Assignment about Circular Motion for Be,

1. Homework:
1. In the banking of curves at optimum angle 𝜃, an
object must move with a certain speed so that it
can move in the curve without friction. Prove that
this speed is 𝑣 = 𝑔𝑅 sin 𝜃.
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.
R
v
v