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:
[tex]N = P[/tex]
[tex]m*a_c = mg[/tex]
[tex]a_c[/tex] is the centripetal acceleration in the loop:
[tex]a_c = v^2/r[/tex]
So we have that:
[tex]mv^2/r = mg[/tex]
[tex]v^2/r = g[/tex]
[tex]v^2 = gr[/tex]
[tex]v = \sqrt{gr}[/tex]
So, using the gravity = 9.81 m/s^2 and the radius = 29 meters, we have:
[tex]v = \sqrt{9.81 * 29}[/tex]
[tex]v = \sqrt{284.49} = 16.87\ m/s[/tex]
The speed of the car is 16.87 m/s at the top.
