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Consider two cases. First, we have a box that a person applies a force to (say to the right). The force of friction (static) is then directed to the left. Second, say that the box is moving at constant velocity v and the person is (still) applying the force. A crate is put on top of the box as it is moving. By putting the crate on top of the box, the friction force of the system (box and crate) doubles, showing that the normal force going upwards is influencing the friction force. Why is this so?

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In the first case when the box is stationary your statement is correct and you asked no question about that case.

In the second case, the box is moving and only the kinetic or dynamic friction is relevant. Assuming the crate you add on top of the box weighs the same as the box, the normal force doubles, and therefore the dynamic friction force doubles. This is because the dynamic friction force is equal to the normal force times the coefficient of friction.

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  • $\begingroup$ but why in the first case do we use the normal force of the person pushing on the box and in the second case we use the vertical normal force? $\endgroup$
    – Дау
    Oct 8 '15 at 0:56
  • $\begingroup$ The force from the person pushing should not be called a "normal force". That name should be reserved for the force normal to the floor. The normal force influences both the force of kinetic friction and the maximum force of static friction. $\endgroup$
    – BowlOfRed
    Oct 8 '15 at 2:42
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Friction is the force parallel to the surface of contact while the normal force is perpendicular. On the micro scale, both are related to the electromagnetic force. This is why $F_{fric} = \mu_k F_N$

So when the normal force is increased by adding the crate on the box, so does the friction.

Note that the normal force is always perpendicular to the surface so it is always vertical in this case.

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