Calculating Net Force and Acceleration in a System

[rafael_josem]

Hi, I have the following problem that I can't resolve...
What's the system aceleration shown in the picture if, m1 = 0.25kg, m2 = 0.5 kg and m3 = 0.25kg?
http://www.arnusa.org/system.jpg
I don't know what to do or how to start...
thanks...

 

[Astronuc]

On has to determine the forces on the blocks. M1 and M2 each have a force M1g and M2g (gravity) pulling down. M3 also has a force M3g downward, but it is supported by the table, and will only move laterally in the direction of whichever block M1 or M2 is heavier. M2 is heavier.

Now does friction apply here, because M3g will have resistance force fM3g, where f is the coefficient for friction. Tensions, T2 and T1, simply transmit the forces from M1 and M2.

 

[RoKe]

Draw a free-body diagram for each of the masses, set up coordinates *hint: it's much easier if you assign the x-axis as the direction of motion for each block, so that the coordinates shift, like the direction of motion*, and set up net force equations for each using Newton's second law. You should be able to find some common variables in each that allow you to substitute and isolate what you're looking for.

That should get you started.

 

[andrevdh]

The tensions at M1 and M2 are also T1 and T2. That will give you three equations with three unknowns T1,T2 and a(which is the same for all three masses since they are connected together).

 

[dx]

You don't have to determine the accelerations of the blocks individually. They will have the same acceleration. What is the net force on the system? and what is the total mass of the system? Tensions can be ignored when considering the net force because they are internal.