Friction in vertical directions

[moonbase]

Homework Statement

Two blocks (m1 and m2) are being pushed to the right along a frictionless table with such a force that the left block (m1), which is smaller, is above the table and not falling. It is pushed up against m2 (which is on the table), and they have a coefficient of static friction of 0.4 between them. The mass of m1 is 16 kg and m2 is 80 kg. What is the minimum applied force from the left required to keep m1 from sliding down m2?

Homework Equations

f_s≤u_sF_normal
F_net=ma

The Attempt at a Solution

I drew a force body diagram and found that since there is no vertical movement for m1, the net force is zero so the downward weight force must cancel with the upward frictional force of m2 on m1. Since the weight = 156.96 N, the frictional force must also. This is set equal to 0.4F_normal to find that the minimum normal force required is equal to 392.4 N. Since this force acts opposite to the applied force, the applied force must be greater than or equal to this number. However, the system is not accepting my answer of 392.4 N. Can anyone point out to me what I did wrong?

 

[SammyS]

Homework Statement

Two blocks (m1 and m2) are being pushed to the right along a frictionless table with such a force that the left block (m1), which is smaller, is above the table and not falling. It is pushed up against m2 (which is on the table), and they have a coefficient of static friction of 0.4 between them. The mass of m1 is 16 kg and m2 is 80 kg. What is the minimum applied force from the left required to keep m1 from sliding down m2?

Homework Equations

f_s≤u_sF_normal
F_net=ma

The Attempt at a Solution

I drew a force body diagram and found that since there is no vertical movement for m1, the net force is zero so the downward weight force must cancel with the upward frictional force of m2 on m1. Since the weight = 156.96 N, the frictional force must also. This is set equal to 0.4F_normal to find that the minimum normal force required is equal to 392.4 N. Since this force acts opposite to the applied force, the applied force must be greater than or equal to this number. However, the system is not accepting my answer of 392.4 N. Can anyone point out to me what I did wrong?

Let's see if I understand this. An applied force pushes to the right on m₁ which in turn pushes m₂ to the right.

If the normal force the blocks exert on each other is 392.4 N, then you can find the acceleration of m₂. But m₁ also has that acceleration.

The applied force must be sufficient to give m₁ + m₂ that acceleration.

 

[moonbase]

Ahh I see, I ignored m2's opposing force. Thanks!