How Is the Force Calculated for Two Masses on a 30 Degree Incline?

AI Thread Summary
The discussion focuses on calculating the force required to pull two masses (200 kg and 150 kg) up a 30-degree incline with a constant velocity, factoring in a coefficient of kinetic friction of 0.2. Participants clarify the need to include both masses in the calculations, leading to a total mass of 350 kg. They discuss the relevant equations, including the forces acting parallel and perpendicular to the incline, and the role of friction. The applied force (Fa) is defined as the force needed to overcome both gravitational pull and friction. The conversation emphasizes that knowing the velocity is unnecessary for solving the problem, as it serves only to validate the use of the kinetic friction coefficient.
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Two masses are being pulled up a 30 degree incline by a force F parallel to the incline. The velocity is constant and up the incline. The force is applied to a 200 kg mass and a string connects the 200 kg mass to a 150 kg mass. The coefficient of kinetic friction is 0.2. The force F = ?

So I drew a free body diagram, and it has F parallel to the inclined plane (Fx) and the normal force = Fy. There is mg, which is pointed directly down. The friction is pointed in the -Fx direction. I know F=uFn, I also know that Fx = mgcos(theta) and Fy = mgsin(theta). Do I include the 2nd mass in my calculations? I'm assuming I do, in which case the mass is 350 kg. If the velocity is constant, acceleration = 0. Do I need to find the velocity to solve this problem?
 
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I don't think you need to know the velocity. It is just there to justify using the kinetic friction coefficient for both masses.
 
That's what I thought, but I have no idea how to do this problem. I used the Fx equation I listed above but it doesn't include the friction coefficient.
 
draw a *FBD*

F_{y}=mg\times cos \phi

F_{x}=F_{A}-mg\times sin \phi + F_{f}

and F_{f}=\mu \times F_{N} = \mu \times mg\times cos \phi

therefore

F_{A}=mgsin\phi + \mu \times mg\times cos \phi
 
Thanks, Bright Wang. That helped a lot. The Fa you used in that equation, is that the parallel force?
 
applied force
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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