Solve 3 Mass, 3 Pulley Homework

[jkw]

Homework Statement

--------------
I I I = string
O O O = massless frictionless pulley
I II I
' O " . = mass 1
: : = mass 2
" = mass 3

Find acceleration of each mass.

Homework Equations

F=ma
conservation of String

The Attempt at a Solution

Tension is same
T-m1g = m1a1
2T-m2g = m2a2
T-m3g = m3a3

a1=a3=1/2a2 <- I am not sure how to use conservation of string... shouldn't a1 is equal to a3 because there are connected to same sting..
so my question is how to get relationship between/among accelerations

 

[azizlwl]

Homework Statement

--------------
I I I = string
O O O = massless frictionless pulley
I II I
' O " . = mass 1
: : = mass 2
" = mass 3

Find acceleration of each mass.

Homework Equations

F=ma
conservation of String

The Attempt at a Solution

Tension is same
T-m1g = m1a1
2T-m2g = m2a2
T-m3g = m3a3

a1=a3=1/2a2 <- I am not sure how to use conservation of string... shouldn't a1 is equal to a3 because there are connected to same sting..
so my question is how to get relationship between/among accelerations

Once you assume the direction, you have to be consistent with it.
I quess you assume m2 is going down.
Thus m2g is greater then 2T.

Add: There 3 possibilities of movement. m1 or m2 or m3 accelerating downward.

 

[rl.bhat]

Hoi jaw, welcome to PF.
When m2 moves through a distance x in tthe downward direction, how much m1 and m2 move in the upward direction?

 

[jkw]

If m2 move downward by x
Then should it be m1 move up by x/2 and m3 move up 1/2.
Since string is constant <length
a1+2a2+a3=o

Am I right?

 

[Nickie]

of different masses?

To find the relationship between the accelerations of the different masses, you can use the fact that the string is inextensible. This means that the length of the string remains constant, and therefore the displacement of all masses connected by the string must be the same.

Since the displacement is the same for all masses, the velocities of the masses must also be the same. This means that the accelerations of the masses must also be the same, since acceleration is the rate of change of velocity.

Therefore, the relationship between the accelerations of the masses is a1 = a2 = a3. This means that all three masses will have the same acceleration, and you can solve for this acceleration using the equations you have already written.