What is the Mass of the Suspended Block in a Two-Block Pulley System?

[xmflea]

A light rope is attached to a block of mass 4.10kg that rests on a horizontal, frictionless surface. The horizontal rope passes over a frictionless, massless pulley and a block of mass is suspended from the other end. When the blocks are released, the tension in the rope is 11.0N

ok so i was able to find the acceleration of either block, which was 2.8 m/s^2
but them I am asked to find the mass of the hanging block

what i did so far was take 11.0N and divided it by 2.8m/s^2 since both blocks are supposed to have the same acceleration. but i get the same mass as the block on the table, which is a wrong answer.. so then i took 11.0N and divided it by 9.8, and i still get a wrong answer. how else am i supposed to approach this?

 

[hage567]

You must consider ALL of the forces on the mass. You have the tension, and what else? There is one more. You need to use both of these in your F = ma equation.

 

[xmflea]

uhmm, all i have is the 2.68 accleration, the mass of the block on the table which is 4.1 and the 11.0 tension... oh and 9.8 gravity ... still don't know where to go.

 

[hage567]

Think of only the forces on the hanging block. Yes, you need gravity.

 

[xmflea]

the only thing i can think of to find the mass of the hanging block is taking the tension 11.0 and dividing it by gravity. how am i supposed to think of forces on the hanging block if i don't even know its mass? unless there is some relation of the 2.6 accleration that is supposed to be on both blocks.

 

[hage567]

You are trying to find the mass! Think of Newton's second law. The net force is equal to the acceleration times the mass. So, you have two forces acting on the hanging mass (draw a diagram). The tension, and gravity (the weight of the mass). The tension is acting in the upwards direction, gravity is acting downwards. So write an expression for Newton's second law based on this. The only thing you don't know in this expression is the mass. What you need to do is isolate and solve for it.

 

[xmflea]

ok i know I am dumb. so what i did was.. took the tension 11.0 and subtracted gravity from it 9.8 and got 1.2 and then plugged this into F=ma to get 1.2=m x 2.68, and solved for m to get 0.44, which is still not right.

 

[hage567]

subtracted gravity from it 9.8

But weight is not "9.8" (weight is a force, "9.8" is not). It is m*g, where g is 9.8. So if you subtract m*g from T (tension) and set that equal to m*a, what does m work out to be? Leave things in terms of the letters until the last step, that might help you keep track of what you have.

 

[xmflea]

ok so i subtract m*g from T and set it equal to ma. but, where am i supposed to get m from in the first place in order do to m*g so that i can subtract that from T and plug it into ma, the ONLY m that i have is 4.1

 

[hage567]

You are solving for m of the hanging block! Of course you don't know it! The mass of the other block is irrelevant. Rearrange your equation that you described to get all m terms on one side so you can solve for it. It's just algebra from here.

 

[xmflea]

ok so i did... 11.0 - 9.8m = 2.68m, that is how i arranged the equation. because i am supposed to take m*g and subtract that from tension, and set it equal to m*a which is 2.68 m. i moved 9.8m over to the other side to get 11.0=12.48m then solve for m to get .88, which is a wrong answer.

 

[hage567]

OK, I know what's wrong. I should have looked harder at the first part of the question.
Since the block will move downwards, it will accelerate it that direction, so you can choose to take that direction as positive. So you have the weight downwards and the tension upwards. So in this case you get mg - T = ma. If you solve for it this time you should get the right answer.

 

[xmflea]

sweet, got the right answer. thanks for all your time, i know i was difficult to work with.