Why not? (What does ##F_N## equal?)
Yes ##\mu mg##. But the answer in my book says ##F=\frac{\mu mg}{\sqrt{1+\mu^2}}##
Something is fishy here, can you post some sort of figure that perhaps exists in the book for this problem?
Did you provide the complete problem statement?
No. This is the complete question. There is no mentioning of any angle as you can see.I don’t know why they are applying force at an angle.
So you are saying that the diagram you just posted has nothing to do with this problem?
I am saying they have solved the problem assuming force at an angle. That diagram is not the part of question but of the answer.
That's a bit hard to believe.
Because that lowers the normal force and therefore the horizontal force required to move the block. Since the problem did not say anything about the direction, in order to find the minimal force, you need to find an expression for the required force as a function of the angle and then minimise with respect to the angle.
.Everybody makes bloopers or misread problems sometimes. Obviously, stating explicitly that the force could be at an angle would make it more obvious, but technically it is also fair game with the problem just stating to find the minimal force.OK , well I am not sure if that "the force applied must be at an angle " should be part of the problem statement or the student would have to think it. I was not smart enough to think it, and I am deeply sorry for myself
The problem asks specifically for the magnitude of the force. That's a very broad hint here.
It can help to put yourself into the problem. If you had to tug a heavy mass across a floor, how would you do it?OK , well I am not sure if that "the force applied must be at an angle " should be part of the problem statement or the student would have to think it. I was not smart enough to think it, and I am deeply sorry for myself
I don't know how you think but according to my thinking and intuition I would push it with horizontal force.
So you just learned something practically useful!
Maybe you need to do more manual labour!
To apply minimum force the force of friction has to be less and will become less when we decrease the normal force and that would mean a tilted block.
No, it would not necessarily tilt the block. Why do you think so? There is a separate set of equations (based on torque balance) that would tell you whether the block tilts or not.
Why not? They are valid as long as the coefficient of friction remains the same.
If it will not leave the ground at least from one side how the friction will decrease ?
By decreasing the normal force. Maximal friction is proportional to normal force.
Are you saying applying a force at an angle can decrease the friction without actually lifting it. That there is some ##0<F_N<mg##
You should be able to figure out the answer to this. What does force and torque balance on the block tell you? For simplicity, consider a homogeneous block with mass ##m## with a vertical string being pulled up attached to one of its sides. Will the block start tilting at the first minimal application of force? If not, how hard can you pull before it does?
No. I think if we apply some upward force block will not move because ##F_N+ F_a=mg##. We need to increase the ##F_a=mg##. Then block will move. So we can apply a force to decrease the normal without actually lifting it up.
Not be lifted up, when does it start tilting? Did you draw a free body diagram and do the torque analysis?
I have not studied about torque. Sorry. It’s in future chapters.
That is fine. Just as long as you are aware that until you reach and have learned those chapters, you will not really be able to tell when things tip over etc.
