Question

what is the minimum value of force (in the following two cases) required to pull a block of mass m on a horizontal surface having coefficient of friction nu also find the angle this force makes with the horizontal
a)if force is parallel to the horizontal surface
b)if force is in any direction (also find the angle of this force makes with the horizontal)

Answer 1

Explanation:

the Normal reaction N on the block and Vertical component of the force F are opposite to weight.

We need only horizontal motion no vertical motion so vertical force should be balanced that is net force in vertical direction should be zero, i.e., N+FCosθ−Mg=0 or N=Mg−FCosθ , put F=Mg as given in the question. so by putting so we get N=Mg(1−cosθ)

.

Now putting another condition to make F able to pull the block horizontally the Fsinθ should be greater than or eual to Static friction and we know that maximum value of static friction is μN

so we have Fsinθ≥μN

putting value of N we get Sinθ=μ(1−cosθ)

put cosθ=1−2Sin

2

2

θ

and sinθ=2sin

2