Relationship between normal force and sum of the force in elevator problem

[516aldnsdhfl]

Homework Statement

A 80.8 kg man inside a 40.0 kg dumb-waiter pulls down on the rope. At that moment the scale on which he is standing reads 200N. Determine the elevator's acceleration
(basically the man is inside the elevator pulling a rope that goes around the pulley, which makes the elevator move upward)

Homework Equations

Fnet=ma

The Attempt at a Solution

Man:
80a= -T-200+784
Elevator:
40a=T+592

I keep getting wrong answer. The answer key says 0.2 m/s^2 upward.
And I really don't know why the normal force of the man is supposed to be
the net force of the man.
Thank you in advance!

 

[chrisphd]

Forces Acting on Man are the elevator pushing the man upwards and Tension in the rope pulling the man upwards because he is pulling the rope, you can think of the rope pulling him up. Also gravity force is 800 assuming g=9.8. The tension force is positive because it is pulling him up, the elevator force (200N) is positive as it is pushing him up and the gravity force is negative as it is pulling him down.

Therefore, Forces Acting on Man
80a = T + 200 - 784
Therefore re-arranging gives,
T = 80a + 584 (1)

Also three forces are acting on the elevator. The elevator is being pushed down by 200 N by the man standing on it, and the elevator is also being pulled up with tension T and being pulled down by 400 N due to gravity.
So,
40a = T - 200 - 392 (2)

Substitute (1) into (2) gives,
40a = 80a +584 - 200 - 392
Re-arranging gives,
40a = 8
a = 0.2m/s/s

 

[516aldnsdhfl]

Thank you for responding me!
But when dealing with pulley,
the directions of the ropes are supposed to be
opposite no? Or it could be making them the same charges..im just confused..

 

[chrisphd]

It sometimes requires a lot of thought to work out what direction the force is, that is acting on the body. Consider the forces on the elevator. The force of gravity is clearly downward, so that is negative. The rope is pulling the elevator upwards, so the Tension must be positive. The man is pushing the elevator downwards with his feat, so 200N is negative on the elevator.

Consider the man. The man is being pulled downwards by gravity, so gravity is negative. He is being pushed upwards by the elevator, so the 200N is positive. We also need the force the rope is exerting on the man. To do this, we know the man is exerting a force on the rope by pulling it down, so by Newton's 3rd law, the rope is exerting a force on the man pulling him upwards, so the Tension is pulling the man upwards and is positive.

The fact the rope is attached to a pulley does not change these fundamental equations. All it means is that the Tension in the rope pulling the man up has the same value as the tension pulling the lift up.

 

[516aldnsdhfl]

Thank you so much! your responses help me to understand it
very clearly now! Thank you for your time!