Free Body Diagrams: Static Equilibrium

[hunter007]

Homework Statement

Blocks A & B each have mass 5kg, and all contact surfaces are frictionless.

Determine the force F needed to keep the blocks in static equilibrium, and the forces on all contact surfaces.

Homework Equations

I know I need to find where Fx= 0 and where Fy= 0.

The Attempt at a Solution

Fx = Fcos20
Fy= Fsin20 - 5 kg

Am I even close?

 

[rl.bhat]

Hi hunter007, welcome to PF.
When you apply force F to the systemis, the acceleration of the system is
a = F/(Ma + Mb)...(1). It is parallel to the ground.
Since block A is not attached to the block B, due the inertia, it will experience an equal and opposite acceleration. The block A will remain rest when component of the weight of the block A balances the component of the acceleration.
Equate these components and find a. Put this value in equation(1) to get F.

 

[hunter007]

Could you explain a little more on how to get a? Once I find that I could find F.

 

[rl.bhat]

mg*sinθ = a*cosθ.
Find a.

 

[hunter007]

a = 5(9.8)*tan(30)
= 28.3

F= 28.3(5+5) = 283 N.

Did I do it right?

 

[rl.bhat]

The given angle is 20 degrees.