Forces and Motion Challenging Qs!

[Saad]

Just recently NASCAR has increased the incline of their race track curves to 18 degrees at the bottom of the curve and 20 degrees at the top. The bottom part of the track (18 degrees incline) has a radius of 60m, where as the top part of the track (20 degrees incline) has a radius of 70m.

a) Using the apropriate free body diagram, derive the equation for the maximum safe speed to negotiate a frictionless banked curve.

b) Neglecting friction, what percentage increase in velocity can be achieved at the top part of the curve (compared with the traditional 18 degrees bank)?

c) If the radius of curvature of the curve for the bottom is 60m and 70m at the top, would the car at the top be able to pass a car on the bottom if they went around half of a circular path at their maximum speeds?

[HallsofIvy]

Have you made no attempt at all on this? Please look at the "read this before posting" for forum "rules"- basically that you make some attempt yourself and show us what you have tried. That way we have a better idea of what you know and can give suggestions without just giving the answer. It does not do you any good to have someone else do your homework for you.

"a) Using the apropriate free body diagram, derive the equation for the maximum safe speed to negotiate a frictionless banked curve. "

Draw the "gravity" force vector straight down, then draw the components perpendicular to the track and down the banked curve (this is a cross section of the track of course).
Draw the centripetal force vector for a car going around the curve at some speed v.
The "maximum safe speed" is where the net component up the banked curve is 0 (so the car will not go off the track).

"b) Neglecting friction, what percentage increase in velocity can be achieved at the top part of the curve (compared with the traditional 18 degrees bank)?"

After you have done (a) for both top and bottom and found the maximum speed in both positions, what is the percentage increase of top over bottom?

") If the radius of curvature of the curve for the bottom is 60m and 70m at the top, would the car at the top be able to pass a car on the bottom if they went around half of a circular path at their maximum speeds?"

Go back and do (a) over again, swapping the radii. Is it possible for the maximum speed of a car at the top to be greater than the maximum speed of a car at the bottom?

[Saad]

Has anyone been able to figure this one out?? This one seems to be very challenging...plz try!

[cookiemonster]

What progress have you made on the problem?

cookiemonster

[NateTG]

Has anyone been able to figure this one out?? This one seems to be very challenging...plz try!

Millions of high school and college students every year. Dosen't seem that tough to me.