What is the frictional force between two objects on an incline plane?

[endaman95]

Homework Statement

To illustrate there is an incline plane (Mass=M) on a frictionless horizontal plane. It is being pushed by an F force on its non incline side. There is also an m mass on the incline. Mass m does not slide over M. Angle of the incline is Beta. sin B= 0.6, cos B= 0.8, M= 3, m=1, coefficient of friction between two objects= 0.5

If F=30N what is the magnitude of the frictional force between M and m?

Homework Equations

The Attempt at a Solution

The asnwer to the question is zero but no matter how I try I can't seem to solve the problem. I tried drawing free body diagrams but don't know what to do next.

 

[micromass]

The asnwer to the question is zero but no matter how I try I can't seem to solve the problem. I tried drawing free body diagrams but don't know what to do next.

So you actually did some effort to try and solve the problem? Can you please show your attempts so far?

Please urgent

Then you should have asked earlier.

 

[endaman95]

Well I drew it for both of the blocks. The small mass m has the normal force upwards perpendicular to the incline and its own weight. The incline plane has the normal force acting on it self and the F force pushing it. How should I approach the next phase? How is it possible for the friction force to be zero when there is normal force exists.

 

[BvU]

You drew something we can't see, and you don't show how you use the relevant equations (none provided?) to work them out towards an answer, so you can not expect any help in getting you on the right path.

"The small mass m has the normal force upwards perpendicular to the incline and its own weight" Which of the two is it ?

"How is it possible for the friction force to be zero when there is normal force exists" You are asked to calculate the friction force, so you don't know it.

Finally, since you seem to be in a hurry: don't forget to add units to your variables. 3 stone or 3 grams makes a difference if the force is 30 lbf.

 

[endaman95]

I am not asking for the answer as I know the answer is zero. This is what I drew and do not know what to do next. What I am trying to ask is what is holding the mass m so the friction force is zero. I found the normal force 12.5 N and mgsinB is 6 N. What could be holding that block instead of friction force.

 

[BvU]

Fair enough. I do notice that you chose not to draw a friction force. That is a dangerous omission ! Unless you did so because you don't know which way it points -- but even then: drawing it is better than not drawing it. If it points the wrong way, then you can expect a minus sign to pop up at some point, or something else that puts you right.

Now it's time to make use of the given information in writing down some equations.
Are you familiar with one of Newton's laws that states $\vec F = m \,\vec a$ ?

If not, we have to do some serious catching up. If only you had mentioned this in your origibnal post, both you and I would have saved a lot of time.

If yes, then you will notice that I wrote this down as a vector equation. We can choose a convenient coordinate system to work in and get going.

 

[BvU]

Since I am rather late with my reply, here's a hint: What can you do with the given that the block does not slide on the incline ?

 

[endaman95]

Yes I am most certainly familiar as I can solve easier dynamics problems and such but I understand your concern. I should have posted a full attempt to try and solve the problem. Anyway If it doesn't slide there should be friction force opposite of mgsinB right?

 

[BvU]

Not necessarily. But if it doesn't move wrt the incline, the acceleration of the incline and of the mass lying on the incline must be the same.

Now choose a convenient coordinate system and write out the F = ma four times: for the incline and for the block on the incline, in x and in y direction. See what is useful and what is not...