Coeffecient of train and the tracks?

[Thegiver431]

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

μ_kN=F_k

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 ))

 

[Narwhalest]

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 )

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 .

I hope this helps point you in the right direction :)

 

[haruspex]

i have everything except friction force

The braking force you (correctly) calculated is the friction force.

 

[Thegiver431]

Thank you for everybody that answered, I get it now :)

 

[HalfLostAndSearching]

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.