Mechanics; speed of car travelling around bend.

[axdv]

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 F_c = 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?

 

[irycio]

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.