Vertical Circles and Curves

Rounding A Curve Friction between the tires and the road provides the centripetal force needed to keep a car in the curve

Example A 1000 kg car rounds a curve on a flat road of radius 50 m at a speed of 14 m/s. A) will the car make the turn on a dry day when the μ is.60? B) What about on a day when the road is icy and the μ is.25?

Vertical Circle Weight is acting in the same plane as centripetal force

Example A.150kg ball on the end of a 1.10 m long cord is swung in a vertical circle a) determine the minimum speed the ball must have at the top of its arc so that it continues moving in a circle b) calculate the tension of the cord at the bottom of the swing if it is moving 2x the speed calculated in part a.

Solution At top of swing centripetal force is a combination of mg and F T F r = F T + mg - when just keeping it in a circle, we can assume that the F T = 0 and the centripetal force is supplied only by gravity

At bottom, F r = F T - mg

Example On a roller coaster, a 250kg car moves around a vertical loop of radius 15m with a speed of 13 m/s at the top of the loop and 22 m/s at the bottom of the loop. What weight will he feel at the top and the bottom?