# Homework Help: Train wheels problem

1. Nov 17, 2015

### Jakecp

1. The problem statement, all variables and given/known data
It is basicly on the image attached.

2. Relevant equations

where is the force on the front tires, is the force on the rear tires, is the wheelbase, is the distance from the center of mass (CM) to the rear wheels, is the distance from the center of gravity to the front wheels ( + = [PLAIN]https://upload.wikimedia.org/math/d/2/0/d20caec3b48a1eef164cb4ca81ba2587.png), [Broken] https://upload.wikimedia.org/math/6/f/8/6f8f57715090da2632453988d9a1501b.png is the mass of the vehicle, and is the gravity constant.

But i believe they are worthless because we do not have the measure for them.

3. The attempt at a solution

I think that the small wheel train is for passengers because what we need there is speed. With a small wheel we have the ability to turn it faster than in a cargo. Also i think is like a comparison with big trucks and mini cars. A big truck has massive wheels while a car has just little wheels. I think also the number of wheels affects it. And we can see that locomotive I has bigger wheels than locomotive 2.

My answer would be : A)

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2. Nov 17, 2015

### Jakecp

Also , traction affects? Bigger the wheel , bigger the traction ? Why? Is that true? or the smallest the wheel the bigger the traction? and why?

regards!

3. Nov 17, 2015

### haruspex

Take note of where the shaft from the piston attaches to the wheels.

4. Nov 17, 2015

### Jakecp

I don't really get it , i have seen pistons in photos in google of freight trains and passenger trains. I see that in the locomotive they are the same.
Image of a freight train :
http://previews.123rf.com/images/bo...-closeup-of-wheels-and-boiler-Stock-Photo.jpg

Image of a passenger locomotive train :

http://c8.alamy.com/comp/DWCCB4/gnr...express-passenger-locomotive-built-DWCCB4.jpg

I see the wheel size difference but i don't know why , if you can explain me why would be awesome. I just noticed that there are more wheels in the freight than in the passenger and that there are more pistons in the freight one because of the wheels . But i don't see a position change of the pistons , i see them in the borders and that they way they are crossed in the freight train is not the same as in a passenger train .

5. Nov 17, 2015

### haruspex

Look at where the shaft attaches to the wheel in relation to the radius of the wheel. Think about torque, and the relationship between angular velocity and linear velocity.

6. Nov 18, 2015

### Jakecp

To be honest i have not seen angular nor linear velocity yet at school so i have no idea. I will do some research . I have observed that ( the shaft relation ) and you are right , but why is that? why is it better to put the shaft like that?

7. Nov 18, 2015

### haruspex

Have you studied levers and mechanical advantage?

8. Nov 18, 2015

### Jakecp

Yes but why is it different , i mean , both need more MA right? , one needs to go faster but that does not means it needs less MA. What kind of lever is it? Type 1 , 2 or 3?

9. Nov 18, 2015

### haruspex

The categorisation of levers into those three types is a bit artificial. I think it is only taught in schools because it is easy to teach. The shaft/wheel/rail system does not fit neatly into it.
Let's label the centre of the wheel O, the point of attachment of the beam B, and the point of contact of the wheel with the rail R.
The power stroke from the piston occurs while B is below O. How would you assign the roles of fulcrum etc. to these three points?

It is more appropriate to consider the mechanical arrangement of the engine to be applying a couple to each wheel: during the power stroke, there is a roughly horizontal force from the axle at the centre of the wheel and a roughly equal and opposite force from the drive shaft where it attaches to the wheel. The result is a torque tending to rotate the wheel.
Correspondingly, the frictional force from the rail exerts an opposing torque.
How does the distance ratio OB:OR affect these torques?

Last edited: Nov 18, 2015
10. Nov 18, 2015

### Jakecp

The fulcrum i believe would be B right? And the rest i have no idea. I have gathered data and will ask my teacher about this today.

11. Nov 19, 2015

### haruspex

The fulcrum is generally taken to be a point that is fixed. Which of the three points is (for the instant) stationary?

12. Nov 19, 2015

### Jakecp

Yes , the fulcrum would be in the wheel. Because it would never move. In the side where the piston moves would be the input and near the fulcrum the outpput (near the wheel) and it would reverse as it rotates.

13. Nov 19, 2015

### haruspex

Sorry, but I'm not at all sure what you are saying there.
My previous post was trying to get you to say that the fulcrum must be the point R, since that is stationary instantaneously. However, this leads to a bizarre result. This demonstrates the traditional type classification of levers has some issues.
As I mentioned, the engine exerts two horizontal forces on the wheel. The piston pushes backwards at point B. In doing so, the reaction pushes forwards on the piston, creating a forward force on the engine, and thus a forward force on the wheel axis. This combination of forward and backwards forces on the wheel generates a torque.
For the purposes of this question, think in terms of the reference frame of the engine. It is trying to push the rails backwards. Thinking this way, you can take the wheel centre O as the fulcrum and the rails (point R) as the load.

14. Nov 19, 2015

### Jakecp

Newtons third law of action reaction . One force pushing forward and one backwards.... Yes i get that point , But i do not understand why R is the fulcrum and not the center of the wheel. If the center of the wheel won't move also.

