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Why is this statement false: If the normal force on an object increases, the static friction must increase? Thank you! Is it because they did not state what normal force is referring to?

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    $\begingroup$ Where does it say that? By the way it is preferable that you ask your question in the body of the question and add a descriptive title. $\endgroup$ – Gonenc May 17 '15 at 8:35
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Imagine a box on a horizontal surface. If you just push it down should there be a friction force? If yes to which direction?

Now imagine a box on an inclined surface. Static friction balances the component of weight that is along the surface. If you apply more force normal to the surface, does that component change?

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    $\begingroup$ The point is that friction is a retarding force. It only exists to oppose another force. Therefore there is are two limits to friction, (normal contact force * coefficient of friction), and (sum of other forces acting on the object). $\endgroup$ – Aron May 17 '15 at 10:03
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What is meant by this is the force normal to the surface of contact between an object and what it is resting on. In most problems like this, this object boundary is taken to be flat.

The question is slightly mischievous: it's asking you to be precise to test your understanding of friction: to make the statement precise, you need to say that if the normal {\it component} of the contact force increases, the maximum tangential component of the contact force that could be supported by the contact increases. In other words, there is no friction if the force is wholly normal, and this situation does not change if the only thing you do is increase the normal force in some way (by adding more weight). Friction does not appear unless there is another force trying to slide the object (for example,=: if there is a tangential component of the weight).

What is true is that if you impart this tangential component, the bigger the normal component of the force, the bigger the tangential component you will need to impart to make slip happen. This is a linear homogeneous relationship for many contacts, and the co-efficient of friction $\mu$ tells us the maximum tangential component $F_T= \mu\,F_N$ the contact will support without slipping, where $F_N$ is the normal force component.

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I used to be really confused by friction and the fact that frictional force = (mu) * normal force. However, this is wrong. Frictional force is actually less than mu times normal force, and below that limit only opposed applied forces parallel to the surface. If there are two blocks on the floor of the same mass except I'm pushing one down, and my friend pushes both to the side with equal force, if they dont move then they also both experience the same frictional force in the other direction to oppose the hypothetical motion; its magnitude is precisely the amount of force applied by my friend. If my friend continues to increase his pushing magnitude, the block without my push down moves first because its maximum frictional force is less.

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