# Forces On a Moving Train Traveling Around a Curve

## Summary:

Forces Involved Of A Moving Train Travelling Around A Curve

## Main Question or Discussion Point

Hello all

I am trying to work out the forces involved of a moving train around a curve travelling at a constant speed.

I have the following:- The image on the left is a cross section of a train travelling around a curve, you can think of the train moving away from you.

The image on the right in the same train but in plane view but illustrates the radius.

I am trying to work out the Forces F1, F2 and F3.

I know the following:-

- Speed = 200mph

- Weight = 101605kg

- Gravity = 9.81m/s^2

- Distance between Rails = 1.2m

- Height Difference between Rail A and Rail B = 0.090m

- Angle = 4.30 deg

The first thing that I tried to do was to convert the train weight of 101605 kg into a Mass by dividing by 9.81 m/s^2, however I ended up with some strange units:-

101605kg / 9.81m/s^2 = 10357.28848 (kg s^2)/m - ???????

The reason why I wanted to find the Mass was because I wanted to use the F = MA equation to work out Force in Newtons.

Because I didn't get far with this I tried to convert the speed of the train which is 200mph into an acceleration but since the train is travelling around the curve at a constant speed of 200mph there is no acceleration which I am struggling to come to terms with.

Can I ask how would the Forces F1 F2 and F3 be worked out?

Can anyone point me in the right direction?

Thank you.

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BvU
Homework Helper
Weight = 101605 kg
Do you mean mass = 101605 kg ? The kilogram is a unit of mass.

constant speed of 200mph there is no acceleration
There is: the velocity of the train changes. Not in magnitude but in direction.

For a circular motion a centripetal force is needed. Can you find out how big it has to be in this case ?

200 mph is a disaster speed for a curve radius of 500 m

cjl

200 mph is a disaster speed for a curve radius of 500 m
It's not entirely unreasonable if the train is a roller coaster...

BvU
Homework Helper
200 mph, 500 m -- not a roller coaster

cjl
I know, I was being a bit facetious (though the fastest roller coaster is 150mph, so that's not that far off). That would be just about a 2G curve though, so it would be pretty ridiculous (and it would require 60 degree banking).

EDIT: Maybe it's 5km? That bank angle from OP's diagram is still not quite enough even in that case, but it at least seems to kind of work out as reasonable...

I don't see the position of the center of mass of the car noted anywhere. That will of course determine the actual disaster speed.

osilmag
Gold Member
F3 would be the weight multiplied by the cosine of the incline.