Help Midterm tomorrow Pulley, Newton's Laws Problem

[aatgomez]

1. Homework Statement
An object consists of 3 connected masses as seen in the figure. None of the surfaces have friction except the surface on m1 which has the coefficients μs=0.4 y μk=0.3.
What is the acceleration of each one of the masses?
It looks like the following image but m1 is the table and m2 is equal to m3 or the block that's hanging from the pulley of the table.

2. Homework Equations
∑Fx = m1a → τ - fk = m1a
∑Fy = 0 → n- m1g = 0
T= μkm1g+ m1a
∑Fy = m2a → m2g - T =m2a
m2g - (μkm1g+m1a) = m2a
a = m2 - μkm1/m1 + m2



3. The Attempt at a Solution
I got up to the finally equation but I can't figure out how to solve the equation without mass. Thanks!

 

[BvU]

Good luck with your test! Post is now incomprehensible, but what the heck.

 

[PhanthomJay]

The masses are equal , call them m. But your last equation solving for "a" has algebra errors. Correct your algebra...maybe you don't need to know m.
If I interpret your problem correctly, wording is confusing.

 

[Doc Al]

Followups here: https://www.physicsforums.com/showthread.php?p=4838835#post4838835

 

[HalfLostAndSearching]

I would recommend reviewing the fundamental concepts of Newton's Laws of Motion and pulley systems before attempting to solve this problem. It is important to understand the relationship between forces, mass, and acceleration in order to solve this type of problem.

To start, we can apply Newton's Second Law, 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 (m1, m2, and m3) connected by a pulley, so we need to consider the forces acting on each individual mass.

For m1, the only horizontal force is the tension (T) from the rope, which is equal to the force of friction (fk) acting in the opposite direction. We can set up the equation ∑Fx = m1a to solve for the acceleration of m1.

For m2 and m3, the only vertical force is the weight (mg) acting downwards, and the tension (T) from the rope acting upwards. We can set up the equation ∑Fy = m2a and ∑Fy = m3a to solve for the acceleration of m2 and m3, respectively.

Once we have these equations, we can substitute in the given values for the coefficients of friction (μs and μk) and the masses (m1, m2, and m3) to solve for the unknown accelerations.

It is also important to note that the masses are connected by a pulley, meaning that they will have the same acceleration. This allows us to set the two equations for m2 and m3 equal to each other and solve for the acceleration (a).

I hope this helps and good luck on your midterm tomorrow! Remember to review the fundamental concepts and take your time to carefully solve the problem.