Forces Question

[S_100]

On the left is a diagram of a parachute delivering boxes and B. Parachute (top part) is subject to air resistance of 600N. Parachute has mass 10kg and is subject to air resistance 600N
Box A has a mass of 50 kg and is subject to air resistance of 300N. Box B subject to 400N air resistance. Ropes between boxes and parachute are light and inextensible. Given that parachute and boxes are moving at constant speed find the tensions of the two ropes and mass of box B.

I am confused about what the force diagrams would be for the parachute, box A and box B

T_AP = Tension acting on A directed to P
T_BA = Tension acting on B directed to A

I considered the forces acting on a parachute , P, to be :


10g - 600 - T_AP = 0
* T_AP = -502


At B:

50g - 300- T_AP-T_BA = 0
50g - 300- T_AP = T_BA
50g-300 - (-502) = T_BA


but the last part of my method is wrong as the answer for T_BA , as it should be T_BA = 50g-300 - 502 NOT

50g-300 - (-502) = T_BA .

and Tension T_AP = 502 N not -502.

So where Have I gone wrong in signs and why? and secondly I think I have considered wrong forces acting on P and A, I considered T_AP to be acting upwards on P as shown on the equation of motion *. Is this wrong? Is it an equal and opposite force to the tension of the string acting on Parachute P? Likewise an opposite and equal reaction to the tension of the string acting on A due to B?

 

[skeeter]

using [MATH]g = 9.8 \, m/s^2[/MATH] (g = 10 would make the arithmetic easier),
[MATH]T_1 [/MATH]= tension between parachute and box A,
[MATH]T_2[/MATH] = tension between boxes A and B

Since [MATH]F_{net}=0 [/MATH] on each mass in the system, note that each initial equation is in the scalar form
(magnitude of forces acting up) = (magnitude of forces acting down)

forces acting on the parachute are in equilibrium
[MATH]R_p = 10g + T_1 \implies T_1 = R_p - 10g = 600 - 98 = 502 \, N[/MATH]
forces acting on box A are in equilibrium ...
[MATH]T_1 + R_A = T_2 + 50g \implies T_2 = T_1 + R_A - 50g = 502 + 300 - 490 = 312 \, N[/MATH]
forces acting on box B are in equilibrium ...
[MATH]T_2 + R_B = Mg \implies 312 + 500 = Mg \implies M \approx 83 \, kg[/MATH]