15. Nov 19, 2015

### Jakecp

The fact is that i can't picture that in my mind but i will try to draw it and get some conclutions & will tell you my conclutions here later.

16. Nov 19, 2015

### haruspex

No, the centre of the wheel must move, or the train would not advance.
But my point there was that taking R to be the fulcrum does not in fact work. I was trying to show that the simplistic view of levers is not general enough to deal with this case.
You can get the right answer by taking the centre of the wheel as the fulcrum, but it is far from obvious why that is the right role assignment and the other is wrong.

17. Nov 19, 2015

### Jakecp

Oh ok , i understand your point now.... You wanted to mean that this kind of levers didn't fit in the class 1,2,3 lever clasification.

18. Nov 19, 2015

### Jakecp

In here traction and motion takes a big role because of Newton Second law of motion which says that acceleration is produced when a force acts on a mass. The greater the mass (of the object being accelerated) the greater the amount of force needed (to accelerate the object).So we have :

F = MA

And here Traction gets into action because with more traction you are able to move more mass. It takes a big role because in one case we need to get into motion a large quantity of weight and in the passenger train we just need to move it faster. Getting smaller and more wheels gives the engine the ability to rotate less times per wheel rotation than having less wheels and bigger wheels. This gives more traction because the engine produces more force without the need to rotate fast or more times.

We can compare this with trucks and cars. We see that trucks ( big trucks )have more wheels than cars and that their wheels are bigger.

Also , here the third law of newton applies also . It states that for every action there must be a reaction . The action would be the wheel pushing the rail backwards and the rail pushing the train forward.

Taking this into comparison with big trucks , using the second law of newton and seeing that traction takes a big role in this experiment i would say that the answer is (a) . In any other experiment we should take air resistance into account and also that in cargo trains there is the need to go backwards or do more stops which require the train to have a different kind of body. In this case we can not see any drastic or noticeable changes on the body because of air resistance or maneuverability .

Bibliography

Csep10.phys.utk.edu,. (2015). Newton's Three Laws of Motion. Retrieved 20 November 2015, from http://csep10.phys.utk.edu/astr161/lect/history/newton3laws.html

Physics Forums - The Fusion of Science and Community,. (2015). Train wheels problem. Retrieved 20 November 2015, from https://www.physicsforums.com/threads/train-wheels-problem.843739/

reddit,. (2015). Passenger vs Freight locomotives? • /r/trains. Retrieved 20 November 2015, from http://www.reddit.com/r/trains/comments/30ezzx/passenger_vs_freight_locomotives/

Teachertech.rice.edu,. (2015). Newton's 3 Laws of Motion. Retrieved 20 November 2015, from http://teachertech.rice.edu/Participants/louviere/Newton/law2.html

19. Nov 19, 2015

### haruspex

I mean that it is not clear how to fit it into that classification.
But it does turn out that if you settle on the wheel centre as the fulcrum, the shaft attachment as the applied force, and the rail (i.e. its frictional force on the wheel) as the load you will get the right answer. Stick with this, the answer is all about mechanical advantage and ratios! (Your post #18 is completely irrelevant.)
Study the two pictures, viewing the radius of the wheel from O to B to R as a lever. Look at the ratio of the distances OB, OR. Taking O as the fulcrum, what does this ratio say about mechanical advantage? How is the ratio different between the two trains?

20. Nov 19, 2015

### Jakecp

That is my answer to the homework (#18) . Well , i think the train for freight has a better ratio because the wheels are smaller.

In here : http://c8.alamy.com/comp/DWCCB4/gnr...express-passenger-locomotive-built-DWCCB4.jpg

OB distance is very small and OR is quite a big distance. Thinking of it as a lever it may have a MA under 1 . Because it would be like : Input to fulcrum distance : about 25 cm . (OB) Fulcrum to output about 100 cm (OR)so it would be ¼ or .25 .

In here : https://c2.staticflickr.com/6/5024/5787221601_92b16728f0_b.jpg

i would say that O B is of about 10 cm and O R is about twice as 0 B so it would be ½ . I don't know if i am or not correct.

21. Nov 20, 2015

### haruspex

Yes, that looks roughly right, but to answer the question you were given, you need to be referring to the two pictures there.
There, A has OB:OR about 1:3 or 1:4, B has more like 2:3.
But what do you mean by a 'better' ratio. Which ratio will give the greater top speed? Which ratio will give the greater tractive force?

22. Nov 20, 2015

### Jakecp

A has moré tractive force and b more speed

23. Nov 20, 2015

### Jakecp

But why ?

24. Nov 20, 2015

### haruspex

The engines are essentially the same, so the pistons operate at the same rates. Suppose the max speed of the piston end is 30kph. If it attaches near the rim of the wheel, the max tangential speed of the wheel (and hence the max speed of the train) won't be much more. If it attaches only a thrid of the way from the centre of the wheel to the rim, the tangential speed at the rim can go up to 90kph.

25. Nov 20, 2015

### Jakecp

Thanks a lot!