Tensile stress with unequal forces

[juraj5]

I need to find the stress σ (defined as normal force/area, in N/m^2) for the following simple situation. The forces are not equal. I can't wrap my head around what's going on - the whole system should be accelerated, so what's the final force that should be used for calculating the stress?

 

[Spinnor]

Shouldn't it depend where along the length of the sample you evaluate the stress? I think the stress will be greatest at the "front" end, the end moving forward?

 

[PhanthomJay]

The force and hence the stress in the accelerating sample is variable, and at a maximum, as Spinnor has noted, at the 'front' end. You should draw a Free Body Diagram and apply Newton's 2nd Law to find what force acts at any given section, and in particular, what is the force at the front end? Back end? Middle?