A 23 mm diameter glass marble with a mass of 15 g rolls without slipping down a track toward a vertical loop of radius R = 13 cm, as shown in the figure. Approximate the minimum translational speed umin the marble must have in order to complete the loop without falling off the track when it is a height H = 25 cm above the bottom of the loop.

A 23 mm diameter glass marble with a mass of 15 g rolls without slipping down a track toward a vertical loop of radius R = 13 cm, as shown in the figure. Approximate the minimum translational speed umin the marble must have in order to complete the loop without falling off the track when it is a height H = 25 cm above the bottom of the loop.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Angular speed, acceleration and displacement

Angular acceleration is defined as the rate of change in angular velocity with respect to time. It has both magnitude and direction. So, it is a vector quantity.

Angular Position

Before diving into angular position, one should understand the basics of position and its importance along with usage in day-to-day life. When one talks of position, it’s always relative with respect to some other object. For example, position of earth with respect to sun, position of school with respect to house, etc. Angular position is the rotational analogue of linear position.

Question

A 23 mm diameter glass marble with a mass of 15 g rolls
without slipping down a track toward a vertical loop of radius
R = 13 cm, as shown in the figure.
Approximate the minimum translational speed Umin the
marble must have in order to complete the loop without
falling off the track when it is a height H = 25 cm above the
bottom of the loop.
Umin =
m/s
R
Figure is not to scale.

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