# How can a train locomotive generate enough traction to pull all the coaches?

Sorry for posting what may be an obvious question but we just learning about friction at school and my teacher couldn't explain well enough to me and I would appreciate your inputs.

Consider the following 3 cases:

1) A load of mass $m_2$ lies on a surface. The coefficient of friction between the load and the ground is $\mu$. You need to exert a force $F=\mu\cdot m_2\cdot g$ to pull the load, right?

2) A driver, e.g. locomotive of mass $m_1$ sits on the same surface and has the same coefficient of friction $\mu$ to it. The maximum force that this can exert is $\mu\cdot m_1\cdot g$, right?

3) Now, how can the locomotive pull the load at all? After all, it can just about pull itself? Now, I know that locomotives are able to pull their loads without issues. I mean, I am not getting some important concept here. Does the maximum traction that a locomotive can achieve increase if we hang a large load at it's back? That seems counterintuitive to me.

I would appreciate your help in understanding this. And thanks for your patience with a physics newbie.

Regards, Victor

When the train pulls the carriages their wheels are rolling not sliding. That means the coefficient of friction of the carriage wheels with the rails is not relevant. The engine just has to be able to produce enough force to overcome whatever drag exists in the carriage axles and wheel bearings.

• I'd add that the coefficient of friction between the locomotive wheels and the rails does matter - if it is too low, the wheels will slip instead of rolling. Feb 14 '13 at 18:10

yes the question is right.how can the locomotive pull the load at all? i don't know exactly about working of the locomotive ,but as per my knowledge there may be some arrangement like hydraulic compressor , as in road rollers used to compress roads. hence to produce traction on railway tracks ,may be used , here Newton's third law of motion is applied"every action there is equal and opposite reaction".

• Are you saying that the wheels would 'squeeze' the rails as they turned to increase friction? Jan 17 '14 at 8:30

The locomotive connects the bogies well above the center line of the loco wheel. When the loco pulls the frictional force (rolling) times the bogies total weight makes the rear wheels of loco to exert more vertical force (due to moment arm) and this adds up to the loco dead weight. The pulling frictional force of loco becomes thus more than the total bogies weight times rolling friction. This makes loco to pull the bogies without slip. Also when the loco starts it gives a jerk while pulling, this contributes to rolling contact friction.