Problem 7.46: Riding a Loop-the-loop

[annabelx4]

Homework Statement

A car in an amusement park ride rolls without friction around the track shown in the figure . It starts from rest at point at a height above the bottom of the loop. Treat the car as a particle.

What is the minimum value of (in terms of ) such that the car moves around the loop without falling off at the top (point )?

If the car starts at height 4.00 and the radius is = 25.0 , compute the speed of the passengers when the car is at point , which is at the end of a horizontal diameter.

Homework Equations

mgh = 1/2 mv^2

The Attempt at a Solution

we know that h = 2 R because it's the diameter but other than that i am lost

 

[member 553083]

. For the minimum value, I believe it is 4R. For the speed, we use the equation mgh = 1/2 mv^2. mgh = 1/2 mv^2(4)(9.8)(25) = 1/2 (20)(v^2)1960 = 10v^2196 = v^214.1 m/s = v