1 To have a certain object rotating around the radius 44 m a

1. To have a certain object rotating around the radius 4.4 m at the tangential velocity of 13.9 m/s, a centripetal force of 9.6 N had to be applied. How much force has to be applied in order to rotate the same object at 6.0 m/s around the radius of 15.2 m?

2. A 2856.3-lbf truck rounds an unbanked curve on the highway at a speed of 47.0 mph. If the maximum frictional force between the surface of the road and all four of the tires is 1158.7 lbf, calculate the minimum radius of curvature for the curve to prevent the truck from skidding off the road.

3. An amusement park ride called the Rotor consists of a room in the shape of a vertical cylinder 3.67 m in radius which, once the riders are inside, begins to rotate, forcing them to the wall. When the room reaches the angular speed of 2.8 rad/s, the floor suddenly drops out. It is deemed that this rate of rotation will be sufficient to keep a 400 lbf person pinned against the wall of the cylinder.

What is the minimum angular speed required to keep a 200 lbf person pinned against the wall of the cylinder?

Solution

the centripetal force is

    F = mv^2/r

then

   F₂/F₁ = [mv₂²/r₂] / [mv₁²/r₁]

F₂ = [v₂ / v₁]²*[r₁/r₂]*F₁

       = [6/13.9]²*[4.4 / 15.2]*9.6

             = 0.5177 N

             = 0.52 N