How Do You Calculate Tension and Acceleration in a Two-Mass Pulley System?

[xcgirl]

[SOLVED] Pulley w/ two hanging masses

Homework Statement

Two objects with masses of 2.00 kg and 6.00 kg are connected by a light string that passes over a frictionless pulley as in Figure P4.34.

(a) Determine the tension in the string.

(b) Determine the magnitude of the acceleration of each mass. (c) Determine the distance each mass will move in the first second of motion if both masses start from rest.

Homework Equations

f = ma
w = mg

The Attempt at a Solution

i tried to do this:

2(9.8) + 6(9.8)

this was wrong

i also tried to subtract them

this was wrong

can someone get me started?
]

 

[hotcommodity]

You have two different masses, so you'll need to draw two different free-body diagrams to represent the forces acting on each mass. Set up your coordinate system so that the acceleration will be along the same positive axis is each diagram. This should help you set up the equation for the net force for each mass. Keep in mind that the 6kg mass is heavier than the 2kg mass, so you'll know which way the masses are accelerating. Can you show me how you would set up the two net force equations?

 

[xcgirl]

well i thought that i should find the force of the 6kg mass and subtract the force of the 2kg mass to get the net force. so like:

m2(g) - m1(g) = F
9.8(6) - 9.8(2) = F
39.2 = F

 

[hotcommodity]

When you say "the force of" I assume you mean the force of the weight. The equation above doesn't take the tension into account. If I have a mass tied to a rope, I know that two forces are acting on that mass, the weight force, and the tension force. I also know that the sum of these two forces will be equal to the mass times the acceleration of the mass. Knowing this, I can write the equation for the net force on the mass. If I take upwards to be positive, I'd have:

Net Force = Tension Force - Weight Force = Mass(acceleration)

Since you have two masses, you'll have two of these equations. So you'll have two equations with two unknowns. Let me know if you're still confused.

 

[xcgirl]

there just doesn't seem to be enough information. all i have is those two masses. i don't see how i can get the tension from that.

 

[hotcommodity]

You get the tension by using Newton's Second Law for each mass. What are the two forces acting on the 6kg mass? What are the two forces acting on the 2kg mass?

 

[xcgirl]

6kg - gravity and the 2 kg mass

2kg- gravity and the 6 kg mass

so to find the tension you would do f = ma

but i feel like its more complicated than that

 

[hotcommodity]

So each mass has a weight force, but where does the tension act? I think you may be picturing situation wrong. It would look something like this:

http://www.hazemsakeek.com/Physics_Lectures/Mechanics/mechanicsimages/lectur4.gif

So the forces acting on each mass would look like this:

http://s62.photobucket.com/albums/h116/pepsi_in_a_can/?action=view&current=untitled8.jpg

Knowing this, how would you set up your two net force equations?

 

[xcgirl]

i think i got it now

m1g - T = m1a

T - m2g = m2a

so

6(9.8) - T = 5a

T- 2(9.8) = 2a

then i'll just solve for a in one of the equations and use substitution

Thanks for all the help!

 

[hotcommodity]

You've got it, excellent :)