Finding acceleration of a three-object pulley system

In summary, three blocks connected on a rough table with coefficients of friction and masses given are asked to find the magnitude of acceleration for each block. The equations and steps to solve for the acceleration are provided, but a sign error may have been made in the acceleration of m3.
  • #1
kathyt.25
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Homework Statement


"Three blocks are connected on a table as shown in the figure below.
http://i4.photobucket.com/albums/y111/kathy_felldown/sb-pic0550.png

The table is rough and has a coefficient of kinetic friction of 0.360. The three masses are m1 = 3.74 kg, m2 =1.39 kg, and m3 = 1.86 kg, and the pulleys are frictionless. Determine the magnitude of the acceleration of each block."

I think I've figured out how to do it, but I keep on getting the wrong answer. I denoted left to be the POSITIVE x-direction, and down to be the POSITIVE y-direction, since that's the direction of movement. Can someone check my equations to see if I have them right?


Homework Equations


Fnet=ma
f(k)=u*n (where u=coefficient of friction)


The Attempt at a Solution


For m1, the 3.74kg mass:
Fnet(y) = m1*g - T1 = ma
Therefore, T1 = m1*g - m1*a --> EQUATION #1

For m2, the 1.39kg mas on the table:
Fnet(y) = m2*g - n = 0
Therefore, n = m2*g

Fnet(x) = T1 - T3 - f = ma
Therefore, T1 - T3 - u*n = ma --> EQUATION #2

For m3, the 1.86kg mass:
Fnet(y) = -T3 +m3*g = ma
Therefore, T3 = m3*g - m3*a --> EQUATION #3


I then substituted equations #1 and #3, into equations #2, and isolated for acceleration "a".
 
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  • #2
kathyt.25 said:
For m3, the 1.86kg mass:
Fnet(y) = -T3 +m3*g = ma
Therefore, T3 = m3*g - m3*a --> EQUATION #3
You've made a sign error. The acceleration of m3 is upward and must have the appropriate sign.
 
  • Like
Likes MegaJoules
  • #3
If m1 has acceleration a downwards, the acceleration of m3
is a upwards (or -a downwards if you prefer)
 

What is the purpose of finding the acceleration of a three-object pulley system?

The purpose of finding the acceleration of a three-object pulley system is to understand the motion and forces involved in the system. This information can be used to design and improve mechanical systems, as well as to predict and analyze the behavior of the system.

What is the difference between linear and angular acceleration in a three-object pulley system?

Linear acceleration refers to the change in speed or velocity of an object in a straight line, while angular acceleration refers to the change in rotational speed or velocity of an object around an axis. In a three-object pulley system, both types of acceleration may be present depending on the arrangement and movement of the objects.

How is the acceleration of a three-object pulley system calculated?

The acceleration of a three-object pulley system can be calculated using Newton's second law of motion, which states that the net force acting on an object is equal to its mass times its acceleration. By analyzing the forces acting on each object in the system, the acceleration can be determined.

What factors can affect the acceleration of a three-object pulley system?

The acceleration of a three-object pulley system can be affected by various factors, such as the mass and weight of the objects, the type and tension of the pulleys and ropes, and any external forces acting on the system. Friction and air resistance can also play a role in the acceleration of the system.

How can the acceleration of a three-object pulley system be used in real-world applications?

The acceleration of a three-object pulley system has many practical applications, such as in engineering and construction, where it can be used to design and optimize complex mechanical systems. It can also be used in physics experiments and simulations to study and understand the laws of motion.

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