Help with 3 objects/masses connected by string over frictionless pulley?

In summary, the problem involves three masses connected by light strings on a frictionless pulley. Using the equations SigmaF=ma and mg=fg, the downward acceleration of the m2 mass is found to be -1.413 m/s^2. However, after trying different equations and approaches, the correct solution is found to be 1.413 m/s^2 using the equation A= [(M1-M2)/(M1+M2)] * G. The provided diagram in the conversation helped in solving the problem.
  • #1
miamirulz29
62
0

Homework Statement


Three masses connected by light strings are shown in the figure below (I will try my best in describing the figure):
There is light, frictionless pulley with two masses, M2 and M3, on the left and one mass, M1, on the right. They are all connected by light strings. Given m1 = 10 kg, m2 = 7.48 kg, m3 = 8.01 kg, and g = 9.8 m/s2. The acceleration of gravity is 9.8 m/s2 . Find the downward acceleration of m2 mass. answer in units of m/s^2


Homework Equations


SigmaF= ma
mg=fg

The Attempt at a Solution



I drew three separate free body diagrams for each of the masses.
For M1:
Ft-MG=MA
Ft-98=10a

For M2:
MG-Ft=MA
7.48(9.8)-Ft=7.48a
73.304-Ft=7.48a

So I combined the two equations and got -1.413 m/s^2. I though because it is downward, I didn't need the negative, so I put in UT, 1.413, it was wrong, I also put -1.413, it was also wrong. Then I tried using M3 and combined the acceleration of M3 and M2, which was 8.387, which is also wrong. Then I read on another thread that you can use the equation:
A= [(M1-M2)/(M1+M2)] * G. I got 1.413. I honestly don't know what to do at this point, can somebody please help me. Thanks in advance.
 
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  • #2
Anybody? Please?
 
  • #3
miamirulz29 said:
Anybody? Please?

If you could post the diagram that would help a lot so we would know where to start...
 
  • #4
Diagram posted. It is on the last page, number 018 (part 1of 3).
 

Attachments

  • problem_pdf.pdf
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  • #5
Please can anybody help? I even posted the diagram.
 
  • #6
Nevermind, figured it out.
 

1. What is the purpose of using a frictionless pulley in this scenario?

The purpose of using a frictionless pulley in this scenario is to eliminate the effects of friction, allowing for a more simplified and accurate analysis of the forces acting on the objects connected by the string.

2. How does the mass of the objects affect the system?

The mass of the objects affects the system by determining the magnitude of the forces acting on them. Heavier objects will experience a greater force due to their weight, while lighter objects will experience a smaller force.

3. What is the relationship between the acceleration of the objects and the tension in the string?

The acceleration of the objects is directly related to the tension in the string. As the tension increases, the objects will experience a greater acceleration, and vice versa.

4. How does changing the angle of the strings affect the system?

Changing the angle of the strings will affect the system by altering the direction of the forces acting on the objects. This can result in a change in the acceleration and tension in the string.

5. What is the significance of the objects being connected by a string?

The string serves as a medium for the transfer of forces between the objects. It allows for a simplified analysis of the system and can help determine the overall motion and acceleration of the objects.

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