2. An amusement park ride consists of a rotating vertical cylinder with rough canvas walls. The floor is initially about halfway up the cylinder wall as shown to the right. After the rider has entered and the cylinder is rotating sufficiently fast, the floor is dropped down, yet the rider does not slide down. The rider has a mass of 50 kg, the radius R of the cylinder is 5 meters, the period of the cylinder is 3.14 seconds and the coefficient of static friction between the rider and the wall of the cylinder is 0.6.
a. On the diagram above, draw and identify the forces on the rider when the system is rotating and the floor has dropped down.
b. Calculate the centripetal force on the rider when the cylinder is rotating and state what provides the force.
c. Calculate the upward force that keeps the rider from falling when the floor is dropped down and state what provides that force.
d. At the same rotational speed, would a rider of twice the mass slide down the wall? Explain.
1 point for each correct force2 point
b. Fnet = ma
Using the cos component of the tension1 point
The correct answer of m = TcosΘ/g1 point
c. For realizing the centripetal force is provided by the sin component of tension1 point
For setting TsinΘ = mv2/r1 point
Using r = lsinΘ1 point
The correct answer of v = 1 point
d. For stating the ball will move horizontally in the direction of the tangential velocity1 point
For stating that it will begin to accelerate down due to gravity1 point
1 point for each correct force3 points
b. For stating that the normal force provides the centripetal force1 point
For using mv2/r to calculate the correct force of 1000 N1 point
c.For stating that the frictional force provides the upward force1 point
For using f = uN to calculate the correct force of 490 N1 point
d. For stating that since f = uN and the normal force is related to the mass, any increase in 1 point
mass will increase the friction by the same amount as the weight going down