Solve Newton Applications: Find Acceleration of 1, 2, 3kg Masses

[rokas]

Homework Statement

Find the acceleration of the masses based on the figure below.

m1 = 1kg
m2 = 2kg
m3 = 3kg

Homework Equations

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The Attempt at a Solution

I am completely lost, I've tried thinking and thinking over and over again about this problem,
wouldn't the acceleration be 0 since m1 and m2 are on one side and m3 is on the other side, and both sides have 3kg?
I've attached an image of the drawing which you must see in order to understand the problem, could someone point me to the right direction?

Appreciated.

 

[TagutoAza]

It'd be best to think of the problem in terms of energy. Even though both sides have the same masses, m3 has gravitational potential energy. Assuming it is a massless and frictionless pulley, you can look at the masses as one big system (the advantage of that being all the internal tensions cancel out) and draw a simple force diagram. Hope this helps!

 

[rokas]

I see... I still have no idea how to set up an equation or find acceleration...
I can find weight of m3 which is (3)(9.81) = 29.43. I can find normal forces of m1 and m2. But I'm clueless..

 

[TagutoAza]

As I said earlier, it's best to look at the whole thing as one system with mass of 1+2+3 or 6kg total.

Now think about the problem this way, there are essentially 2 directions the system can go in. Left and right, right is pulled by the gravitational force of the m3 (I know it's a bit weird to think of it this way since the force is going down, but you can think of it as a general direction). Now what's countering force going to the left? None! Therefore the gravitational force of m3 would actually be your unbalanced force. You have the mass and the unbalanced force, calculating acceleration should be easy from there.

Also, the normal forces of the 2 blocks on the table are canceled out by the blocks' gravitational forces themselves, so they do not contribute to the unbalanced force, and therefore do not contribute to acceleration of the system.

 

[rokas]

Wouldn't their acceleration be 9.81 then?

 

[TagutoAza]

Newton's 2nd law: F=ma

Some rearrangement yield a=F/m

The total mass of the system is 6kg.

The unbalanced force is defined by the gravitational force of m3, or 9.8(3)=29.4N

>__> hope that's obvious enough. The acceleration in this case is not simply the gravitational acceleration, but rather the relationship between the unbalanced force and the mass of the system.

 

[rokas]

TagutoAza, I'm really sorry that I don't comprehend as fast as you wish. I try :/. I really want to learn. So would I use the 29.4N as F and mass of a box in m to find a in the formula, a=F/m?

If so, then m1 = 29.4 m/s2 ; m2 = 14.7 m/s2 ; m3 = 9.8 m/s2

 

[TagutoAza]

It's quite alright. Not everyone learn at the same pace. Here's something to think about, all the boxes are linked together with strings, so naturally the whole thing has to move at the same pace. In another word, all the masses must have the same acceleration!

Is it possible that the boxes would be accelerating at different rate when they're all moving together as one? Absolutely not! That's the advantage of thinking about all the masses as one big system, you can essentially treat the 3 boxes as one big box.

Since we're looking at the masses all together, imagine that the 29.4N is pulling not only on m3, but rather the whole thing, or m1+m2+m3. In essence the 29.4N is the unbalanced force for the whole system. Since the 29.4N is acting on the whole system, the mass you should use is the total mass. And the acceleration that results would apply to all 3 masses.

 

[rokas]

Thanks. I understand now.

 

[kim032688]

help pls i need some help to this question:if the mass is 1 g and the force is 1dyn the acceleration is what?

b.)if weight is 320lbs and the force is 1lb what is the acceleration?
kindly reply pls..