Question

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?

Answer 1

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`