WEBVTT

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This is Giancoli Answers
with Mr. Dychko.

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Here's a free body diagram
of the woman,

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the force exerted by the scale
on the woman is upwards

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and it's 0.75 times her weight,

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so, 0.75 times <i>Fg</i>

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and this arrow is a little bit shorter
than the arrow downwards

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and the narrow down
represents gravity

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and so the net force
is the force upwards

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minus a force downwards,

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that's a scale force up

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minus the gravity
force down equals <i>ma</i>.

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And we'll solve this for acceleration
by dividing both sides by <i>m</i>

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and then switch the sides around.

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And the scale force
is 0.75 <i>Fg</i>.

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So, that's a substitution
for this made here.

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And minus <i>m</i> <i>Fg</i>

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and that's a common factor that
can be factored out in the next line.

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And then...

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So that's <i>Fg</i>
times 0.75 minus 1

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and <i>Fg</i> is <i>mg</i>.

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And then you can see
that <i>m</i> is a common factor

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on top and bottom,
so, it cancels.

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So, we're left with <i>g</i>
times negative 0.25

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that's 0.75 minus 1.

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And 9.8 times negative 0.25
gives an acceleration

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of negative 2.5 m/s squared.

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The negative means
the acceleration is downwards.