A block with mass m1 = 9.2 kg is on an incline with an angle θ = 25.0° with respect to the horizontal. For the first question there is no friction between the incline and the block.
The coefficient of static friction was deterimined to be μ = .121
The premise of this question is that there was a spring holding the box up(the spring only exerting force in the X direction), but this spring was replaced by a STRING that is parallel to the horizontal, thus making a 25° angle with the incline.
Word for word, it is:
The spring is replaced with a massless rope that pulls horizontally to prevent the block from moving. What is the tension in the rope?
Fgx = mgsin(theta)
Fgy = mgcos(theta)
Fty = Ftsin(theta)
Ftx = Ftcos(theta)
Ff = μN
N = mg + Fty
The Attempt at a Solution
This problem has been frustrating me a lot, I've probably been stuck for hours on this one part on my already done homework... I just want to know how it's done because I'm definitely not going to be able to get credit at this point...
I've figured that Ff = 9.886 + μ(Fty) and so the force of friction is dependent on the tension force in the Y direction. Also, the tension force is dependent on the force of friction because Ftx = Fgx - Ff. It seems impossible for me because every time I try to setup a systems of equations, I end up with 0 = 0, which doesn't really help me. I've tried dozens of approaches, this one seems to be the closest because it factors in the tension in the Y direction into the normal force, which incorporates into the frictional force, but I can't figure it out.
A solution would be greatly appreciated.