Suppose there is a wooden block resting on a friction less surface. You give it a little push (force, F) and then it starts moving. Since there is no friction acting on the block at its bottom surface, would you feel a counter force against F? If you feel it, does this originate due to the friction acting on particles/ molecules (because you are pushing those molecules) those make up the wooden block?
[Physics] What would be the counter force
forcesnewtonian-mechanics
Related Solutions
The answer to your dilema is that there is no need for any counter force.
Statistically it's likely that many molecules would come into the region where the vacuum was - however no force pushes them there.
In the kinetic theory of gases, intermolecular forces and collisions are ignored, but there will be, by chance, many molecules travelling towards the vacuum region. They continue in a straight line with no force acting, as in Newtons 1st Law.
Since there were no molecules in the vacuum region to leave, it just happens by chance that a short time later, more molecules will be in the region than before and the vacuum region has been 'filled'.
In my opinion, the requirement that the string be nonextensible creates conceptual issues.
On the one hand, it is stated that the string is nonextensible. On the other hand, it is stated on the diagram the "External force $F$ is applied such that the block remains at rest". The problem is if the string is nonextensible, and initially has no slack, then the block cannot move to the left, i.e., it will always be "at rest", regardless of the force $F$ to the left.
But more importantly, it makes it difficult to explain (1) why the static friction force counters the applied force before the tension in the string and (2) why when equilibrium is reached the friction force no longer exists.
To facilitate the answers to these questions I will replace the string with an ideal spring (see the figures below). An ideal spring, like the string, is massless. But unlike the string, it is extensible to the degree allowed by the spring constant. The magnitude of the tension in the spring is equals the magnitude of its restoring force, or $T=k\Delta x$ where $k$ is the spring constant and $\Delta x$ is its extension beyond the "relaxed" stated.
Now consider the following where the block is considered a rigid (nonextensible) body:
The spring, like the string, is initially relaxed so there is no tension. FIG 1 shows the block with no external force and the relaxed spring attached to the wall
In Fig 2 we gradually apply an increasing external force $F$ that is less than the maximum static friction force. Since the block cannot move, the spring cannot extend and thus the tension in the spring is still zero. This explains, for a physically real scenario, why the applied force $F$ is countered first by the static friction force.
In FIG 3 the applied force reaches the maximum static friction force and the friction force becomes kinetic friction, which is generally considered constant. Since kinetic friction is usually less than static friction, if the applied force $F$ is maintained at the value of the maximum static friction there will initially be a net force to the left causing the block to move to the left. (Note that actual value of the friction force during the transition from static to kinetic is undefined for the standard model of friction). At the same time, however, the spring extends creating an opposing tension force. So during this phase before the extension of the spring is a maximum, we have
$$F-f_{k}> T$$ $$\mu_{s}mg-\mu_{k}mg>k\Delta x$$
and the block is moving to the left.
- When the extension of the spring is such that the tension in the spring equals the applied force $F$, it's extension is maximized and we have
$$F=T=k\Delta x_{max}$$
Substituting into the first equation,
$$f_{k}=0$$
Meaning there is no net force for friction to oppose.
Note that in this example, the stiffer the spring (the greater $k$ is) the less the block needs to move before the tension equals the applied force, i.e., the quicker the tension rises. The nonextensible string is simply a spring with an infinite $k$.
Hope this helps.
Best Answer
According to Newton's Third Law, each force has an equal and opposite reaction force. In this case, the reaction force will be the same as if you pushed the object on a surface which did have a non-zero coefficient of friction, but in this case, the object would gain velocity faster, because there was no friction force countering the force applied by your push.
The force you feel when you push on the object, or any object, the reaction force you feel is due to the object's inertia, its resistance to change in motion, as described by Newton's First Law.
The difference between an object on a surface with friction and an object on a surface without friction is simply the resultant acceleration of the object after the forces are applied, not the reaction force on your hand when you push it.
Example
If you could travel through space freely, at any velocity you like, and you flew to the moon and tried to push it, you would still feel a reaction force against your hand, because you're pushing against the surface. Is there a wall behind the moon that is preventing you from pushing it through friction-less space? No, it is simply the mass of the moon that resists the change in velocity that you are trying to impose on it.