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

Answer:

16.87 m/s

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:

$mv^2/r = mg$

$v^2/r = g$

$v^2 = gr$

$v = \sqrt{gr}$

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

$v = \sqrt{9.81 * 29}$

$v = \sqrt{284.49} = 16.87\ m/s$

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