Calphy

Classical Mechanics Level 4

An object with weight $W$ is dragged along a horizontal plane whose $\mu=1.5$ (coefficient of friction) by a force acting along a rope attached to the object. If the rope makes an angle $\theta$ with the plane, then the magnitude of the force is:

$F=\dfrac{\mu W}{\mu\sin \theta + \cos \theta}$

where $0\leq \theta \leq \dfrac{\pi}{2}$ .If there exists a value $\alpha$ for $\theta$ such that $F$ is minimized, find the value of $\tan \alpha$ .

The answer is 1.5.

2 solutions

Aakash Khandelwal
Mar 29, 2016

$dF/d\theta$ = 0 , for minima.

We get $\mu=tan\alpha$

This solution is not complete.You also need to check the extreme boundaries.

Nihar Mahajan - 5 years, 2 months ago

It Is the definition of angle of friction that is tan(x) = coefficient of friction

Prakhar Bindal - 5 years, 2 months ago

Haha, didn't know that. Actually it was meant to be a pure calculus question, but someone edited it to CM :P

Nihar Mahajan - 5 years, 2 months ago

@Nihar Mahajan – You will study it soon in class 11 Laws of motion (If you have ncert part 1). It is called angle of repose on inclined plane and angle of frictio on horizontal plane

Prakhar Bindal - 5 years, 2 months ago

@Nihar Mahajan – Exactly. This was a direct question.

Swapnil Das - 5 years, 1 month ago

@Swapnil Das – It was meant to be a pure calculus question! If it is seeming to be so direct, want me to delete it?

Nihar Mahajan - 5 years, 1 month ago

@Nihar Mahajan – Nope, no need to delete it. Not all people know about the angle of friction, so they can themselves derive the fact. See, this is level 4 till now.

Swapnil Das - 5 years, 1 month ago

Abhishek Chopra
Mar 30, 2016

Although got it correct but how can coefficient of friction be greater than 1.

Why not! ,,,, It can be

Aniket Sanghi - 5 years, 2 months ago

Are you talking about practical situation's?

Abhishek Chopra - 5 years, 2 months ago

For practical situations , I am not sure........but in questions I have seen

Aniket Sanghi - 5 years, 2 months ago

It is the ratio of frictional force to the normal force on a body. If an object is kept on a table then the normal force is equal to it's weight. So I don't see why the frictional force can't be greater than the normal force ie coefficient of friction. What if the object is very light then the normal force will be very less then the coefficient of friction can easily be greater than 1.

Kushagra Sahni - 5 years, 2 months ago

Calphy

The answer is 1.5.

2 solutions

0 pending reports