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A 1.3 kg toaster is not plugged in. The coefficient ofstatic friction between the toaster and a horizontal countertop is 0.35. To make the toaster sta

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asked 2021-04-20
A 1.3 kg toaster is not plugged in. The coefficient ofstatic friction between the toaster and a horizontal countertop is 0.35. To make the toaster start moving, you carelesslypull on its electric cord.
PART A: For the cord tension to beas small as possible, you should pull at what angle above thehorizontal?
PART B: With this angle, how largemust the tension be?

Answers (1)

2021-04-22
F \(\displaystyle{\cos{}}\) x = u.m.g then
\(\displaystyle{F}={u}{m}\frac{{g}}{{\cos{{x}}}}={\left({0.35}\right)}{\left({1.3}\right)}\frac{{{9.8}}}{{\cos{{x}}}}\)
\(\displaystyle{F}=\frac{{4.46}}{{\cos{{x}}}}\)
a. taking differential of this we have :
\(\displaystyle{F}'={0}{\left({\cos{{x}}}\right)}-{\left({4.46}\right)}\frac{{-{\sin{{x}}}}}{{{\cos}^{{{2}}}{x}}}={4.46}\frac{{\sin{{x}}}}{{{\cos}^{{{2}}}{x}}}\)
taken its stationary we'll have
\(\displaystyle{F}'={4.46}\frac{{\sin{{x}}}}{{{\cos}^{{{2}}}{x}}}={0}\rightarrow{\sin{{x}}}={0}\rightarrow{x}={0}^{{{o}}}\)
b. \(\displaystyle{F}=\frac{{4.46}}{{\cos{{0}}}}=\frac{{4.46}}{{1}}={4.46}{N}\)
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