The track near the top of your favorite roller coaster has a circular shape with a diameter of 36 m. When you are at the top, you feel as if you weigh only one-fifth of your weight on the ground. What is the speed of the roller coaster?
see other post.
To find the speed of the roller coaster, we need to use the concept of centripetal force and gravitational force.
First, let's determine the weight of the person on the top of the roller coaster. We are given that the person feels as if they weigh only one-fifth of their weight on the ground. Let's denote the weight on the ground as W and the weight on the top of the roller coaster as W'.
W' = (1/5) * W
Now, let's relate the forces acting on the person. At the top of the roller coaster, we have two forces: the weight acting downward and the centripetal force acting perpendicular to the track towards the center of the circular motion.
The weight can be determined using the formula: W = m * g
Where:
m is the mass of the person
g is the acceleration due to gravity (approximated as 9.8 m/s²)
To determine the centripetal force, we'll use the formula: F = m * (v² / r)
Where:
m is the mass of the person
v is the speed of the roller coaster
r is the radius of the circular track (half the diameter)
Since the person is in equilibrium, the centripetal force is equal to the weight on the top of the roller coaster. Therefore, we can set up the following equation:
W' = F
(1/5) * W = m * (v² / r)
Now, we need to solve for v. Rearranging the equation, we get:
v² = (W' * r) / m
v = √[(W' * r) / m]
Now we have the formula to calculate the speed of the roller coaster. We can plug in the given values to get the final result.