WEBVTT
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This is College Physics
Answers with Shaun Dychko.
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We have a free body diagram of the
cart being pushed by the nurse.
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It consists of an applied force at an
angle of 35 degrees below the horizontal
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and has friction force going
straight back 60 newtons.
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There’s a normal force going
straight up and gravity going down.
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The mass of the cart is 28 kilograms
and its acceleration is zero
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because we’re told that it’s going
to be pushed at constant speed.
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So the net force
in the *x* direction
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is the *x* component of this
applied force minus the friction
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and that’s going to be
mass times acceleration
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but we know that acceleration is
zero so we replace that with a zero
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on the right side.
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On the left side, we’ll replace *Fax*
with the applied force times *cos theta*
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because *Fax* is the adjacent
leg of this triangle here.
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Ultimately we’re trying to find
out what is this applied force
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needed to move at
constant speed.
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So we’ll add friction
to both sides
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and then divide both
sides by *cos theta*,
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and we get the applied force is
friction divided by *cos theta*,
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so that’s 60 newtons
divided by *cos 35*
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which is 73.2 newtons.