(Solved): N6M.11 Consider the situation shown below: a cart of mass \( \mathrm{m}_{\mathrm{A}} \) on an incli ...

N6M.11 Consider the situation shown below: a cart of mass \( \mathrm{m}_{\mathrm{A}} \) on an incline tilted at angle \( \theta \) is connected by a rope to a hanging weight of mass \( m_{B} \). Assume that \( m_{B} \) is large enough that the cart accelerates up the incline. Assume also that the cart's wheels are frictionless and that the pulley and rope are ideal. (a) Make a guess: will the tension on the rope be greater, less than, or equal to the weight of mass \( B \), or does the answer depend on the values of \( m_{A}, m_{B} \), and/or \( \theta \) ? Don't calculate anything yet. Reason qualitatively, and explain your thinking. (b) Draw what might be appropriate coordinate systems on your copy of the drawing, and explain why you drew them as you did. (c) Then, actually calculate \( F_{T} \) in terms of \( m_{A}, m_{B}, g \) and \( \theta \) using free-body diagrams based on these coordinate systems. Did you guess well in part (a)? Explain your thinking.