Final answer:
The roller coaster that goes up and down is called a vertical loop roller coaster. To calculate the speed at the top of the loop, use the formula for centripetal acceleration with the given radius of curvature and downward acceleration. The speed is approximately 4.74 times the square root of the acceleration due to gravity.
Step-by-step explanation:
The roller coaster that goes up and down is called a vertical loop roller coaster.
It is designed with a smaller radius of curvature at the top than on the sides, allowing for a greater downward centripetal acceleration at the top.
This greater acceleration keeps the passengers firmly pressed into their seats.
To calculate the speed of the roller coaster at the top of the loop, you need to know the radius of curvature and the downward acceleration of the car.
With a radius of curvature of 15.0 m and a downward acceleration of 1.50 g (where g is the acceleration due to gravity), you can use the formula for centripetal acceleration to find the speed:
centripetal acceleration = (speed^2) / radius of curvature
Plugging in the values, the formula becomes:
1.50 g = (speed^2) / 15.0 m
Solving for speed, we can rearrange the formula:
speed = sqrt(1.50 g * 15.0 m) = sqrt(22.5 g) ≈ 4.74 sqrt(g)
So the speed of the roller coaster at the top of the loop is approximately 4.74 times the square root of the acceleration due to gravity.