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Frictional force($f$) is calculated as the product of coefficient of friction and the normal forces. $$f=\mu N$$

If suppose an external force $F_{ext}$ is applied on a block (at rest) at an angle $\theta$ with the horizontal, then would $N = mg$ (weight of block) or $N =mg+F_{ext}sin\theta$ (I want to know the effect on friction due to change in $N$)?

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    $\begingroup$ None of these. The box isn't being lifted (doesn't move upwards), I'll assume, so simply sum up all forces along the vertical axis and set it equal to zero. $\endgroup$
    – Steeven
    Oct 28, 2020 at 11:34

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Sum of forces in the $y$-direction $=$ $$F\sin \theta + N - mg$$ (using the standard Cartesian axes). Although you haven't stated it explicitly, I will assume that the block has no motion along the $y$-axis (if it does, $N = 0$). Hence $$F\sin \theta + N - mg = 0$$

So $N = mg - F\sin\theta$, where $mg$ is implicitly assumed to be positive.

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  • $\begingroup$ With what convention can the latter result be true? $\endgroup$
    – Steeven
    Oct 28, 2020 at 11:36
  • $\begingroup$ @Steeven if for some reason you decide to take gravity in the positive $y$-direction $\endgroup$ Oct 28, 2020 at 11:47
  • $\begingroup$ Nihar Placing the positive y-direction as downwards, wouldn't that flip the signs not only of $mg$ but also of the force as well as of $N$? $\endgroup$
    – Steeven
    Oct 28, 2020 at 11:48
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    $\begingroup$ @Steeven, you're right, edited $\endgroup$ Oct 28, 2020 at 12:27
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Of course there is a mathematical way to know the answer as given in Nihar Karve's answer but I would like to give you some physical insights of it.

Actually , Normal force arises due to electromagnetic nature of materials (also linked with quantum mechanics but just ignore it for simplicity).

Since electromagnetic forces depend on the distance between charges so a lesser distance means a greater force and a greater distance means a lesser force.

So when there was no external force , the body was compressing the surface below it to some amount because of its weight and thus the molecules of each surface were experiencing a normal force in the upward direction.

But when you applied an external force , the force had some component in the upward direction which decreased the amount of compression and thus the distance between the molecules get increased and thus from here you can think yourself that the Normal force will decrease and the new magnitude of the Normal force is given in Karve's answer.

If the external force was applied in the opposite direction, then it would have some components in the downward direction and this would have brought the molecules closer and in this case the Normal force would have increased.

Hope it helps 🙂.

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