Atwoods MAchine with two pulleys and three masses

[karabear1919]

Homework Statement

A system contains two pulleys, over the first pulley there is mass 3, m_3, on one end of the rope. the other end of that rope is connected to the second pully. Hung on the second pulley are mass 2, m_2, and mass 1, m_1. Find the acceleration constraint in terms of a_1 and the tension in the string of the second pulley.

Homework Equations

ma=Fnet

The Attempt at a Solution

the change in the string over pulley 1 causes a_3=.5*a_2 and a_2=a_1 (not sure?)
so a_1=2a_3?

 

[physics girl phd]

I would suggest first drawing free body diagrams for all the masses involved, then using those to find the net force on the masses (and relate the net force to accelerations of the objects using the equation you give). You'll get a number of equations that you'll just have to substitute into each other to find the relationship (constraint) you desire. Seeing those steps in more detail would be productive.

 

[thomate1]

First, it is important to clarify some terminology. The term "acceleration constraint" is not commonly used in physics. It is possible that the homework question is referring to the acceleration of the masses, in which case the equation should be ma = ΣF, where m is the mass and a is the acceleration. This equation states that the net force on an object is equal to its mass multiplied by its acceleration.

Now, to solve this problem, we can use Newton's second law of motion, which states that the net force on an object is equal to its mass multiplied by its acceleration. In this case, we have three masses, so we need to consider each one separately.

For mass 3 (m3), the only force acting on it is the tension in the rope, which is pulling it upwards. Therefore, we can write the equation as m3a3 = T, where T is the tension in the rope.

For mass 2 (m2), there are two forces acting on it: the tension in the rope pulling upwards, and the weight of the mass pulling downwards. Therefore, we can write the equation as m2a2 = T - m2g, where g is the acceleration due to gravity.

For mass 1 (m1), there are also two forces acting on it: the tension in the rope pulling upwards, and the weight of the mass pulling downwards. Therefore, we can write the equation as m1a1 = T - m1g.

We also know that the acceleration of mass 3 (a3) is equal to half the acceleration of mass 2 (a2), as they are connected by the same rope. So we can write a3 = 0.5a2.

Now we can solve for the unknown variables. First, we can substitute a3 = 0.5a2 into the equation for mass 3, giving m3(0.5a2) = T. This can be rearranged to solve for T: T = 0.5m3a2.

Next, we can substitute this expression for T into the equations for masses 2 and 1, giving m2a2 = 0.5m3a2 - m2g and m1a1 = 0.5m3a2 - m1g.

Finally, we can solve for a1 in terms of a2 by rearr