Question

The normal force equals the magnitude of the gravitational force as a roller coaster car crosses the top of a 58-m-diameter loop-the-loop. What is the car's speed at the top?

Answer 1

16.87 m/s

Step-by-step explanation:

To find the speed of the car at the top, when the normal force is equal the gravitational force, we just need to equate both forces:

`N = P`

`m*a_c = mg`

`a_c` is the centripetal acceleration in the loop:

`a_c = v^2/r`

So we have that:

`mv^2/r = mg`

`v^2/r = g`

`v^2 = gr`

`v = √(gr)`

So, using the gravity = 9.81 m/s^2 and the radius = 29 meters, we have:

`v = √(9.81 * 29)`

`v = √(284.49) = 16.87\ m/s`

The speed of the car is 16.87 m/s at the top.