Yahoo Answers is shutting down on 4 May 2021 (Eastern Time) and the Yahoo Answers website is now in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Physics 101 question?
A ball is hung by a string from the inside roof of a van. The van is moving with a
constant velocity, v, around a curve (radius R = 150 m) on an unbanked road.
(a) What angle does the ball make with respect to the vertical?
(b) Derive an expression for the maximum velocity before the car starts slipping
sideways on the road?
(c) What angle would you need to tilt the road (banked curve) to maintain the van’s
motion in a circle, if the tires were without a frictional force?
Please explain as to how you derive the answers and what approaches you used.
1 Answer
- az_lenderLv 73 years ago
(a) Vertical force on the ball is mg; centrifugal force on the ball is mv^2/r.
So the ratio of vertical to horizontal force is gr/v^2 = (9.8 m/s^2)(150 m)/(v^2), and the angle is
arctan[v^2/(1470 m^2/s^2)].
(c) You need the roadway tilted at the same angle to the horizontal that was found for the string's deflection from the vertical. That is, arctan[v^2/(1470 m^2/s^2)].
(b) I'm not sure whether to apply a coefficient of kinetic friction (because the car is moving), or a coefficient of static friction (because the car is NOT to move in the radial direction). Hmm.
Anyway, if you look at it as a static friction problem, you need
(mu)mg greater than or equal to mv^2/r =>
v less than or equal to sqrt[r(mu)g], where mu is the coefficient of friction.