1. ## A Moving Train

A train is traveling up a 4.4 incline at a speed of 3.10 when the last car breaks free and begins to coast without friction. How long does it take for the last car to come to rest momentarily?

The way I approached it that I reduced the speed to its x and y components. But I don't know what kinematic equations to use that relate the those two dimensions. Help?

2. ## Re: A Moving Train

Originally Posted by Manni
A train is traveling up a 4.4 incline at a speed of 3.10 when the last car breaks free and begins to coast without friction. How long does it take for the last car to come to rest momentarily?

The way I approached it that I reduced the speed to its x and y components. But I don't know what kinematic equations to use that relate the those two dimensions. Help?
The only forces acting on the car are that of gravity and the normal reaction from the rails. The normal reaction will be balanced by the component of the gravitational force normal to the incline, leaving the only effective force on the car the component of the gravitational force acting along the incline.

So start by resolving the gravitational force into components parallel to the incline and normal to it.

Let $\displaystyle f_p$ denote the parallel component (I will assume forces/accelerations etc in the plane of the incline as positive in the upward direction) then the acceleration. The the equations of motion in the plane of the incline are:

$\displaystyle a=f_p/m$

and $\displaystyle v(0)=3.10$

CB

3. ## Re: A Moving Train

How would I equate the force of gravity if I'm not given a mass nor acceleration?

4. ## Re: A Moving Train

Originally Posted by Manni
How would I equate the force of gravity if I'm not given a mass nor acceleration?
The acceleration due to gravity is 9.81 m/s^2, and the mass will cancel out.

CB

5. ## Re: A Moving Train

Oh right! I forgot the masses would cancel out. Thanks a lot!