Say I push a book along a table (applying continuous force until I reach the edge of the table). I apply as much force needed for the book to travel in constant velocity. Since the book is traveling in constant velocity across the table, Newton's first law would have it that the net force applied horizontally would be zero, meaning that the force of my push on the book is counter-acted by friction. However, if the net force is zero, how is the book able to move at all?
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$\begingroup$ Newton's first law. an object at rest stays at rest and an object in motion stays in motion at that same velocity unless acted upon by an unbalanced net force $\endgroup$– user256872Commented Apr 21, 2021 at 17:37
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1$\begingroup$ This is a key concept that you MUST accept and internalize if you intend to learn physics. What it means is that an object will always continue at a constant velocity (same speed and same direction) until a net force acts on it. $\endgroup$– David WhiteCommented Apr 21, 2021 at 18:21
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4 Answers
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However, if the net force is zero, how is the book able to move at all?
A force greater than the opposing kinetic friction force, for a net force, was initially required to accelerate the book to a certain velocity, per Newton's second law.
Then when the applied force is reduced to exactly equal the opposing kinetic friction force, for a net force of zero, the book continues at constant velocity per Newton's first law.
So the thing that throws me off, is that when I try to push the book I don't feel myself changing the amount of force once I overcome static friction. But in practice, even though I may not sense it, you're saying that I am indeed reducing the amount of force to match the friction?
Once you overcome the maximum static friction force, the friction force transitions to a kinetic friction force. That force is generally less than the maximum static friction force. So in theory, if you continued to apply the same force that overcame the maximum static friction force, the book would accelerate and not move at constant velocity.
So you either subconsciously reduced your applied force when the book broke free so that the book moved at constant velocity, or the book acceleration may have been too small for you to notice without conducting some sort of controlled experiment.
To get a feeling for what is happening in the transition from static to kinetic friction, check out the "friction plot" at the Hyperphysics website: http://hyperphysics.phy-astr.gsu.edu/hbase/frict2.html#kin
Hope this helps.
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$\begingroup$ So the thing that throws me off, is that when I try to push the book I don't feel myself changing the amount of force once I overcome static friction. But in practice, even though I may not sense it, you're saying that I am indeed reducing the amount of force to match the friction? $\endgroup$ Commented Apr 21, 2021 at 17:57
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$\begingroup$ Yes, that's correct. See update to my answer to explain further what is happening. $\endgroup$– Bob DCommented Apr 21, 2021 at 18:07
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$\begingroup$ Thank you Bob, you're terrific. $\endgroup$ Commented Apr 21, 2021 at 18:22
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Force equal zero means constant velocity, not zero velocity. You had to apply more force get to overcome the static friction (usually higher than sliding friction) to get the book moving and to accelerate to the target speed. Then you must have reduced the force to that equal and opposite to the sliding friction so as keep the velocity constant.
answered Apr 21, 2021 at 17:14
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Your last sentence reflects a misunderstanding of Newton's Laws. A direct consequence of $\vec{F}=m\vec{a}$ (I'm assuming constant mass so that $\vec{F}=\dot{\vec{p}} = m\vec{a}$) is that an object will move at constant velocity when the net force on it is zero. In other words, a force isn't required to keep something moving, only to change its state of motion (i.e., its velocity). You seem to be thinking along the lines of Kepler, who proposed that $\vec{F}=m\vec{v}$. Obviously, this is wrong. Just watch a cart sliding along an air-track (very low friction) and you'll see that force doesn't have this kind of proportionality with velocity.
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Let's say that when you initially applied a force (greater than the limiting static friction) ,you accelerated the book from a state of rest to motion and then after a time interval, you decreased the force in such a way that now the applied force and the kinetic friction cancel ; this is a situation when the net force is zero so, now the state (which is motion) cannot be changed. This situation is clear for everyone to understand
Now what if the applied force was exactly equal to the magnitude of limiting friction, in this case the object is not going anywhere as the net force is zero, the state of rest cannot be altered.
Now if the applied force is even infinitesimally greater than the limiting friction ,then the static friction would give out and kinetic friction would act now (which is always lesser in magnitude than limiting static friction) , so for an infinitesimally smaller instant the applied force would act and the body would now be moving.
TL;DR : kinetic friction is less than static friction and this transition leads to motion.
This is just my take on the problem Hope it helps
