Solve 3 Mass, 3 Pulley Homework

In summary, the problem involves three masses connected by a string over a massless and frictionless pulley. Using the equations F=ma and conservation of string, the tension in the string is determined to be the same for all masses. From there, it is found that the acceleration of m1 and m3 are equal and half of the acceleration of m2. The relationship between the accelerations is given by a1+2a2+a3=0.
  • #1
jkw
2
0

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
 

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  • #2
jkw said:

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.
 
Last edited:
  • #3
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?
 
  • #4
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?
 
  • #5
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.
 

FAQ: Solve 3 Mass, 3 Pulley Homework

1. How do I determine the mass of each object in a 3-pulley system?

The mass of each object can be determined by using the equation F=ma, where F is the force applied, m is the mass, and a is the acceleration. This equation can be applied to each object in the system and the masses can be solved for.

2. What is the relationship between the number of pulleys and the force required to lift an object?

The more pulleys in a system, the less force is required to lift an object. This is due to the distribution of weight and the use of multiple ropes to lift the object, reducing the overall force needed for each individual pulley.

3. How does the angle of the ropes affect the forces in a 3-pulley system?

The angle of the ropes can affect the forces in a 3-pulley system by increasing or decreasing the mechanical advantage. A smaller angle will result in a greater mechanical advantage, requiring less force to lift the object, while a larger angle will decrease the mechanical advantage, requiring more force.

4. How can I calculate the tension in the ropes of a 3-pulley system?

The tension in the ropes can be calculated by using the equation T=mg, where T is the tension, m is the mass of the object, and g is the acceleration due to gravity. This equation can be applied to each rope in the system to determine the tension in each one.

5. How do I account for friction in a 3-pulley system?

To account for friction in a 3-pulley system, the coefficient of friction can be included in the calculations. This will affect the forces and accelerations in the system, as well as the overall mechanical advantage. Additionally, friction can be reduced by using lubricants or smoother ropes in the system.

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