"A 60kg student lifts herself from rest to a speed of 1.5m/s in 2.1s. The chair has a mass of 35kg."
All information is included in the accompanying image. In short, it is a basic kinematic and dynamic equation. Currently, we are only working on problems that involve constant acceleration or zero acceleration. Anyway, the book only gives one answer to one part of the problem, and it states that the force of the rope is 500N, while I'm getting ~998N as can be seen in the image below. I am at a complete loss as to where I'm going wrong. Hopefully, my writing is legible enough for you to understand what I did.
Also, though I know I'd need to indicate position on my force diagrams, this isn't homework, just practice for an exam this Monday. I was wondering though if the chair needs a force for both gravity and the student since both are acting on it? If so, did I label it right? Our instructor never showed us how to label multiple forces acting on an object in one direction yet.
The only equations I am concerned about are the ones involving the dynamics. I feel I have the kinematics down sound. However, I am not sure of how to go about setting up the dynamics for this problem to solve for the force of the rope?
The Attempt at a Solution
Well, here is what I was doing:
1) Setting the rope as a positive force in the equation
2) Calculated the gravitational force of the student to be 588N (60kg*9.8m/s^2)
3) Calculated the gravitational force of the chair to be 343N (35kg*9.8m/s^2)
4) Set up my dynamic equation as:
F(rope) - F(student) - F(chair) = [m(chair) + m(student)] * .71 (rate of acceleration)
F(rope) - 588N - 343N = 95 * .71
F(rope) = 998.45N
Since the answer the solution page had for the force of the rope was 500N, I know something is wrong here, but I have no clue what?