Question

A roller coaster car crosses the top of a circular loop-the-loop at twice the critical speed. Part A What is the ratio of the normal force to the gravitational force? What is the ratio of the normal force to the gravitational force? n/FG=2n/FG=2 n/FG=3n/FG=3 n/FG=4n/FG=4 n/FG=5n/FG=5

Answer 1

n/(FG) = 3.

Step-by-step explanation:

At the top of the loop-the-loop, the normal force is directed downwards as well as the weight of the car. So, the total net force of the car is

`F_(net) = N + mg`

By Newton's Second Law, this force is equal to the centripetal force, because the car is making circular motion in the loop.

`F_(net) = ma = (mv^2)/(R)\\N + mg = (mv^2)/(R)`

The critical speed is the minimum speed at which the car does not fall. So, at the critical speed the normal force is zero.

`0 + mg = (mv_c^2)/(R)\\v_c = √(gR)`

If the car is moving twice the critical speed, then

`N + mg = (m(2v_c)^2)/(R) = (m4gR)/(R) = 4mg\\N = 3mg`

Finally, the ratio of the normal force to the gravitational force is

`(3mg)/(mg) = 3`