A 0.115-kg remote control 15.8 cm long rests on a table, as shown in the figure...

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A 0.115-kg remote control 15.8 cm long rests on a table, asshown in the figure below, with a length L overhanging itsedge. To operate the power button on this remote requires a forceof 0.370 N. How far can the remote control extend beyond the edgeof the table and still not tip over when you press the powerbutton? Assume the mass of the remote is distributed uniformly, andthat the power button is on the end of the remote overhanging thetable.
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4.2 Ratings (703 Votes)

Length of the remote L ' = 15.8 cm

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 0.158 m

Mass of the remote m = 0.115 kg

Force F = 0.370 N

Weight of the remote W = mg

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 1.127 N

Center of mass of the remote x = L ' / 2

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 0.079 m

For moment of forces , F L = W ( x-L)

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â L = ( W/ F ) (x-L)

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 3.0459 ( x- L)

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 0.2406 - 3.0459 L

4.0459 L = 0.2406

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â L = 0.05947 m

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 5.947 cm

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A 0.115-kg remote control 15.8 cm long rests on a table, as shown in the figure...

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Physics

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