A 20kg metal block is place on a horizontal surface. The block just begins to slide when horizontal force of 100 N is applied to it. 1) Calculate the coefficient of static friction. 2) If coefficient of kinetic friction is 0.4 then find.......?

A 20kg metal block is place on a horizontal surface. The block just begins to slide when horizontal force of 100 N is applied to it.
1) Calculate the coefficient of static friction.
2) If coefficient of kinetic friction is 0.4 then find minimum force to maintain its uniform motion?

1 Answer
Apr 8, 2017

I got:
mu_s=0.51
F=78.4N

Explanation:

At the start the 100N force is just enough to overcome static friction so we can write:
"Force"="Static Friction"
F=mu_sN
where mu_s is the coefficient of static friction and N= Normal Reaction that in an horizontal case such this will be equal to the weight of the block, so N=mg.

We get:

F=mu_s*mg
in numbers:
100=mu_s*20*9.8
mu_s=100/(20*9.8)=0.51

When the movement starts, kinetic friction kicks in and we have that to have uniform motion we need acceleration equal to zero (constant velocity).

We use Newton's Second Law: SigmavecF=mveca
or in our case:
"Force"-"Kinetic Friction"="mass"*"acceleration"

or

F-mu_kN=0 because acceleration has to be zero.
F-mu_k*mg=0

in numbers:
F-0.4*20*9.8=0
F=78.4N