it is at a height 17 cm going up the hoop? (c)What is the direction of the net force on the ball at the top of the hoop? Î =

A uniform drawbridge must be held at a 37° angle abovethe horizontal to allow ships to pass underneath. The drawbridge weighs45,000 N and is 14.0 m long. A cable is connected 3.5 m from thehinge where the bridge pivots (measured along the bridge) and pullshorizontally on the bridge to hold it in place. What is the angular speed of the drawbridge as it becomes horizontal?

Yo-Yo man releases a yo-yo from rest and allows it to drop, as he keeps the topend of the string stationary. The mass of the yo-yo is 0.059 kg, its moment of inertia is2.5 * 10–5 kg · m2, and the radius r of the axle the string wraps around is 0.0068 m. Whatis the linear speed v of the yo-yo after it has dropped through a height of h = 0.50 m?