Centripetal acceleration and force

[Batman121]

The cars on a theme park ride each have a mass of 500 kg and travel around a vertical loop of diameter 20m.
What is the minimum speed at which the cars must enter the loop in order to remain in contact with the track and What will then be the maximum reaction of the track?
M=mass
g=gravity
r=radius of loop

i don't know how to work out the mimimum speed required becuase there is no time value or angular acceleration given.
to work out the maximum reaction
Square root of (MgXr)
500X9.81=4905
4905X10=49050
square root of 49050 = 221.472 Newtons (not sure on the forumla though)

 

[tiny-tim]

Hi Batman121! Welcome to PF!

Hint: what equation must you apply at the top of the loop for the car to remain in contact with the track?

 

[Batman121]

the only one i can think of is
centripetal force + gravity has to equal the centrifugal force acting on the cars

 

[tiny-tim]

the only one i can think of is
centripetal force + gravity has to equal the centrifugal force acting on the cars

That's the one!

So … putting the numbers in … the minimum velocity, at the top, for a car to remain in contact with the track is … ?

 

[Batman121]

so it would be mass of 500 X acceleration to get centrigufal force. but i don't know acceleration or how to work it out.

 

[tiny-tim]

so it would be mass of 500 X acceleration to get centrigufal force. but i don't know acceleration or how to work it out.

Acceleration of something moving in a circle of radius r with speed v is $$\frac{v^2}{r}$$ towards the centre of the circle.

That also equals $$\omega^2r$$, where $$\omega$$ is the angular velocity, v/r.