AP Physics test question... help?

Question

There are 2 blocks. One with large mass (M) and the other with lighter mass (m). The two block are next to eachother on a frictionless, flat plane. A very small bug (assume no mass) sits in between the two blocks.
In which case would the bug inbetween the blocks be less likely to be squished (recieve the least amount of force)?
1.) A horizontal force, F, pushes the block mass M into block mass m.
2.) A horizontal force, F (same force as in question 1), pushes the block mass m into block mass M.

Explain how you got plz. Thanx!

Answer 1

1) Is the answer.

Look at the forces on the bug in each case
Call the force Fb

For case 1
F-Fb1=M*a
Fb1=m*a
dividing
Fb1/(F-Fb1)=m/M
Fb1=(F*m/M)/(1+m/M)
Fb1=(F*m)/(M+m)

For case 2
F-Fb2=m*a
Fb2=M*a

dividing
Fb2/(F-Fb2)=M/m
Fb2=F*M/(m+M)

Fb2/Fb1=M/m

Fb2 is larger than Fb1

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