Question

The normal force equals the magnitude of the gravitational force as a roller coaster car crosses the top of a 40-m-diameter loop-the-loop. What is the car's speed at the top?

Answer 1

Answer:

Explanation:

Given

Diameter $d=40\ m$

radius $r=20\ m$

From diagram, at top point

If Normal force is equal to Gravitational force

$N=mg$

where N=normal reaction

m=mass of car

Normal reaction will provide centripetal force

$N=\frac{mv^2}{r}$

thus

$\frac{mv^2}{r}=mg$

$v=\sqrt{2gr}$

$v=\sqrt{2\times 9.8\times 20}$

$v=19.79\ m/s$