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

[queenspublic]

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?

 

[cjl]

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.

 

[queenspublic]

Well. that's what I kind of did when I got those two equivalent equations.

 

[queenspublic]

For block two, we assumed that acceleration is moving downward.

 

[queenspublic]

Does anyone know how to get 3.58?

 

[queenspublic]

Never mind. I got it!

 

[queenspublic]

You set them equal to each other and solve for a.

 

[cjl]

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.