The figure above shows an 80 kilogram person standing on a 20 kilogram platform suspended by a rope passing over a stationary pulley that is free to rotate. The other end of the rope is held by the person. The masses of the rope and pulley are negligible. You may use g = 10 m/ s2. Assume that friction is negligible, and the parts of the rope shown remain vertical.
a. If the platform and the person are at rest, what is the tension in the rope?
My problem is that I'm not identifying the direction of the forces in the free body diagram.
On the left side of the pulley i have this: The Mg of the platform and the person doing down and the Tension of the rope going up. On the other side of the pulley I have the force of the person holding the rope down and the Tension of the rope up. (This is where I feel I'm wrong I just need an explanation if I am)
As result I get the T=1000N.
The Attempt at a Solution
I know the answer is T= 500 N because the equation is supposed to be 2T=1000N