Maximum acceleration of train

[Claus Berner]

Homework Statement

What is the maximum acceleration the train can achieve?

Engine effect=6500kW
μ(Friction Coefficient (between rails and wheels))=0.45
g=9.82N/kg
m(Train weight)=120,000kg
α=0

Homework Equations

F_μ=F_n*μ
Fn=cos(α)*m*g
a=F/m

The Attempt at a Solution

We've used the equations for objects, to determine the amount of force is needed to move. F>F_μ if the object is to move.

But for an object, a higher friction coefficient means the need for more force to pull. Therefore, a higher friction at constant force, means lower acceleration.
But for vehicles, a higher friction means a higher acceleration, because it can convert more of it's rotational energy to translational energy.

I asked my teacher, but he explained that when the train is moving the friction force, must be the same as the trains forward force. Therefore the maximum acceleration becomes, the friction force divided by mass. a=F_μ/m.

But in my head that's a very oversimplified explanation, i cannot see the correlation to rotational mechanics and the friction between rails and wheels. In my head the friction describes how much of the engine power can be converted to translational energy, and that the limit of the force is due to the fact that maybe if you use more force than the friction force, then the wheels will simply spin without grip.

I feel like I'm missing something which binds these things together, but my teacher refused to tell me, or he didn't know :/

 

[jbriggs444]

In my head the friction describes how much of the engine power can be converted to translational energy, and that the limit of the force is due to the fact that maybe if you use more force than the friction force, then the wheels will simply spin without grip.

Yes, if the engine turns the wheels more forcefully than the coefficient of static friction can support then the wheels will spin. Their "grip" on the rails is limited by the coefficient of static friction.

Once the wheels start slipping, they will not spin completely without grip. This is when the coefficient of kinetic (or "dynamic") friction comes into play. The force between slipping wheels and rails is limited by the coefficient of dynamic friction multiplied by the normal force. The coefficient of dynamic friction will not be larger than the coefficient of static friction. Accordingly, the force from dynamic friction will not be larger than the limiting force of static friction.

The maximum acceleration will be achieved when the wheels are being turned as forcefully as possible, just barely below the threshold of beginning to slip.

Note: In this problem, we are given only a "coefficient of friction". One can assume either that the coefficients of static and of dynamic friction are both 0.45 or that the coefficient of static friction is 0.45 and that the coefficient of dynamic friction is smaller. Both assumptions yield the same answer.