Solving Tension in Wires for Fixed Plate

[Alex.malh]

Homework Statement

A plate is fixed to the ceiling by two wires and to the wall by a single wire.
The wall wire is cut. Calculate the tension in the two remaining wires.

mass = 800 kg
g = 10m/s²
Dimensions in sketch

Homework Equations

The Attempt at a Solution

Equations:
Ra*cos30 + Rb*cos30 = m*g + m*av
Ra*sin30 + Rb*sin30 = -m*ah
ah*sin30/cos30 = av

Solve to:
(Ra+Rb)=6928N
ah=-4.33m/s²
av=-2.5m/s²

But now I'm having troubles getting the individual wire tensions.
Any help is welcome.

Thank you.

 

[SteamKing]

You know the force of gravity acting on this plate, and you have calculated the horizontal and vertical accelerations the plate experiences when the horizontal string is cut.

The tensions in the vertical wires will be a combination of the static and dynamic forces acting on the plate. You can assume these forces act thru the center of gravity of the plate, the location of which is indicated in the sketch.

To calculate the dynamic forces: (Hint: F = ma)

 

[haruspex]

I'll offer a different hint: will the plate rotate?

 

[Alex.malh]

Thanks for the quick reply!
so i solved it to:
Ra= 1826N
Rb= 5102N

What i still don't get though is why av is negative?
I would expect the plate to have a downward acceleration with the same sign as gravity acc.
But now i solved it by having an upward acceleration.