Tension in cables pulling a box

[oceanflavored]

Homework Statement

A 400-kg box is lifted vertically upward with constant velocity by means of two cables pulling at 40.0^o on either side of the vertical direction. What is the tension in each cable?

Homework Equations

Force = mass(acceleration)
Weight = mass(gravity)

The Attempt at a Solution

My free-body diagram had the two forces: one west of north, the other east of north; the normal force pointing in the upward vertical direction; and the weight pointing in the downward vertical direction.
Then, I reasoned that since the box was moving with constant velocity, the acceleration would be zero, meaning the net force would be zero:
So, net force = 2(F cos 40.0^o) + N - W = 0
The problem with this equation of mine is that my normal force and weight cancel out, leaving me with 2(F cos 40.0^o) = 0, which doesn't exactly give me an answer.

The book says the answer is 2560 N. Please tell me what I'm doing wrong :|
Thank you so much!

PS: All the people on this site are LIFESAVERS :) I'm pretty sure if I get a 100 on my test next Friday, it's because of all the people who keep answering my questions, so THANK YOU! :D

 

[ahmadmz]

You added a force that's not there. Since the box is being pulled by the strings, there is gravity downwards and the tensions on the strings that cancel it. So just get that extra force out and see if it works.

 

[oceanflavored]

Thank you so much :)

That did work, but I'm still confused, as to why there wouldn't be a normal force pointing upwards? I always thought that if weight is pointing downwards, there would always be the normal force (the reaction force) pointing upwards?? :|

 

[ahmadmz]

Well the normal force is a force perpendicular (normal) to the surface of contact. For example if the box was just sitting on the ground, then you would have a normal force equal to the weight of the box acting up.
In your question the box was being lifted up, so it's not touching the ground.

 

[oceanflavored]

GOT IT )))))))

Thank you SO SO SO SO much! :D