a carnival ride is made so that at a certain point the floor can be lowered and the people inside don't fall. if this carnival ride has 2.0 m radius and rotates 1.1 times per second: a) find the speed of the ride.
B) find the centripetal acceleration of a rider
C) what produces this acceleration?
D) when the floor drops down, the rider's weight is balanced by friction. What coefficient of friction in needed to keep the riders from slipping?
a) 14m/s
b) 98 m/s^2
c) ?
d) 0.10
To answer these questions, we can use some principles of circular motion and friction.
a) To find the speed of the ride, we can use the formula for linear speed in circular motion.
Linear speed = 2 * π * radius * rotational speed
Given:
Radius (r) = 2.0 m
Rotational speed = 1.1 rotations/second
Substitute the values and calculate:
Linear speed = 2 * π * 2.0 * 1.1 = 13.82 m/s
Therefore, the speed of the ride is 13.82 m/s.
b) To find the centripetal acceleration of a rider, we can use the formula:
Centripetal acceleration = (linear speed)^2 / radius
Given:
Linear speed = 13.82 m/s
Radius = 2.0 m
Substitute the values and calculate:
Centripetal acceleration = (13.82)^2 / 2.0 = 95.73 m/s^2
Therefore, the centripetal acceleration of a rider is 95.73 m/s^2.
c) The centripetal acceleration is produced by the inward force acting on the riders. In the case of this carnival ride, this inward force is provided by the normal force between the riders and the floor of the ride. As the floor drops down, the normal force increases, providing the necessary inward force for the centripetal acceleration.
d) To find the coefficient of friction needed to keep the riders from slipping, we can use the formula:
Friction force = coefficient of friction * normal force
Given:
Centripetal acceleration = 95.73 m/s^2
Weight of the riders = mass of riders * gravitational acceleration (which is equal to normal force)
Since the weight of the riders is balanced by friction:
Friction force = weight of the riders
Substitute the value of centripetal acceleration to calculate the normal force (which is equal to the weight):
Normal force = centripetal acceleration * mass of riders
When the floor drops, this normal force is acting towards the center of the ride, providing the necessary friction force. Therefore, the coefficient of friction can be calculated as:
Coefficient of friction = friction force / normal force
Substitute the values and calculate the coefficient of friction.
Please provide the mass of the riders to proceed with the calculation.