Question

the net force ,F networks , needed to push a block along a horizontal surface is directly proportional to the mass, m kg , of the block. when m =5, f = 49. (1) find an equation connecting F and m . (2) find the value of F and m =14. (3) calculate the value of m when F =215.6. (4) draw the graph of F against M.​

Answer 1

Answer:

Let us first calculate the force F required to bring m into motion in terms of angle θ. Equation using laws of motion are as follows:

N=mg−Fsinθ

and Fcosθ=μ

s

N

Fcosθ=μ(mg−Fsinθ)

⇒F=

cosθ+μ

s

sinθ

μmg

We have to find the angle θ for which this force F is minimum.

Substituting μ

s

=tanϕ ( for simplification), we get

F=

cosθ+tanϕsinθ

mgtanϕ

=

cos(θ−ϕ)

mgsinϕ

F is minimum if cos(θ−ϕ) is maximum. Hence, F is minimum for θ=ϕ=tan

−1

μ

s

and F

min

=mgsinϕ.

To bring m into motion with least effort, force should be applied at an angle tan

−1

μ

s

and should have a magnitude equal to

F

min

=mgsinϕ=

1+μ

s

2

μ

s

mg