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If the coefficient of static friction between your coffeecup and the horizontal dashboard of your car is, how fast can you drive on a horizontal roadw

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asked 2021-02-24
If the coefficient of static friction between your coffeecup and the horizontal dashboard of your car is, how fast can you drive on a horizontal roadwayaround a right turn radius of 30.0 m before the cup starts toslide? If you go too fast, in what direction will the cupslide relative to the dashboard?

Answers (1)

2021-02-25

The idea is that your car is moving in circ motion and youwant the coffee cup to move with the car (i.e. not slide). So thecoffee cup must also turn in a circle.
The force keeping it in a circle is the friction force whichis \(F = u\) mg where u is the coeff offriction also, in circ motion the force must equal: \(F= \frac{mv2}{R}\)
So: \(\frac{mv2}{ R}= u\) mg or

\(\displaystyle{v}{2}={u}{g}{R}={0.8}\times{9.8}\times{30}={235.2}\) take the sq root and \(v = 15.3 m/s\) Done! Please rate me,thanks!

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