Clamping Problem (Wedge & Friction)

[MITranger]

Yikes... I'm having a huge brain-fart and need help with some really embarrassingly basic physics for a real world engineering application.

Basically, I'm clamping a drafted part and I'm concerned that the wedging force will pop it out of the fixture. I'm trying to ultimately find F_z, or the force necessary to pull it out of the "vise" or UP as shown in the picture.

Variables:
Static Coefficient of Friction on Both Surfaces (mu) = ~0.5
Draft Angle (θ) = 0-15 deg (variable)
Clamping Force (F_x) = ? lbs.
Weight of Part (mg) = 1-10 lbs.

I think that's all the variables I need to define F_z, but I'm pretty sure my equation is way off and Newton would kill me:

F_z = [mg+2*mu*F_x*(cos(θ))^2]-[2*F_x*sin(θ)*cos(θ)]

Close? Wrong?

 

[LightHero]

Help me out here!No, your equation is not right. The force necessary to pull the part out of the vise is the sum of two forces: the weight of the part and the normal force of the clamping surface on the part. The normal force can be calculated using the static friction equation: F_z = μ*F_x + mg Where F_x is the clamping force, μ is the static coefficient of friction, and mg is the weight of the part. Hope this helps!