Homework:

1. In the banking of curves at angle , Prove that the speed of an object moving around that curve without friction is .

2. A 3.0-kg rock swings in a horizontal circle of radius 2.0 m. If it takes 2.0 s to complete one revolution, what is its tangential speed? What is its centripetal acceleration? What is the tension of the string used? Draw the FBD of the rock.

3. In the frictionless loop-the-loop apparatus, derive the equation of the normal force at the top of the loop in terms of the mass of the cart m, the radius of the loop R, the tangential speed v, and the acceleration of gravity g. Note: Draw FBD.

Rv

v