Three blocks connected by strings

[chawki]

Homework Statement

Three identical blocks, each of mass 0.6 kg, are connected by light strings. Assume that they lie on a frictionless, horizontal surface and are observed to have an acceleration of 4.0 m/s2 under the action of a force F.

Homework Equations

Calculate F and two tension forces T_bc and T_ab

The Attempt at a Solution

by applying Newton second law on each block and then by projection on xx axis, we get:
On A:
F-T_ab=m*a----(1)
On B:
T_ab-T_bc=m*a----(2)
On C:
T_bc=m*a----(3)

(1)+(2)+(3) $$\RightarrowF=3*m*a$$
F=7.2N

And then from (3) we have T_bc=m*a=0.6*4
T_bc=2.4N
From (1) we get -T_ab=(m*a)-F
-T_ab= (0.6*4)-7.2
T_ab=4.8N

 

[PhanthomJay]

looks good! You can check your work by drawing FBD's of blocks A and B together, and B and C together, to see if your values check out..

 

[chawki]

what is FBD

 

[a.ratnaparkhi]

Free Body Diagram. In this diagram, all the forces acting on the body are shown

 

[chawki]

This one ?

 

[ashishsinghal]

Yeah that is an FBD

 

[chawki]

I noticed that T_ab is greater than T_bc
maybe this is always the case ?
also ..how to check?
i noticed that F=T_ab+T_bc..maybe it's a coincidence?

 

[PhanthomJay]

I noticed that T_ab is greater than T_bc
maybe this is always the case ?
also ..how to check?
i noticed that F=T_ab+T_bc..maybe it's a coincidence?

Tab is greater than Tbc because it has to accelerate 2 masses whereas Tbc just accelerates one. Tab + Tbc = F in this case because the masses are equal..this is not generally the case. The knowledge of how to draw good FBD's is an essential to mastering Physics (along with mastering the plus and minus sign ). To check your work, you can draw a FBD of the last 2 blocks together, where the net external force acting, Tab, must equal Ma, where M is the mass of the 2 blocks (1.2) and a = 4. Thus Tab = 4.8, which checks your earlier result. Try it also by drawing a FBD of the first 2 blocks.