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Suppose a block of mass $1$ kg is kept on a rough horizontal surface. Let the friction coefficient be $0.2$. Now let's say, I apply a force of $1$N in the east direction. Friction will act in the west direction and will easily be able to balance $1.5$ N . Now suppose if I again apply $1.5$ N force on the block (while still applying $1.5$N force in east direction) but in north direction. Will friction act in the south direction and the west direction respectively, or will friction act only in the south west direction combined and the block move in the north east direction with some acceleration ?

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3 Answers 3

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Friction always acts opposing the motion of the object. So if you have a resultant force in a particular direction, friction will always act in the opposite direction. So if your particle is moving north-west due to a force, friction will act to oppose that motion (hence south-east), hope that helps.

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  • $\begingroup$ I have a follow up question. Can i ask? $\endgroup$ Commented Jun 29, 2020 at 14:24
  • $\begingroup$ If it's not extremely related then ask a new question. Otherwise, go on and ask it in the comments. $\endgroup$
    – user258881
    Commented Jun 29, 2020 at 14:33
  • $\begingroup$ @FakeMod you decide: I will delete it if it doesn't fit site policy. Suppose at some instant block has an accleration in east direction and velocity in north direction., in which direction will friction act? $\endgroup$ Commented Jun 29, 2020 at 14:36
  • $\begingroup$ @Ohw Acceleration doesn't matter/factor in while finding the direction. Only the direction of instantaneous velocity matters when it comes to finding the direction of friction. $\endgroup$
    – user258881
    Commented Jun 29, 2020 at 14:38
  • $\begingroup$ @FakeMod but answer says friction opposes resultant force and as far as i know acceleration is in direction of net force. $\endgroup$ Commented Jun 29, 2020 at 14:39
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This is how I deal with problem of finite friction.

  1. Assume friction is infinite and find the required friction force needed to resist all relative motion. Lets say this results into two co-planar friction forces $F_x$ and $F_y$.
  2. Calculate the magnitude of the required friction force $F = \sqrt{F_x^2+F_y^2}$
  3. Compare the magnitude $F$ to the actual available traction $F \leq \mu \,|N|$ where $N$ is the total normal force (like weight).
  4. If the required friction is more than the available traction, then cap the friction forces proportionally. Find the reduction factor $f = \tfrac{ \mu |N| }{F}$ to bring the magnitude of the friction down the available traction.
  5. Set the actual friction forces as $f\,F_x$ and $f\,F_y$ and proceed with the solution allowing relative motion between the parts.
  6. If the required friction is less than traction, then no modifications are needed.

This follows the logic of a friction circle but in a somewhat simplified fashion (as the radius is constant with direction).

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Will friction act in the south direction and the west direction respectively, or will friction act only in the south west direction combined and the block move in the north east direction with some acceleration ?

As @Warrenmovic pointed out, the friction force will be in the opposite direction of the resultant force, i.e., $\sqrt 2$ N in the south west direction, which is still less than the maximum possible static friction force of 1.96N (0.2x1x9.8). But like any force, the friction force can be resolved into components, in this case, 1 N south and 1 N west.

Regarding your follow up questions in the comments:

Suppose at some instant block has an accleration in east direction and velocity in north direction., in which direction will friction act?

It will still act in the direction opposite to the resultant force due to the forces applied in the east and north direction. However, since there is now relative motion between the block and the surface, the force applied to the block has exceeded the maximum static friction force of 1.96 and the opposing friction forces are now kinetic friction. The coefficient of kinetic friction is generally less than the coefficient of static friction.

Since the block is accelerating in the east direction it tells me that the applied force in the east direction is greater than the opposing kinetic friction force in the west direction, for a net force in the east causing acceleration. Since the block is moving at constant velocity in the north direction it tells me that the applied force in the north direction exactly equals the opposing kinetic friction force in the south direction, which can happen as explained below.

..answer says friction opposes resultant force and as far as i know acceleration is in direction of net force.

That is true, but you need to be careful about what "opposes resultant force" means. If the friction force is static friction, than friction opposes relative or impending motion between the block and the surface. The block will not move as in your original example.

But if the block is moving the opposing force is kinetic friction. Kinetic friction does not prevent relative motion. It retards or resists the relative motion that is occuring. For the example of the block moving at constant velocity in the north direction, the kinetic friction force is equal and opposite to it in the south direction, for a net force of zero. Per Newton's first law, an object at rest or moving at constant rectilinear motion is subjected to a net force of zero.

Once the force to the north exceeds the maximum static friction force, the block breaks free. Since kinetic friction is generally less than static friction, the block will accelerate if the applied force that broke it free is maintained at the same magnitude. But if the applied force is backed off somewhat until it exactly equals the kinetic friction force, the net force will be zero and the block continue at constant velocity.

Hope this helps.

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