Suppose the vertical loop has a radius of 8.92 m. What is the apparent weight (Wap) of a rider on the roller coaster at the bottom of the loop? (Assume that friction between roller coaster and rails can be neglected. Give your answer in terms of m and g.)
wouldn't it depend on the velocity of the rider?
To find the apparent weight (Wap) of the rider on the roller coaster at the bottom of the loop, we need to consider the forces acting on the rider.
In this case, at the bottom of the loop, the rider will experience two forces: the gravitational force (mg) and the contact force exerted by the roller coaster (N).
Since the rider is at the bottom of the loop, they are in contact with the roller coaster, and the contact force provides the necessary centripetal force to keep the rider moving in a circular path. At the bottom of the loop, the direction of the contact force is upwards, opposite to the gravitational force.
To calculate the apparent weight (Wap), we need to find the net force acting on the rider at the bottom of the loop. The net force is the vector sum of the gravitational force and the contact force.
Since the rider is moving in a vertical loop, the net force should provide the necessary centripetal force, which is given by the formula:
Fc = mv^2 / r
Where Fc is the centripetal force, m is the mass of the rider, v is the speed of the rider, and r is the radius of the loop.
Since we want to find the apparent weight (Wap) of the rider, we can rewrite the formula as:
Fc = m * g - Wap
Where g is the acceleration due to gravity.
Since the apparent weight (Wap) is equal to the normal force (N), we can rewrite the formula as:
Fc = m * g - N
Solving for N, we get:
N = m * g - Fc
To find the value of N, we need to know the mass of the rider, the acceleration due to gravity (g), the speed of the rider, and the radius of the loop.
Given:
Radius of the loop (r) = 8.92 m
Note: The speed of the rider is not provided in the question. Without the speed, we can't find the apparent weight directly. Speed can be calculated using conservation of energy principles or additional information is required to solve the problem completely.