0

Is the direction of kinetic friction always opposite to the direction of velocity of the object? I have found various contradicting statements about this. Which side has it right? The interesting case is when the velocity is in x-direction but the acceleration is (partly) in y-direction.

To clarify what I mean, let's introduce some formulas.

Let $\vec{x}(t)$ be the position vector of the object. It is moving with velocity $\vec{v}(t)$. There is an external force $\vec{F}_{ext}$ acting on the object. There is also a friction force acting on the object.

Assume that $\vec{v}(t)\neq0$. Then there is only kinetic friction $\vec{F}_{fric}$. We get that

$$m\vec{a}(t)=\vec{F}_{ext}+\vec{F}_{fric}.$$

Now the question is: what is the direction of the vector?

Of course, if $\vec{v}(t)$ and $\vec{F}_{ext}$ are parallel, then $\vec{F}_{fric}$ is also parallel to these vectors. But in general, they may not be parallel.

Suppose that $\vec{v}(t)$ and $\vec{F}_{ext}$ are perpendicular. Is the friction force parallel (but in opposite direction) to $\vec{v}(t)$? Or may it have a component in the $\vec{F}_{ext}$ direction?

Riemann
  • 1,430
  • 3
    Neither of the latter two links describe kinetic friction acting in any direction other than opposite motion. The first question doesn't even use kinetic friction at all (a car's tires are pointwise static on the ground unless it's skidding). The second question uses kinetic friction, but doesn't discuss its direction at all. – Nuclear Hoagie Jan 25 '24 at 15:38
  • So a moving object can have a static friction component and a kinetic friction component simultaneously? – Riemann Jan 25 '24 at 16:02
  • No. If the object is moving relative to the surface, it's kinetic, if it's not, it's static - it's impossible for the object to be both moving and not moving relative to a surface. The car tires in the first question only exhibit static friction, the second question only exhibits kinetic friction. – Nuclear Hoagie Jan 25 '24 at 16:05
  • I removed the examples and links because they only made it more confusing. – Riemann Jan 25 '24 at 21:04

4 Answers4

1

  • Kinetic friction tries to reduce the relative motion between two objects.

  • Static friction tries to prevent relative motion between two objects.

You then apply those statement to all the scenarios including those that you have mentioned in your post.

Note that there is no direct mention of velocity or the direction of the velocity.

Is the direction of kinetic friction always opposite to the velocity of the object?

Consider a crate on the back of a lorry which is moving in a straight line to the right and the velocity of the lorry is increasing in that direction.
If there are frictional forces between the lorry and the crate then there are two possibilities:

  • The frictional force is large enough so that there is no slippage between the crate and the lorry. The static frictional force on the crate due to the lorry is in the same direction as the velocity and acceleration of the lorry.

  • The frictional force is not large enough so that there is slippage between the crate and the lorry. The kinetic frictional force on the crate due to the lorry is in the same direction as the velocity and acceleration of the lorry. So you can thing of it as the force due to the lorry as trying to speed up the motion of the crate to reduce the relative motion between them and the force due to the crate as trying to slow down the motion of the lorry to reduce the relative motion between them.

So the answer to your question is, No

Note that the direction of the frictional force on the lorry is equal in magnitude and opposite in direction to that on the crate [N3L].

Farcher
  • 95,680
  • I think that in your example, the velocity and acceleration are in the same direction. But then it is trivial that the friction is in the opposite direction. Therefore the interesting case is when the velocity and acceleration are not parallel. – Riemann Jan 25 '24 at 15:32
  • @Riemann I gave a simple example to illustrate that "opposite to velocity" was not a good definition for the direction of the frictional force. Uniform motion in a circle requires a static frictional force towards the centre of the circle. All the examples you have stated are covered by my two statements regarding static and kinetic friction. The key is that frictional force either prevents or reduces relative motion between two bodies. – Farcher Jan 25 '24 at 15:58
  • In my definition the ground is standing still, so then relative motion equals velocity – Riemann Jan 25 '24 at 21:06
0

Riemann I think you focus a lot on the case where acceleration and velocity do not have the same direction and I don't see anything special in that case. Suppose a body moves in 3D space along the x-axis at constant velocity. If it moves along a surface, friction opposes the motion, so you could say that its direction is -hat{i}. Now let's imagine that this body has an acceleration on the y-axis, this means that there is some force that has been applied to the body in that direction. Depending on the magnitude of the force it will move in one direction or another, but the friction force vector will always oppose the direction of motion of the object.

JL14
  • 37
  • 3
0

Is the direction of kinetic friction always opposite to the direction of velocity of the object?

If you get to pick the frame such that the object it is sliding against is at rest, then yes.

But if you want a general answer that works in any reference frame, then the answer is no.

Imagine you're in a warehouse with a moving conveyor belt and you watch a box get dropped onto the belt. As the belt is moving to the right and the box has no horizontal velocity, it experiences a frictional force to the right and accelerates to the right.

From the frame of the warehouse, both the velocity of the box and the frictional forces are to the right.

From the frame of the conveyor belt, the box is moving to the left and friction opposes that motion so acts to the right.

Also by "velocity", we mean only the material at the interface, not necessarily the object as a whole. We might find a particular pool ball with a lot of topspin has velocity to the right at the same time that the bottom of the ball is moving to the left against the felt of the table. In that case, the kinetic frictional force on the ball would be to the right.

BowlOfRed
  • 40,008
0

Suppose that v⃗ (t) and F⃗ ext are perpendicular. Is the friction force parallel (but in opposite direction) to v⃗ (t)? Or may it have a component in the F⃗ ext direction?

That is the situation of a fan, just after being turned off. The $F_{ext}$ is the centripetal force that hold the blades in the central part. The tangential $v(t)$ is gradually decreasing due to the air friction force, also tangential and opposing to it.

Claudio Saspinski
  • 16,319