Finding Acceleration in a Frictionless System with Multiple Masses

[jessicax07]

Homework Statement

What is the acceleration of the masses as shown in the second attached image. m1 = 0.9kg, m2 = 1.6kg, and m3 = 2.4kg. (Assume the table is frictionless)

Homework Equations

$$\sum$$F=ma
F_mg+F_N = ma

The Attempt at a Solution

I figured everything up to the point a=F/(m1+m2+m3) but without the force given, how do you figure it out?

 

[PhanthomJay]

Draw free body diagrams. Isolate the hanging block...what are the forces acting on it? Then use Newton 2 on that blck to arrive at an equation. Then isolate the 2 blocks together on the table, determine the forces acting on that free body diagram of those 2 blocks, and apply Newton 2 to that system to get another equation. Now you solve 2 equations with 2 unknowns to find he aceleration. Note that the magnitude of the acceleration of each block must be the same.. Note also that the magnitude of the tension in a cord wrapped around an ideal pulley is the same on both sides of the pulley.

 

[jessicax07]

Even by doing that though, I don't see how I'd find a because like you said there would be 2 unknowns...

 

[PhanthomJay]

Even by doing that though, I don't see how I'd find a because like you said there would be 2 unknowns...

Yes, the 2 unknowns are the cable tension, T, and the acceleration, a. Solve the 2 simultaneous equations by the method of your choice.

 

[fizzynoob]

Tension is uniform through out the entire net system. Knowing that, isolate each system (isolate each block), sum the forces in each system and then use substitution to find a. Obviously the forces in the y direction cancel the first two block is zero so you only need to work about Fx. The forces in the x direction for the third block are zero, so you only need to worry about the y direction