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
Gió
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#

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