How Do You Calculate Acceleration in an Atwood Machine?

[physicshard22]

Homework Statement

ATWOOD MACHINE LAB

Draw a free body diagram of m1 and another free body diagram of m2. Using these diagrams,
apply Newton’s second law to each mass. Assume that the tension is the same on each mass
and that they have the same acceleration. From these two equations, find an expression for
the acceleration of m1 in terms of m1, m2, and g. Compare the expression to your result in
Step 5 of Analysis.

Homework Equations

a = fnet/mass <--- Newton's second law of motion
ma = mg - t

The Attempt at a Solution

I have no idea

 

[jbsteele]

where to start. I understand the concept of free body diagrams and Newton's second law of motion, but I'm not sure how to apply it to this problem. Any help would be greatly appreciated.

 

[kerimek]

how to do this.

As a scientist, it is important to break down the problem into smaller, more manageable parts. Let's start by defining some variables:

m1 = mass of the first object
m2 = mass of the second object
g = acceleration due to gravity
T = tension in the string

Now, let's draw the free body diagrams for m1 and m2:

For m1:
- There is a force of gravity acting downwards (mg)
- There is a tension force acting upwards (T)

For m2:
- There is a force of gravity acting downwards (mg)
- There is a tension force acting downwards (T)

Now, let's apply Newton's second law to each mass:

For m1:
- ma1 = mg - T

For m2:
- ma2 = T - mg

Since we are assuming that the tension is the same on each mass and they have the same acceleration, we can set these two equations equal to each other:

ma1 = ma2

Substitute in the expressions for ma1 and ma2:

(m1)a = (m2)a

Divide both sides by a:

m1 = m2

We can rearrange this equation to solve for the acceleration (a):

a = (m2/m1)g

This is the same expression that we obtained in Step 5 of the analysis. This shows that the acceleration of m1 is directly proportional to the mass of m2 and inversely proportional to the mass of m1 and the acceleration due to gravity. This makes sense because the heavier object (m2) will pull down with a greater force, causing m1 to accelerate downwards.