# Forces On a Moving Train Traveling Around a Curve

• tomtomtom1
In summary: F1 would be the normal force (weight multiplied by the sine of the incline) plus the centripetal force. F2 would be the normal force minus the centripetal force.In summary, the conversation discusses the forces involved in a moving train traveling around a curve at a constant speed. The weight, speed, radius, gravity, distance between rails, height difference between rails, and angle are all known factors. The person is trying to convert the weight into mass and use the F=MA equation to calculate the forces, but is struggling due to the constant speed. The concept of centripetal force is brought up and it is mentioned that the given speed and radius may not be realistic for a train. The forces F1,
tomtomtom1
TL;DR Summary
Forces Involved Of A Moving Train Travelling Around A Curve
Hello all

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

I have the following:-

The image on the left is a cross section of a train traveling 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 traveling 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.

Last edited by a moderator:
tomtomtom1 said:
Weight = 101605 kg
Do you mean mass = 101605 kg ? The kilogram is a unit of mass.

tomtomtom1 said:
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

BvU said:

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...

200 mph, 500 m -- not a roller coaster

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.

F3 would be the weight multiplied by the cosine of the incline.

## 1. What is the force that causes a train to move around a curve?

The force that causes a train to move around a curve is known as centripetal force. This force acts towards the center of the curve and keeps the train on its curved path.

## 2. How does the speed of the train affect the forces acting on it while traveling around a curve?

The speed of the train affects the forces acting on it in two ways. Firstly, a higher speed will result in a greater centripetal force needed to keep the train on its curved path. Secondly, a higher speed will also result in a greater centrifugal force, which is the force that tends to pull the train away from the curve.

## 3. What is the relationship between the radius of the curve and the forces acting on a train?

The radius of the curve is inversely proportional to the forces acting on a train. This means that as the radius of the curve decreases, the forces acting on the train increase. This is because a tighter curve requires a greater centripetal force to keep the train on its path.

## 4. How does the mass of the train affect the forces acting on it while traveling around a curve?

The mass of the train does not directly affect the forces acting on it while traveling around a curve. However, a heavier train may require a greater centripetal force to keep it on its path, leading to a higher risk of derailment if the force is not sufficient.

## 5. What are some safety measures that can be taken to reduce the forces acting on a train while traveling around a curve?

Some safety measures that can be taken to reduce the forces acting on a train while traveling around a curve include decreasing the speed of the train, increasing the radius of the curve, and using banking or tilting mechanisms on the tracks to help counteract the centrifugal force. Proper maintenance of the tracks and train also plays a crucial role in ensuring safe travel around curves.

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