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What speed

What speed

College Physics
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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For the normal force in the drawing to have the same magnitude at all points on the vertical track, the stunt driver must adjust the speed to be different at different points. Suppose, for example, that the track has a radius of 2.23 m and that the driver goes past point 1 at the bottom with a speed of 24.0 m/s. What speed must she have at point 3, so that the normal force at the top has the same magnitude as it did at the bottom?

### Figure Explanation for Educational Website **Figure (a): Motorcyclist on a Vertical Loop** This diagram depicts a motorcyclist performing a loop-the-loop stunt inside a circular track. The circle shown is the path traced by the motorcyclist. The circular track has a radius denoted as \( r \). - The motorcyclist enters the loop with an initial forward velocity, allowing them to traverse upside down at the top of the loop. - The red arrow indicates the direction of motion along the loop. - Multiple positions of the motorcyclist are shown to illustrate different points on the loop. **Figure (b): Force Analysis on a Motorcyclist in a Vertical Loop** This free-body diagram illustrates the forces acting on the motorcyclist at four key positions within the loop. The circle represents the loop's path. 1. **Position 1 (Bottom of the Loop):** - The gravitational force \( m\vec{g} \) is directed downward. - The normal force \( \vec{F}_{N1} \) from the loop acts upward, opposing gravity. 2. **Position 2 (Right Side of the Loop):** - The gravitational force \( m\vec{g} \) is still directed downward. - The normal force \( \vec{F}_{N2} \) points inward toward the center of the loop, perpendicular to the loop's surface. 3. **Position 3 (Top of the Loop):** - Both the gravitational force \( m\vec{g} \) and the normal force \( \vec{F}_{N3} \) are directed downward, towards the center of the loop. 4. **Position 4 (Left Side of the Loop):** - The gravitational force \( m\vec{g} \) continues downward. - The normal force \( \vec{F}_{N4} \), similar to Position 2, points inward toward the loop's center. This analysis demonstrates how the normal force and gravitational force vary in direction and magnitude around the loop, maintaining the motorcyclist's circular motion.
Transcribed Image Text:### Figure Explanation for Educational Website **Figure (a): Motorcyclist on a Vertical Loop** This diagram depicts a motorcyclist performing a loop-the-loop stunt inside a circular track. The circle shown is the path traced by the motorcyclist. The circular track has a radius denoted as \( r \). - The motorcyclist enters the loop with an initial forward velocity, allowing them to traverse upside down at the top of the loop. - The red arrow indicates the direction of motion along the loop. - Multiple positions of the motorcyclist are shown to illustrate different points on the loop. **Figure (b): Force Analysis on a Motorcyclist in a Vertical Loop** This free-body diagram illustrates the forces acting on the motorcyclist at four key positions within the loop. The circle represents the loop's path. 1. **Position 1 (Bottom of the Loop):** - The gravitational force \( m\vec{g} \) is directed downward. - The normal force \( \vec{F}_{N1} \) from the loop acts upward, opposing gravity. 2. **Position 2 (Right Side of the Loop):** - The gravitational force \( m\vec{g} \) is still directed downward. - The normal force \( \vec{F}_{N2} \) points inward toward the center of the loop, perpendicular to the loop's surface. 3. **Position 3 (Top of the Loop):** - Both the gravitational force \( m\vec{g} \) and the normal force \( \vec{F}_{N3} \) are directed downward, towards the center of the loop. 4. **Position 4 (Left Side of the Loop):** - The gravitational force \( m\vec{g} \) continues downward. - The normal force \( \vec{F}_{N4} \), similar to Position 2, points inward toward the loop's center. This analysis demonstrates how the normal force and gravitational force vary in direction and magnitude around the loop, maintaining the motorcyclist's circular motion.
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