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

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)


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!

Best answer

expert advice

Have a similar question?
We can deal with it in 3 hours

Relevant Questions

asked 2021-02-19
A 10 kg objectexperiences a horizontal force which causes it to accelerate at 5 \(\displaystyle\frac{{m}}{{s}^{{2}}}\), moving it a distance of 20 m, horizontally.How much work is done by the force?
A ball is connected to a rope and swung around in uniform circular motion.The tension in the rope is measured at 10 N and the radius of thecircle is 1 m. How much work is done in one revolution around the circle?
A 10 kg weight issuspended in the air by a strong cable. How much work is done, perunit time, in suspending the weight?
A 5 kg block is moved up a 30 degree incline by a force of 50 N, parallel to the incline. The coefficient of kinetic friction between the block and the incline is .25. How much work is done by the 50 N force in moving the block a distance of 10 meters? What is the total workdone on the block over the same distance?
What is the kinetic energy of a 2 kg ball that travels a distance of 50 metersin 5 seconds?
A ball is thrown vertically with a velocity of 25 m/s. How high does it go? What is its velocity when it reaches a height of 25 m?
A ball with enough speed can complete a vertical loop. With what speed must the ballenter the loop to complete a 2 m loop? (Keep in mind that the velocity of the ball is not constant throughout the loop).
asked 2021-04-14
A sports car is accelerating up a hill that rises \(\displaystyle{18.0}^{\circ}\) above the horizontal. The coefficient of static friction between the wheels and the road is \(\displaystyle\mu{s}={0.77}\).It is the static frictional force that propels the car forward.
(a) What is the magnitude of the maximumacceleration that the car can have?
(b) What is the magnitude of the maximum acceleration if the car isbeing driven down the hill?
asked 2021-04-06
A race car enters a flat 200 m radius curve at a speed of 20 m/swhile increasing its speed at a constant 2 m/s2. If the coefficient of static friction is .700, what will the speed of thecar be when the car beings to slide?
A) 24.3 m/s
B) 31.5 m/s
C) 37.1 m/s
D) 36.2 m/s
E) 28.7 m/s
asked 2021-03-22
A box is sliding with a speed of 4.50 m/s on a horizontal surface when, at point P, it encounters a rough section. On the rough section, the coefficient of friction is not constant but starts at .100 at P and increases linerly with distance past P, reaching a value of .600 at 12.5 m past point P. (a) Use the work energy theorem to find how far this box slides before stopping. (b) What is the coefficient of friction at the stopping point? (c) How far would the box have slid iff the friciton coefficient didn't increase, but instead had the constant value of .1?