ATTWOOD'S MACHINE (rope + pully)

[twenty5]

Homework Statement

Determine the force of gravity acting on the masses (we want to end up with 9.8m/s²---> My situation : A rope with 2 different masses hanging on each side, is held by a pulley. The heavier mass falls towards one end. (teacher said something about the mass having to cancel out afterwards) or so.

Homework Equations

d=v₁t +1/2at²
I think we can use Newton's second law, F=ma

t=0.9s
d=0.36m
v₁=0m/s

The Attempt at a Solution

I used d=v₁t +1/2at² and got acceleration which came out to be .889m/s²

I was wondering what steps I can take now

 

[Doc Al]

How does the measured acceleration relate to the acceleration due to gravity (g)?

You'll need to apply Newton's laws to analyze the system. Apply F = ma to each mass.

 

[twenty5]

How does the measured acceleration relate to the acceleration due to gravity (g)?

You'll need to apply Newton's laws to analyze the system. Apply F = ma to each mass.

awesome ^^ i just tried that juuust right before you replied haha thanks Now I know I am sort of on the right track^^

 

[twenty5]

ok I am stuck again xD

 

[Doc Al]

Show exactly what you did and where you got stuck.

 

[twenty5]

Show exactly what you did and where you got stuck.

ok So,
step 1:
d = v₁t +1/2at²
got acceleration = .889m/s²

Mass A:

F_A=ma
F_A=0.889a

Mass B:
F_B=ma
F_B=0.889a

I got stuck right there, like what can I do with it? can I find net force because If I subtract F_A and F_b, it'd be 0N O_O, but since I am 100% sure that the Net force isn't 0, what do I do? because Newtons second law states that, if the object is at rest, or at a constant velocity, the net force is 0. but the mass is acceleration towards the floor =P so it cannot be 0

 

[twenty5]

ehhh... anything? I am still stuck there lol...been working on it and still working on it ^^

 

[Doc Al]

You must first identify the forces acting on each mass, find the net force on each (symbolically), and then apply Newton's 2nd law (∑F = ma) to each. You'll get two equations (one for each mass) which you will combine.

 

[Delphi51]

I don't think you can finish it without knowing something about the masses.
The wording is inconsistent, too - it asks for a force, then says it should have units of acceleration. Could you check the question again and make sure it has been copied word for word?

 

[Doc Al]

Also:

ok So,
step 1:
d = v₁t +1/2at²
got acceleration = .889m/s²

This makes sense, assuming you solved for the acceleration correctly.

Mass A:

F_A=ma
F_A=0.889a

Mass B:
F_B=ma
F_B=0.889a

But I don't know what you're doing here. Each mass is different, so call them m1 and m2. Your equations will look something like:

∑F(on m1) = m1*a
∑F(on m2) = m2*a

Note that if m1 has an acceleration of a downward, then m2 must have an acceleration of a upward.

 

[twenty5]

MMMM, i just found out that we can use a value for mass...

m1 = .1kg
m2 = .2kg
and now I need to figure out how to get g = 9.8

 

[Delphi51]

Oh, now you can do it knowing the masses!

Sum of forces = ma, where m is the total mass.
Put in an mg for each force.

 

[twenty5]

ok I'll try that ^^

 

[twenty5]

ok I got... for the sum of forces is the following...

F_A= mg
F_A= .1g N

F_B= mg
F_B= .2g N

F_NET = F_B - F_A
F_NET = .1g N

F_{sum of forces} = .3g
.1g = .3g?

and now I don't know how this will get me to 9.8 ^^

mmmmmmmmmm

I also tried doing...

F_{total force} = ma, where I subbed in the a that I obtained from before...

0.1g = 0.3*0.889
g = 2.6m/s²...

But If I heard the teacher correctly, I believe I heard I'm supposed to get 9.8 or something lol

 

[Delphi51]

sum of forces = ma
.2g - .1g = .3*0.889
you can easily find the ACCELERATION of gravity.
No, it isn't working out to 9.8 as you would expect . . . on Earth.
Your question says find the FORCE of gravity - not sure what that means in this case since there are 2 different masses so two different forces of gravity. Check the wording again?

 

[twenty5]

sum of forces = ma
.2g - .1g = .3*0.889
you can easily find the ACCELERATION of gravity.
No, it isn't working out to 9.8 as you would expect . . . on Earth.
Your question says find the FORCE of gravity - not sure what that means in this case since there are 2 different masses so two different forces of gravity. Check the wording again?

sorry, the question just says

Attwood's Machine - Measure Acceleration, calculate g.

I also did the experiment physically too =P

I made a pulley with a rope and a mass on either end. and I just let it drop, timed it, and measured the distance =P

 

[Briggs]

Are you sure the values of time and distance are accurate? Given those two masses g should be equal to 3a.