Contact Forces in Three-Block System

[Inertialforce]

Homework Statement

Three blocks are placed onto a frictionless horizontal surface. These blocks are side by side and are in contact with each other. Let m1=2m2=5m3. Answer the following exercises.

a)If a force is applied to m1, then show that

i)Fa = 17/2m3a

ii)F12 = 7/2m3a where F12 is the contact force of mass 1 on mass 2

iii)F23=m3a

Homework Equations

F=ma

The Attempt at a Solution

Fx1=m1a Fx2=m2a Fx3=m3a
Fa-F21-F31=m1a F12-F32=m2a F13+F23=m3a
Fa=m1a+F21+F31 F12=m2a+F32 F13=m3a+F23
Fa=m1a=(m2a=F23)=(m3a-F32)
Fa=m1a=m2a=m3a

I'm not quite sure if this is the way to even go about it. Any help with this would be greatly appreciated.

 

[LowlyPion]

Homework Statement

Three blocks are placed onto a frictionless horizontal surface. These blocks are side by side and are in contact with each other. Let m1=2m2=5m3. Answer the following exercises.

a)If a force is applied to m1, then show that

i)Fa = 17/2m3a

ii)F12 = 7/2m3a where F12 is the contact force of mass 1 on mass 2

iii)F23=m3a

Homework Equations

F=ma

The Attempt at a Solution

Fx1=m1a Fx2=m2a Fx3=m3a
Fa-F21-F31=m1a F12-F32=m2a F13+F23=m3a
Fa=m1a+F21+F31 F12=m2a+F32 F13=m3a+F23
Fa=m1a=(m2a=F23)=(m3a-F32)
Fa=m1a=m2a=m3a

I'm not quite sure if this is the way to even go about it. Any help with this would be greatly appreciated.

Welcome to PF.

First of all observe that
Total mass is 1.7m₁.
m2 = .5m₁
m3 = .2m₁

F = m*a = 1.7m₁ = 1.7*(5m₃)*a = 17/2*m₃*a

Figure the subsequent contact forces by looking at the forces acting on the subsequent blocks in isolation.

 

[Inertialforce]

Thanks

After going through what you mentioned, I figured out how to do the question and subsequently the questions that were related to it. Thanks for the help.