A uniform plank of length 2.00 m and mass 30.5 kg is supported by three ropes, with T1 having an angle of 40 degrees. Find the tension in each rope when a 710 N person is d = 0.650 m from the left end.

Question

anonymous · Answer

I'm assuming that the ropes are equally spaced out? 
Ok you want to write down all the forces and where in the plank these forces are occurring
the plank has a F= 30.5kg * 9.8m/s^2 = 299 N -j at x=1m
Force from T1y = sin(40) * T1  j  at x=0 m
Force from person F= 710 N -j   at x= .650 m
If everything is static you want to pick a privet point where there are a lot of forces.
I suggest you pick the center since you have two forces ( The plank and rope 2)
Now you are left with three forces. T1 T3 and the person.

Two of the forces are trying to spin the plank counter clock wise. T3 and the person while T1 is trying to rotate it clockwise. If it is in static then both forces have to equal. 
Fperson + T3 = T1 
but you also have to include the distance between them so you can't forget that but I'm a little rusty so I don't remember how to include it.