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The figure shows 3 crates being pushed over a concrete floor by a horizontal force f of magnitude 440N.

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asked 2021-03-24

The figure shows 3 crates being pushed over a concrete floor by a horizontal force f of magnitude 440N. The masses of the cratesare \(\displaystyle{m}_{{1}}={30}\) kg, \(\displaystyle{m}_{{2}}={10}\) kg, and \(\displaystyle{m}_{{3}}={20}\) kg.The coefficient of kineticfriction between the floor and each of the crates is 0.7. a) what is the magnitude \(\displaystyle{F}_{{{32}}}\) of the force on crate 3 from crate 2? b) If the crates then slide onto a polished floor, where the coefficientof kinetic friction is less than 0.700, is magnitude \(F_{32}\) more than,less than, or the same as it was when the coeffient was 0.700?
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Answers (1)

2021-03-26
\(\displaystyle{m}_{{1}}\)
F pushing right
friction pushing left
\(\displaystyle{m}_{{2}}:\)
\(\displaystyle{m}_{{1}}\) pushing right
\(\displaystyle{m}_{{3}}\) pushing left
friction pushing left
\(\displaystyle{m}_{{3}}:\)
\(\displaystyle{m}_{{2}}\) pushing right
friction pushing left
a) \(\displaystyle{F}={m}{a}\)
first we have to find the net acceleration of the system.
\(\displaystyle{F}_{{a}}-{F}_{{f}}={\left({m}_{{1}}+{m}_{{2}}+{m}_{{3}}\right)}{a}\)
\(\displaystyle{F}_{{a}}-\mu{\left({m}_{{1}}+{m}_{{2}}+{m}_{{3}}\right)}{g}={\left({m}_{{1}}+{m}_{{2}}+{m}_{{3}}\right)}{a}\)
\(\displaystyle{a}={\frac{{{F}_{{a}}-\mu{\left({m}_{{1}}+{m}_{{2}}+{m}_{{3}}\right)}}}{{{m}_{{1}}+{m}_{{2}}+{m}_{{3}}}}}\)
After you find the acceleration, multiply it by \(\displaystyle{m}_{{3}}\) and that wikk be the answer
b) \(\displaystyle{F}_{{{32}}}\) will be higher before.
In our equation, a smaller \(\displaystyle\mu\) will result in a large numerator, and a larger acceleration. Since \(\displaystyle{F}={m}{a}\), a high acceleration will also increase the force.
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