WEBVTT

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This is Giancoli Answers
with Mr. Dychko.

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At the moment
when the crate begins moving,

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the force pulling equals
the maximum static friction force

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and the static friction force
at its maximum

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is going to be equal
to the coefficient of static friction

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times by the normal force.

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Now, since there's no vertical
acceleration of the crate

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that means the normal force upwards
equals gravity down,

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so, we have normal force
equals <i>mg</i> in other words.

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And we'll substitute that
into this normal force

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in our friction formula.

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And so then we get
that the pulling force

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which equals the static friction force
at the moment

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that crate begins moving

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equals <i>muS</i>
times <i>mg</i>.

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And we'll divide
both sides by <i>mg</i>

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to get that the static friction force

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is the pulling
force divided by <i>mg</i>.

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So, that's 35 Newtons
divided by 60 kilograms times 9.8

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which is 0.60.

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And there's no units
for coefficients of frictions

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because it's a force
divided by force

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so, the Newtons cancel
in the top and bottom.

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In this next picture we have
the crate moving now

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and you'll see
that I've drawn this arrow longer

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than the kinetic friction force

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because not only is the box moving
but it's accelerating,

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and that's an important
difference between,

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you know, movement
and acceleration.

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Anyway. So, yeah.

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This arrow is longer than this arrow
that's what I'm trying to say,

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so, we have the pulling force
minus the friction force

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equals mass times acceleration

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because these two forces
make up the net force

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in the horizontal direction,

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and net force is always <i>ma</i>.

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And we'll substitute
for the friction force,

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it's coefficient of kinetic friction
times the normal force

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which we've already
pointed out as <i>mg</i>.

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And we can move this to the right
and move this to the left

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and then switch the sides around.

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And we get <i>muK</i>
times <i>mg</i>

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is pulling force minus <i>ma</i>.

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And then divide
both sides by <i>mg</i>.

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And we get that the coefficient
of kinetic friction is 35 Newtons,

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that's still being applied
for pulling the crate,

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minus 6 kilograms
times acceleration

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of 0.6 meters
per second squared

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divided by the mass
of 6 kilograms times 9.8

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and we get 0.53 is the coefficient
of kinetic friction.