What is the force multiplication in a cable connected train engine and carriage?

In summary: In this case, the engine's pulling force will only tension the cable in one direction, and the carriage will only move in that direction.
  • #1
Bad Monkey
29
0
Consider the following scenario.

There is a train engine on a cliff above a plain. Imagine the engine is directly on the cliff edge. On the plain below, there is a carriage. Both tracks are flat and horizontal.

The engine is connected directly to the carriage by a cable. This cable when taut obviously is oriented at some angle theta below horizontal.

The engine now tries to pull the carriage. Its pulling force tensions the cable. Obviously the carriage will move. The engine applies force H.

The engine is applying only a horizontal force. The carriage can only move horizontally. I appreciate that, in the cable, there will be this horizontal force, plus a vertical element necessary to make up the 'hypotenuse of the triangle'. So there will be a resultant lift force on the carriage, and an opposite downward force on the engine (which the cliff plateau opposes), given by H*tan(theta). Correct?

The cable must therefore have a higher total tension than is actually being applied by the engine.

Question: how do we refer do this force multiplication? Is it a form of leverage?


P.S. The best real world example I can think of is pushing horizontally on the pole of a tent. It is relatively easy to pull out the peg/anchor. Just trying to figure out the language to cover this.
 
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  • #2
Bad Monkey said:
P.S. The best real world example I can think of is pushing horizontally on the pole of a tent. It is relatively easy to pull out the peg/anchor. Just trying to figure out the language to cover this.

Well, the tent example is definitely leverage. Leverage has to do with angle, but distance is also important. Leverage has to do with the ability to turn something. So in the tent example, the angle at which you push is important - but so is how far from the peg you push. The further from the peg, the greater your ability to turn the peg with a small amount of force.

I'm not sure how the train example is related to the tent example.
 
  • #3
It is precisely the same, think about it :)

To transliterate the train example: the train engine is you pushing horizontally on the tent pole. The carriage on the plain below is the peg. The cable connecting the two is the peg rope. Where the vertical tent pole offers an opposing force upward, the cliff plateau does the same to the train engine. Got it?
 
  • #4
Bad Monkey said:
To transliterate the train example: the train engine is you pushing horizontally on the tent pole. The carriage on the plain below is the peg. The cable connecting the two is the peg rope. Where the vertical tent pole offers an opposing force upward, the cliff plateau does the same to the train engine. Got it?

In the tent example, the further from the peg you push, the easier it is for you to turn the peg out of the ground. But it doesn't seem like the carriage becomes easier to pull the further the train is from it.:confused:
 
  • #5
Consider the initial state only then, you are right that they only compare at that point. This is what I'm interested in, the train example seemed like the best and most easily visualized model.
 
  • #6
Too hard for all you smart chimps huh?
 
  • #7
atyy said:
In the tent example, the further from the peg you push, the easier it is for you to turn the peg out of the ground. But it doesn't seem like the carriage becomes easier to pull the further the train is from it.:confused:

Hmm. I disagree. Think of the extremes:

If the rope is very long such that the cable is nearly horizontal, it's almost as if the train and carriage were on the same plane. Disregard the weight of the cable of course (^:

On the other hand, if the rope is only an inch longer than the height of the cliff, most of the force is applied to tension (pulling the train down/pulling the carriage up), and very little goes into horizontal motion.

Or am I missing something?
 
  • #8
I think you are missing something. The horizontal force in the line has to always equal the force applied by the engine, with the tension in the cable equal to that plus the vertical force resulting from the 'leverage' for lack of a better term.

I will quote myself:

Bad Monkey said:
The engine is applying only a horizontal force. The carriage can only move horizontally. I appreciate that, in the cable, there will be this horizontal force, plus a vertical element necessary to make up the 'hypotenuse of the triangle'. So there will be a resultant lift force on the carriage, and an opposite downward force on the engine (which the cliff plateau opposes), given by H*tan(theta). Correct?

Imagine a different scenario, whereby the line from the engine is attached to an immovable point on the track below. The engine can now no longer move; nonetheless it tries. It applies a horizontal force by way of its wheels on its track. On the plain below, the point on the track is subjected to a force from the angled cable.

Clearly, this point must provide an equal and opposite force. 1) Horizontally - it has to be equal to that of the engine, otherwise it will move as the carriage would. 2) Vertically, clearly it must resist the force given by H*tan(theta), else it will pop out and fly upward!
 
  • #9
This is the same scenario by the way, I'm just trying to make it easier to visualize.

Here's a picture, they always help!
 

Attachments

  • Train-leverage.png
    Train-leverage.png
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  • #10
So the red force is that applied by the engine, and the blue force comes from the opposing support force of the plateau. Summed they give a tension in the cable greater than the red H alone.

Is this leverage? What do we call it? Am I wrong completely?
 
  • #11
Aw now c'mon. I refuse to let this die.
 

1. What is a force vector?

A force vector is a representation of a force, which includes the magnitude (strength) and direction of the force. It is often represented by an arrow, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction of the force.

2. What is leverage?

Leverage is the ability to use a small amount of force to move a larger object. It is achieved by using a lever, which is a rigid object that pivots around a fixed point called the fulcrum. The location of the fulcrum and the length of the lever arm determine the amount of leverage that can be achieved.

3. How are force vectors and leverage related?

Force vectors are used to represent the forces acting on a lever, and the direction and magnitude of these forces determine the amount of leverage that can be achieved. By understanding the force vectors and their interactions, scientists and engineers can design levers that can efficiently move objects with minimal force.

4. What is the principle of moments?

The principle of moments states that for an object to be in equilibrium (or balanced), the sum of the clockwise moments must be equal to the sum of the counterclockwise moments. This principle is used in the analysis of force vectors and levers to determine the forces and distances needed to achieve equilibrium.

5. How can force vectors and leverage be applied in everyday life?

Force vectors and leverage are used in many everyday objects and tasks. For example, using a crowbar to lift a heavy object, opening a bottle with a bottle opener, and even using scissors to cut paper all involve the use of force vectors and leverage. By understanding these concepts, we can use them to our advantage to make tasks easier and more efficient.

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