Engineering Dynamics: Solving Train Decel on Slope

[JaredPM]

Homework Statement

The 160-Mg train travels with a speed of 80 kmlh when it starts to climb the slope. If the engine exerts a traction force F of 1120 of the weight of the train and the rolling resistance F D is equal to 1/500 of the weight of the train, determine the deceleration of the train. slope is y=1 and x=10

****See attached files for picture.

Homework Equations

I summed the forces in the x and y directions because it is going up a slope.

The Attempt at a Solution

the solution I keep getting is in the right direction, but is 1.0m/s^2 off. i.e. -1.5m/s^2 roughly.

 

[JaredPM]

The engine exerts a traction force of F(1/20) of the weight of the train. Not 1120

 

[vela]

Show your work. Simply telling us the wrong answer you got isn't very helpful in seeing where you might have gone wrong.

 

[JaredPM]

∑F(x)=Fcos(5.7)-F(Resistance)cos(5.7)-F(Normal)cos(84.3)-mg*cos(84.3)=ma
∑F(y)=Fsin(5.7)-F(Resistance)sin(5.7)+F(Normal)sin(84.3)-mg*sin(84.3)=ma

I uploaded a free-body diagram.

 

[vela]

Can you explain your reasoning behind the equations?

 

[JaredPM]

Well I wanted to prove that the axis didn't need to be rotated. It certainly makes things easier if you do, but I wanted to break everything down into components to get a better understanding of how all of the forces are represented in the problem by using vectors. I want a fool proof way to begin dynamics. I did the above equation way wrong. I didn't give acceleration components for x or y most importantly.

I'm just trying to find a common approach to problems. Pulleys are different.