How to know the direction of friction?

[jofree87]

For the problem here, I am given the kinetic friction of the blocks, and I am suppose to find the acceleration of the blocks. I set the x-axis along the incline with x-positive directed towards the right, and I set both the resultant forces of of A and B down the incline since I don't which one goes up or down. Now since A and B will move in opposite directions, how do I know which way to set the frictions?

Here is a diagram of the problem, and a solution I found online,

They also set the resultant forces in the same direction but they set the frictions in different directions.

 

[kuruman]

Is the free body diagram yours or what you found on the web? Setting the resultant forces on each mass (and hence their accelerations) in the same direction provides an inconsistent picture. Look at the rope connecting the masses. It has fixed length. If mass A is accelerating down the incline (positive x-direction) the bottom part of the rope connected to mass A will get longer. This means that the top part connected to mass B will get shorter which in turn means that the acceleration of mass B is in the negative x-direction. The diagram shows both accelerations in the same direction which is inconsistent.

 

[jofree87]

Is the free body diagram yours or what you found on the web? Setting the resultant forces on each mass (and hence their accelerations) in the same direction provides an inconsistent picture. Look at the rope connecting the masses. It has fixed length. If mass A is accelerating down the incline (positive x-direction) the bottom part of the rope connected to mass A will get longer. This means that the top part connected to mass B will get shorter which in turn means that the acceleration of mass B is in the negative x-direction. The diagram shows both accelerations in the same direction which is inconsistent.

I found the diagram online but I set the resultant forces in the same manner.

I did this because I don't know exactly which block goes up or down. If I work out the problem correctly, then one of the accelerations should end up being negative. But my question is how do I know which way the frictions will go? Can I set them in any direction like how I did with the resultant forces so that it will work out in the end?

 

[kuruman]

No you cannot set the frictions in any direction you want. You have to know which way they are for the free body diagram to work. It is a good bet that the bottom block is moving down the incline, in the same direction as the component of the pulling force P along the incline. This would not be the case if the system were moving uphill after being given some initial velocity uphill and before it slides back down again. Are there words in the statement of the problem that say this is the case? If no, then assume that the bottom block is moving downhill.

 

[rwisz]

I would like to clarify that the direction of friction is dependent on the direction of motion of the objects involved. Friction acts in the opposite direction of the motion of an object, so in this case, the direction of friction for block A would be down the incline, and for block B it would be up the incline.

To determine the direction of friction, you can use the right-hand rule. Point your thumb in the direction of motion and your fingers will curl in the direction of friction. Alternatively, you can also use the equation Ff = μN, where Ff is the force of friction, μ is the coefficient of friction, and N is the normal force. The normal force is always perpendicular to the surface, so the direction of friction can be determined by the direction of the normal force.

In this specific problem, the direction of friction for block A is down the incline because it is moving down the incline. The direction of friction for block B is up the incline because it is moving up the incline. This is consistent with the solution provided in the diagram.

It is important to note that the direction of friction can change if the direction of motion changes. So if block A were to move up the incline, the direction of friction for block A would be up the incline as well.

In summary, the direction of friction is dependent on the direction of motion of the objects involved and can be determined using the right-hand rule or the equation Ff = μN.