WEBVTT
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This is College Physics
Answers with Shaun Dychko.
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This is the same picture as
we have in example 9.1,
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with the addition of a new weight
here due to the seesaw.
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So it’s *w* subscript *s* for seesaw,
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and it’s positioned at some distance
from the pivot *r* subscript *s*,
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so this is the center of mass of the seesaw.
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And it’s going to exert a
counter-clockwise torque
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in the same direction as the
torque exerted by this boy.
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We know that for static
equilibrium to occur,
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we have the total counter-clockwise torque
has to equal the clockwise torque.
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And so we create expressions here for each.
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So we have the weight of the boy
multiplied by his distance from the pivot
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and then add to that the
torque due to the seesaw,
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and that’s going to equal the
clockwise torque due to the girl
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which is *m2* times *g* times her
distance from the pivot *r2*.
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And we equate these two,
and then we solve for *r2*
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and we also divide both sides by
*g* and it will cancel everywhere.
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So we have the distance that the
girl needs to sit from the pivot
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is going to be *m1 r1* plus
*ms rs*, all divided by *m2*.
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So it’s 26 kilograms mass of
the boy times 1.6 meters,
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plus 12 kilograms mass of the
seesaw times 0.16 meters,
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divided by 32 kilograms mass of the girl,
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and that gives a position of
1.36 meters from the pivot.
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The next question is what should
this force due to the pivot be,
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and by the way, this force did not
appear in our torque calculation
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because the level arm for this force is
zero because it’s positioned at the pivot.
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And so it doesn’t exert any
torque above the pivot,
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but it does exert a force obviously,
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that’s what supporting this
whole seesaw and the kids.
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And so the total force upwards,
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which is consisting only of this
one force due to the pivot,
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has to equal the total force down,
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which is the weight of the boy
and the girl and the seesaw.
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We can factor out the *g* there, common factor.
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So we have the force of the
pivot is *g* times the total mass,
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so that’s 9.8 newtons per kilogram
gravitational field strength,
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multiplied by 26 kilograms mass of the
oy plus 32 kilograms mass of the girl
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plus 12 kilograms mass of the
seesaw, giving 686 newtons.