Atwood's Machine - One mass and one force

[whoareyou]

Homework Statement

Homework Equations

ƩF_y = ma_y

The Attempt at a Solution

I'm unable to scan my work onto the computer, but I've gotten to the part where I this equation:

a_y = $\frac{F_A - F_{g_block}}{m_A + m_block}$

The problem is now, I have two unknowns ... F_A and m_A. This is where I'm stuck and I don't know if I missing something from before or ...

By the way, this is a question from the 2011 OAPT Physics Contest.

 

[gneill]

You are in a position to draw the FBD for the mass. Write the equation for the acceleration of the mass assuming some tension T is acting in the rope. You're given the acceleration, so T is...?

 

[whoareyou]

This is the work that I have.

I'm stuck here because the m in the equation is for the total mass of the system, but I don't have it. I tried doing something like:

but you still need to know F_A to get the mass, so I don't know what I'm doing wrong :(

 

[gneill]

The only mass that's moving is the one that's hanging on the rope. You have its weight.

 

[whoareyou]

Ok, I solved it --> F_A = 125N.

So basically, what I think I learned from this is that not all forces contribute to a mass / have a mass? I'm a little confused because F = ma, and m is mass, so ...

Normally, when we do normal questions like these, we have one mass on either side of the machine.

 

[gneill]

An external force, applied by unspecified means, has no mass associated with it.

An external force F applied to a given mass M provokes an acceleration A in that mass according to the relationship F = M*A. That's Newton's 2nd law.

Newton's 3rd law states that as a result of force F being applied to the mass, the mass will respond to that force with an equal and opposite force. This is the so-called reaction force, which is also therefore equal to M*A. This type of force is also what's known as an "inertial force" because it arises out of the fact that the object has inertia and "resists" changes in motion (Newton's 1st law).

 

[PhanthomJay]

Ok, I solved it --> F_A = 125N.

No, you are forgetting that the block accelerates upward.

 

[whoareyou]

Is the answer wrong or are you just being picky about no direction when I state my force vector?

 

[PhanthomJay]

Is the answer wrong or are you just being picky about no direction when I state my force vector?

Your answer is incorrect.

 

[whoareyou]

Oops, I think I messed up a sign in my analysis somewhere. I re-did it, hopefully this is the right answer:

 

[lightgrav]

yes.