Mechanics; speed of car travelling around bend.

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SUMMARY

The discussion focuses on calculating the speed of a car navigating a curved roadway with a radius of 112 meters. The horizontal and vertical forces exerted by the car on a passenger are 220N and 530N, respectively. For part (a), the correct speed is 76.8 km/h, while the initial calculation using the formula Fc = mv²/r yielded an incorrect value of 21.36 m/s. In part (b), when the roadway is banked at a 20-degree angle, the speed without relying on friction is determined to be 72 km/h, contrasting with the initial calculation of 4 m/s.

PREREQUISITES
  • Understanding of centripetal force and its equation Fc = mv²/r
  • Knowledge of banking angles in physics and their effects on motion
  • Familiarity with trigonometric functions, specifically tangent
  • Ability to convert between units of speed (m/s to km/h)
NEXT STEPS
  • Study the derivation and application of the centripetal force equation Fc = mv²/r
  • Learn about the effects of banking angles on vehicle dynamics
  • Explore the concept of frictionless motion on banked curves
  • Practice unit conversion techniques, particularly for speed measurements
USEFUL FOR

This discussion is beneficial for physics students, automotive engineers, and anyone interested in understanding vehicle dynamics and safety on curved roadways.

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Homework Statement


A car goes around a curved stretch of flat roadway of radius 112m. The magnitudes of the horizontal and vertical components of force the car exerts on a securely seated passenger are, respectively, x= 220N and Y= 530N.

a) At what speed is the car travelling?

b) This stretch of highway is a notorius hazard during the winter months when it can be quite slippery. Accordingly the LTSA decides to bank it at an angle of 20degrees to the horizontal. At what speed could the car now negotiate this curve without needing to rely on any frictional force to prevent it slipping upwards of downwards on the banked surface?


Homework Equations


Not entirely sure of relevant equations.


The Attempt at a Solution


a) for this question i tried using the equation Fc = mv2 /r this gave me a v value of 21.36 however the correct answer to this question is 76.8. Is there another step which I have missed out, or am I approaching the problem wrong?

b) for this question I used the equation v2 = rgtan(theta) which produces a v value of 4 once again the correct answer is 72. If i subtract 4 from the correct value from (a) this gives me the correct answer, is this a correct method of obtaining the answer or just a coincidence?
 
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Ad a) my guess is that you got your answer in m/s, and the answer in the book is in km/h. They are hence the same.
 

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