Free Body Diagrams: Static Equilibrium


by hunter007
Tags: body, diagrams, equilibrium, free, static
hunter007
hunter007 is offline
#1
Feb3-10, 09:30 PM
P: 3
1. The problem statement, all variables and given/known data

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.



2. Relevant equations

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

3. The attempt at a solution

Fx = Fcos20
Fy= Fsin20 - 5 kg

Am I even close?
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rl.bhat
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#2
Feb4-10, 03:00 AM
HW Helper
P: 4,442
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
hunter007 is offline
#3
Feb4-10, 10:54 AM
P: 3
Could you explain a little more on how to get a? Once I find that I could find F.

rl.bhat
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#4
Feb4-10, 11:26 AM
HW Helper
P: 4,442

Free Body Diagrams: Static Equilibrium


mg*sinθ = a*cosθ.
Find a.
hunter007
hunter007 is offline
#5
Feb4-10, 12:48 PM
P: 3
a = 5(9.8)*tan(30)
= 28.3

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

Did I do it right?
rl.bhat
rl.bhat is offline
#6
Feb4-10, 07:15 PM
HW Helper
P: 4,442
The given angle is 20 degrees.


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