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A $60 \;\text{N}$ force is acting on an object of mass $10 \;\text{kg}$ which is placed against a wall touching it. What is the normal force $N$ applied by the wall?

My method: Since the object cannot move in such condition the net electromagnetic forces between the surfaces in contact is perpendicular. So I can say that there is no friction being applied. So simply $N$ is $60 \;\text{N}$.

My teacher's method: He assumed that if there was no wall the $F_{net}$ will be in the right direction with magnitude $10 N$. $$F_{friction}=N\mu=100\times0.5 = 50\;\text{N} \;\text{to the left}$$ $$F_{net}=60\;\text{N} - 50\;\text{N} = 10\;\text{N} \;\text{to the right}$$

So for acceleration= $0$, a $N$ of magnitude $10\;\text{N}$ must act in left direction. Considering this, one can also say that the friction can take any value less than $50\;\text{N}$ and the normal force will be $60 \;\text{N}$ minus that value.

Who is right?

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  • $\begingroup$ "Considering this, one can also say that the friction can take any value less than $50N$ and the normal force will be 60 minus that value" What makes you think you can arbitrarily change the frictioal force? $\endgroup$ – noah Jun 11 at 14:26
  • $\begingroup$ I consider $\mu$ as a static frictional coefficient, which is a self-adjusting force, so it may have any value between range $0\,N$ to $50\,N$. $\endgroup$ – user9339131 Jun 11 at 14:29
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    $\begingroup$ The whole question is about which acts first, or more immediate, the static friction by the floor or the resistance by the wall, which really goes into how these forces come about microscopically. $\endgroup$ – noah Jun 11 at 15:13
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    $\begingroup$ @noah Right. I transposed 50N an 60N in my head $\endgroup$ – Bob D Jun 11 at 15:14
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    $\begingroup$ @user9339131, in my opinion, the normal force is 60 N to the left. However, the problem as posed is probably indeterminate, as there is no way to determine what fraction of the leftward force is due to friction and what fraction is due to normal force from the wall. Your teacher shouldn't assign problems like this. $\endgroup$ – David White Jun 11 at 15:39
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This question is tricky in that the idealizations make it not totally clear what the correct answer should be, so this is an ill-posed problem. In the real world, there is nothing like instantaneous forces and infinitely stiff bodies. Pushing on the object will internally deform it and make it lean over to the wall without breaking contact with the floor; the exact distribution of forces between the friction from the floor and the resistance of the wall will depend on the microscopic parameters of the bodies and surfaces involved.

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