Answer:
110m
Explanation:
We need first have a couple of equation to give a relation between the maximum force and the centrifugal foce.
We know that the maximum force F=mg, that is the condition for the coster to just stay on the track.
In the other hand we know that the centrifugal force is given by,
[tex]F= \frac{mv^2}{g}[/tex]
where r is the radius of the loop and v the velocity of the coaster.
Assume that both equation are equal, then
[tex]\frac{mv^2}{r} = mg[/tex]
The velocity of the coaster is given by,
[tex]v= \sqrt{2gh}[/tex]
Where h=55m and g=9.8m/s^2
Replacing
[tex]v=\sqrt{2(9.8)(55)}[/tex]
[tex]v= 32.833m/s[/tex]
The maximus radius of the loop is,
[tex]\frac{mv^2}{r}=mg[/tex]
[tex]r=\frac{v^2}{g} = \frac{32.83^2}{9.8}=110m[/tex]
