What Is the Magnitude of the Acceleration in an Atwood's Machine?

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Homework Help Overview

The problem involves an Atwood's machine, which consists of two blocks connected by a cord over a frictionless pulley. The masses of the blocks are given, and the question seeks to determine the magnitude of the acceleration of the blocks.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss drawing free body diagrams and calculating net forces. There is mention of deriving equations based on the forces acting on the blocks. Some participants express confusion about reaching the specific acceleration value of 3.58 m/s².

Discussion Status

Some participants have offered guidance on using free body diagrams and net force calculations. There is a mix of understanding and uncertainty, with one participant indicating they resolved their confusion independently.

Contextual Notes

Participants are working within the constraints of a homework assignment, which may limit the depth of discussion or the sharing of complete solutions.

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Homework Statement



A figure shows two blocks connected by a cord that passes over a frictionless pulley. The arrangement is known as Atwood's machine. Block 1 has mass m1 = 1.30 kg; block 2 has mass m2 = 2.80 kg.

Sorry, no picture.

What is the magnitude of the acceleration of the blocks?

Homework Equations



T = 1.3a + 12.7 N
T = -2.8a + 27.4 N

The Attempt at a Solution



The answer is 3.58 m/s^2 but why and how?
 
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The easiest way to start here is probably to draw a free body diagram of the system. Have you done that?

Once you have that, figure out the net force exerted on the system.
 
Well. that's what I kind of did when I got those two equivalent equations.
 
For block two, we assumed that acceleration is moving downward.
 
Does anyone know how to get 3.58?
 
Never mind. I got it!
 
You set them equal to each other and solve for a.
 
Glad you figured it out.

As you probably know now, once you have the net force on the system (which should work out to be |M1*g-M2*g|), you set the mass equal to the sum of the masses of the two blocks, and then solve for A using F=MA.
 

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