How Does Wheelchair Tension Affect Stability in a Moving Subway?

[Seung Lee]

Homework Statement

So for a project, we decided to do tension strings that would be attached to a wheelchair inside a subway so that when the subway decelerates or accelerates, the wheelchair wouldn't move.
However, due to our inexperience we used only the wheel and solved for equations.
If I'm not mistaken when the subway is deccelerating, the force (ma) is applied to the left, the friction force would also be to the left (since it's movement would keep going right due to inertia) and the Tension would go to the right, even if the tension cables are attached to the left.
Something like it was attached
So what we wanted to find was what was the Tension force necessary so that the wheel wouldn't move.
uk = 0.20
radius = 0.3048m
mass = 89.67
acceleration = +- 1.5m/s^2
Since I can't seem to attach any file
Tension ->
Normal would be going up ^
mg would be going down v
and Force + friction force would be going to the left <-

Homework Equations

Sum of forces in x: T - F - f = 0
Sum of forces in y:N - mg = 0
Torque force = r x F
Sum of torques??

The Attempt at a Solution

Normal force = 878.766
Friction force = 175.752
Applied force = 134.505
Torque force = 0.3048 * 175.752 * sin 90 = 53.5692

The problem is that I am not sure at all on how to use the torque force or if I am supposed to use this in a sum of torques equation etc.

 

[haruspex]

tension strings that would be attached to a wheelchair inside a subway so that when the subway decelerates or accelerates, the wheelchair wouldn't move.

So the wheelchair is facing along the carriage (or the opposite direction), not across?
Where and how are the strings attached? Horizontally at the tops of the wheels?

However, due to our inexperience we used only the wheel and solved for equations.

I don't know what you are saying there.

If I'm not mistaken when the subway is deccelerating, the force (ma) is applied to the left, the friction force would also be to the left (since it's movement would keep going right due to inertia) and the Tension would go to the right, even if the tension cables are attached to the left.

You first need to say which way the decelerating carriage is moving, in your mental image. Sounds like it's to the right.
What force is applied 'to the left', other than friction and the tension? Is this a fictional 'inertial' force in the frame of reference of the decelerating carriage?
Where exactly is this friction?
Tension goes both ways, so whether it's to the left or to the right depends on which of the two objects it's attached to is under consideration.

Since I can't seem to attach any file

How about describing the set up in more detail, assigning labels to points (e.g. O for centre of wheel etc.)?

The problem is that I am not sure at all on how to use the torque force or if I am supposed to use this in a sum of torques equation etc.

Depending on the set-up, torque could lead to the wheelchair toppling, so it may be important.