Mechanical Engineering - Engineering Mechanics - Discussion

@All.

When a body is inclined with an angle ( suppose a ) then force required to move it up is the function of the angle of inclination and the friction. The equation is given by p = w( sin(a) + u cos (a) ). Where u = tan@ = Fr (frictional force)/ Reaction.

Now put u = tan@ in equation of p and take the value of a > @, a=@, and a<@ and you can observe p is minimum when a= @.

Now come to the logic that one of you have given above that " just think logically if something is placed horizontally and something is at an incline at which place force require is more" definitely at horizontal. Having said so you should also keep in mind that frictional angle has nothing to do with inclination. It also applies when the body is at the plane horizontal surface. Frictional angle is an angle between reaction and static frictional force component. You can't relate anything with anything :) And if you are interested in doing so just give me the reason why Boyles law become invalid when you inflate a balloon. Why pressure and volume both increases even though Temp is Constant.

If the inclination of the plane, with the horizontal, is less. The angle of friction, the body will be automatically in equilibrium. If in this condition, the body is required to be moved upwards or downwards, a corresponding force.

Is required, for the same. But, if the inclination of the plane is more than the angle of friction, the body will move down. And an upward force (P) will be required to resist the body from moving down the plane.

Dear friends. please read the question carefully.

1) First angle that is the angle of inclination and angle of friction is the same thing.
2) The second angle they r talking about is the angle of pulling of force with respect to the plane.
It must be equal to angle plane for less effort to pull it.

The force required to move a body up an inclined plane will be minimum, when the angle it makes with the inclined plane is less than the angle of friction. This ensures that the force applied is just enough to overcome the frictional force and initiate motion without unnecessary resistance.

Guys just think logically. Just assume that if you have to pull a weight on a plane.

Which is easier? On an inclined plane or a horizontal one.

Definitely, the answer is on a horizontal plane.

So, the angle should be less than the angle of friction.

Agree @Bharat_kumar.

You must ignore the friction first for the min value of P with ignoring that remains

P= W sin(a) only.
As (a) become smaller P becomes smaller,
So the current answer is Option B only.

Boyle's law states that at constant temperature FOR A FIXED MASS, the absolute pleasure and the volume of a gas are inversely proportional. While inflating a balloon mass is not fixed as we add air in it.

Yes, I agree @Bharat Kumar.

It will be easy and required a min force that can be applied to the body, if and only if the angle is less. It tends to move when the angle is equal to the frictional angle.

Option: A is correct.

Just ready to move a body condition is IMPENDING MOTION (angle of inclined = angle of friction).

Static friction condition is (angle of inclined < angle of friction).

If force is acting on a body to move the body, then definitely friction will occur is opposite direction, in the same plane. So the angles are identically equal.