6.3 Centripetal Force
The inward net force holding a body on a circular path, supplied by tire friction on a flat turn or by the banking of a curve.
5 exercises
6.3 Exercise 11
(a) A 22.0 kg child is riding a playground merry-go-round that is rotating at 40.0 rev/min. What centripetal force must she exert to stay on if she is 1.25 m from its center?
(b) What centripetal force does she need to stay on an amusement park merry-go-round that rotates at 3.00 rev/min if she is 8.00 m from its center?
(c) Compare each force with her weight.
6.3 Exercise 13
What is the ideal banking angle for a gentle turn of 1.20 km radius on a highway with a 105 km/h speed limit (about 65 mi/h), assuming everyone travels at the limit?
6.3 Exercise 15
(a) What is the radius of a bobsled turn banked at 75.0° and taken at 30.0 m/s, assuming it is ideally banked?
(b) Calculate the centripetal acceleration.
(c) Does this acceleration seem large to you?
Integrated Concepts
If a car takes a banked curve at less than the ideal speed, friction is needed to keep it from sliding toward the inside of the curve (a real problem on icy mountain roads). (a) Calculate the ideal speed to take a 100 m radius curve banked at 15.0º. (b) What is the minimum coefficient of friction needed for a frightened driver to take the same curve at 20.0 km/h?
Unreasonable Results
(a) Calculate the minimum coefficient of friction needed for a car to negotiate an unbanked 50.0 m radius curve at 30.0 m/s.
(b) What is unreasonable about the result?
(c) Which premises are unreasonable or inconsistent?
Adapted from College Physics © 2022 Rice University. Licensed under CC BY 4.0. Sources: College Physics 2e, College Physics for AP® Courses 2e. Imported at revision f98d7a7.