What is the correct force exerted by the seat in a pulley and force problem?

[kristen151027]

Here's the question:
A 612 N person is sitting in a 16.0 N seat with one end of a massless rope attached to the seat. The rope runs over an ideal pulley, and the other end of it is in the person's hand. The person pulls the loose end of the rope with a force of 348 N.

The problems asks to determine the acceleration of the person (1.06 m/s^2) and the force that the seat exerts on the person.

I found the force exerted by the seat on the person to be 332 N (348 N - 16.0 N), but that is not the correct answer. What am I missing?

 

[Doc Al]

Start by figuring out the acceleration of "seat + person". What forces act on that system? (Hint: What force does the rope exert on that system? How many places does the rope attach?)

 

[kristen151027]

Got it.
The forces exerted on the person are the tension of the rope in the upward direction, the force of the seat in the upward direction, and its weight (mg) in the downward direction. So,

T + F_seat + (-mg) = ma
348 N + F_seat - 612 N = (62.45 kg)(1.06 m/s^2)
F_seat = 330 N

Thanks!