banked tracks- mechanics question help? (1 Viewer)

[school4nerds]

Hey with a question "a train of mass m is moving with speed v around a curve of radius r banked at an angle theta. THe normal reaction between the rails and the wheels of the train is N, the lateral thrust (up the slope) is T and g is the acceleration due to gravity". I was trying to resolve forces and in the answers the horizontal resolving should be "Nsin(theta) - Tcos(theta)= (mv^2)/r

my question is how do you know the "minus" is supposed to be there??

 

[asianese]

In the horizontal direction,

Nsinx-Tcosx=ma=mv^2/r

You might have got your angles wrong in the triangles so as to confuse you. The orange is what you need to focus on! Opposite directions.