# Pulley question - acceleration of an object across a horizontal surface

• kathyt.25
In summary, a horizontal surface with frictionless motion and a massless string connecting two objects of masses m(1) and m(2) can be analyzed using Fnet=ma to find the acceleration of the sliding object. By equating the net forces in the x and y directions for both objects and considering the tension as the same, the acceleration can be calculated. However, the weight of m(2) is greater than the tension, allowing it to accelerate downwards.

## Homework Statement

The figure shows two objects of masses m(1) and m(2). The horizontal surface allows for frictionless motion. The string ties to the two objects is massless and passes over a massless pulley that rotates without friction. If m(1)=5.63 kg and m(2)=1.57 kg, what is the magnitude of the acceleration of the sliding object?

http://session.masteringphysics.com/problemAsset/1073792/5/12.P71.jpg

We know that:
- tension m(1) = tension m(2) because they're connected
- mass of m(1), therefore we know the weight because W=mg
- mass of m(2) and we can calculate the weight too
- acceleration is a non-zero value, so Fnet=ma

Fnet=ma

## The Attempt at a Solution

- For the FBD for m(1), the larger object, wouldn't Fnet(x direction) = T= Ma, and Fnet (y direction) = 0 because it's on a flat surface, meaning that the normal and weight cancel out? SO the first equation would be Fnet(x)T=Ma (1)
- For the FBD for m(2), the smaller object, wouldn't Fnet(x direction)=0 since the object is just suspended in the air, and Fnet(y direction)=T-mg... so the 2nd equation would be Fnet(y)T=ma+mg (2)

(I equated Fnet in each axis to mass object * acceleration because they're both moving in that direction)

And since the Tension is the same, you could equate them to each other.. I equated
m(1)a=m(2)a+m(2)g, then isolated for a, but got the wrong answer. What am I doing wrong?!

Last edited:
For your smaller object mg is bigger than T otherwise it wouldn't accelerate.
Fnet=mg-T.You can take it from there.

Thanks, that helped a lot. So it turns out that my methods of solving the problem were correct, its just that I didn't realize that W(2) > T... which is what allowed it to accelerate in the direction of W(2). Downwards.