a passenger in a ferris wheel rates 3m/s in a vertical circle of radius 5m. find the apparent the ratio of his apparent weight to his true weight at the top and bottom of the circle
To find the ratio of the passenger's apparent weight to their true weight at the top and bottom of the circle, we need to consider the forces acting on the passenger.
At the top of the circle, the apparent weight will be the sum of the passenger's true weight and the centrifugal force pushing them away from the center of the circle.
At the bottom of the circle, the apparent weight will be the difference between the passenger's true weight and the centripetal force pulling them towards the center of the circle.
Let's break down the solution into four main steps:
Step 1: Calculate the centripetal acceleration:
The centripetal acceleration can be found using the formula:
a = v^2 / r
where v is the velocity and r is the radius of the circle.
Given that the velocity is 3 m/s and the radius is 5 m, we can substitute these values into the formula:
a = (3 m/s)^2 / 5 m
Step 2: Calculate the centripetal force:
The centripetal force can be calculated using the formula:
F = m * a
where m is the mass of the passenger and a is the centripetal acceleration.
Since the mass of the passenger is not given, we can cancel it out in the subsequent step and work with ratios.
Step 3: Calculate the ratios of apparent weight to true weight:
At the top of the circle:
The apparent weight (W_apparent) is the sum of the true weight (W_true) and the centrifugal force (F_cent):
W_apparent = W_true + F_cent
The centrifugal force is equal to the centripetal force:
F_cent = F
At the bottom of the circle:
The apparent weight (W_apparent) is the difference between the true weight (W_true) and the centripetal force (F_cent):
W_apparent = W_true - F_cent
Step 4: Calculate the ratio of the apparent weight to the true weight:
For both the top and the bottom of the circle, we get:
Ratio = W_apparent / W_true
By substituting the values obtained in step 1 for the centripetal force into the above equations, you can find the ratios of the passenger's apparent weight to their true weight at the top and bottom of the circle.