# Direction of friction of a block moving down a plane

Lets say that there is a block is on an incline, but given a horizontal push before being let go. Once the block is let go, friction will oppose the component of gravity acting along the ramp, $$mg\sin(\theta)$$, but also will try to stop the relative horizontal motion between the ramp and the block. So in what direction does friction act? I'm pretty sure that friction will act somewhere in between the vertical along the ramp and the horizontal along the ramp, but I'm not sure.

I've attached this diagram to hopefully make the setup more clear:

If it’s kinetic (sliding) friction the friction force will act parallel to the surface and opposite to the motion of the block already underway.

If it’s static friction the friction force will again act parallel to the surface matching and opposing the force applied to the block to prevent relative motion between the block and the surface up until the maximum possible static friction force is reached, at which time motion is impending.

UPDATE:

I will assume the horizontal "pushing" force was greater than the maximum possible static friction force so that the block is initially sliding horizontally.

Regardless of the direction of motion of the block on the incline surface, the kinetic friction force will always act opposite to the direction of motion and will have a magnitude of

$$f=\mu_{k}N$$ where $$N=mg\cos\theta$$

So you can break the friction force into two components, one acting across the plane opposing motion of the block across the plane causing it to decelerate in the horizontal direction, and one acting up the plane opposing the component of the gravitational force acting down the plane, with an acceleration down the plane equal to the net force divided by the mass of the block.

Hope this helps.

• Yeah but in this case there are two sources of friction, so I'm wondering how much of the total 𝜇𝑁 will go towards stopping the block from sliding down, and how much will stop it from moving horizontally against the ramp (check the diagram in the edit I made in my post), i.e. the direction of the friction vector. Commented Jul 19 at 20:26
• @EmilSriram It would have helped if you had included the diagram in the first place. I'll update my answer. Commented Jul 19 at 20:35
• Sorry about that. I appreciate your help :) Commented Jul 19 at 20:42

friction will oppose the component of gravity acting along the ramp

That's not a given. That's just a consequence of some situations where that force is "trying" to move the block, but static friction opposes it.

Static friction can oppose forces that try to move the block from its location (up to the maximum static friction)

Kinetic friction opposes relative motion.

If the block is moving and you have the normal force, then you know the magnitude of the frictional force. If you know the direction of motion, you know the direction of the frictional force.

• So it will just oppose the horizontal movement initially? Commented Jul 19 at 20:47
• Yes. So even if the friction is sufficient to bring the object to a stop, it will have a path that bends down the incline. Commented Jul 19 at 20:49

Kinetic friction will always oppose motion, not other forces. A good tip is to always remember friction (kinetic or static) as a force that tries to prevent motion as its only purpose.

So, the question here is, what trajectory will the block take - what is its path? I would expect a nonlinear, curving path, so the kinetic friction force will start out horizontally leftwards, but will then gradually turn upwards as the motion direction turns downwards.

At any moment when the kinetic friction force is not horizontal nor vertical, then you can of course resolve it into its components along each axis. But they will be different at each new moment in this kind of scenario.