Coeffecient of train and the tracks?

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In summary, the coefficient of friction between the train and the track is -.676, which is why the braking force needed to stop the train was -13520 newtons.
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Homework Statement


What is the coefficient of friction between the train and the track, given that the train has 20,000 kg and is going at velocity of 26m/s. Note that when the train conductor saw a pedestrian he started braking and also the distance between the pedestrian to the train is 500m
Other given information:
X= 500m
A= -.676 ( because he was stopping the train)
braking force is -13520 N

Homework Equations


μkN=Fk

N means normal force in this case[/B]

The Attempt at a Solution


So at first I tried using the simple friction formula and tried isolating the coefficient of friction so that i would have ----------- μ=Nf---------- but i have everything except friction force. So i then thought from that I thought i can just divide a and m to get the force, which in turn is the friction force. Overall i am not sure if this is correct because i thought you can just divide the breaking force and the mass for the friction force. It's either one or the other, although i am not completely sure :))))
 
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  • #2
In this problem, it's more about the Work done to the train to get it to come to a halt. First they give you the train's mass and velocity.
(Remember: Kinetic Energy http://www.sciweavers.org/upload/Tex2Img_1418868535/render.png [Broken] )

If we look at the the energy of the system, it goes to zero. As you've said before, there is a frictional force which acts on the system. This (frictional) Work must then equal the Kinetic Energy lost when braking the train.

Also, Work is equal to the force applied over a distance http://www.sciweavers.org/upload/Tex2Img_1418868266/render.png [Broken] .

I hope this helps point you in the right direction :)
 
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  • #3
Thegiver431 said:
i have everything except friction force
The braking force you (correctly) calculated is the friction force.
 
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Thank you for everybody that answered, I get it now :)
 
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I can provide a more detailed and accurate response to this problem. The coefficient of friction is a measure of the resistance between two surfaces in contact. In this case, it represents the resistance between the train and the tracks as the train is braking.

To calculate the coefficient of friction, we can use the formula μ = F/N, where μ is the coefficient of friction, F is the friction force, and N is the normal force. In this problem, we are given the braking force (-13520 N) and the mass of the train (20,000 kg). However, we also need to consider the normal force, which is the force perpendicular to the surface of contact between the train and the tracks.

To determine the normal force, we can use the formula N = mg, where m is the mass of the train and g is the acceleration due to gravity (9.8 m/s^2). Plugging in the values, we get N = (20000 kg)(9.8 m/s^2) = 196000 N.

Now we can plug in the values for F and N in the coefficient of friction formula to solve for μ. μ = (-13520 N)/196000 N = -0.069. This means that the coefficient of friction between the train and the tracks is approximately 0.069.

However, it's important to note that this value may not be entirely accurate as there are other factors that can affect the coefficient of friction, such as the condition of the tracks and the type of material used for the train wheels and tracks. Additionally, the braking force and distance may also affect the coefficient of friction. Further experimentation and data collection would be needed to determine a more precise value.
 

1. What is the coefficient of friction between a train and its tracks?

The coefficient of friction between a train and its tracks refers to the measure of the resistance to motion experienced by the train as it moves along the tracks. It is affected by various factors such as the weight and speed of the train, the condition of the tracks, and the materials used in the construction of both the train and the tracks.

2. How is the coefficient of friction between a train and its tracks calculated?

The coefficient of friction can be calculated by dividing the force required to keep a train moving by the weight of the train. This value is then compared to the force required to start the train moving, which is known as the static friction coefficient. The average of these two values is used as the coefficient of friction between the train and its tracks.

3. What is the relationship between the coefficient of friction and the speed of the train?

The coefficient of friction is directly related to the speed of the train. As the speed of the train increases, the coefficient of friction decreases. This is because at higher speeds, the train has more momentum and is less affected by the resistance of the tracks.

4. Why is the coefficient of friction important for train safety?

The coefficient of friction is important for train safety as it affects the train's ability to brake and stop. If the coefficient of friction is too low, the train may have difficulty stopping, leading to accidents. It is also important to regularly monitor and maintain the coefficient of friction to ensure the safe operation of trains.

5. How can the coefficient of friction be improved for trains and tracks?

The coefficient of friction can be improved by using materials with better gripping properties, such as steel or rubber, for the train wheels and tracks. Regular maintenance and cleaning of the tracks can also help to improve the coefficient of friction. Additionally, reducing the weight and increasing the traction of the trains can also improve the coefficient of friction between the train and its tracks.

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