### Physics Problem: Amusement Park Ride Dynamics**Problem Statement:**At an amusement park, there is a ride in which cylindrically shaped chambers spin around a central axis. People sit in seats facing the axis, with their backs against the outer wall. At one instant, the outer wall moves at a speed of $3.70 \, \text{m/s}$, and an $87.0 \, \text{kg}$ person feels a $565 \, \text{N}$ force pressing against his back. What is the radius of the chamber?**Solution:**Given data:- Speed of the outer wall ($v$) = $3.70 \, \text{m/s}$- Force experienced by the person ($F$) = $565 \, \text{N}$- Mass of the person ($m$) = $87.0 \, \text{kg}$We need to find the radius of the chamber ($r$).Using the formula for centripetal force:\[ F = \frac{m v^2}{r} \]Rearranging to solve for $r$:\[ r = \frac{m v^2}{F} \]Substitute the given values:\[ r = \frac{87.0 \, \text{kg} \times (3.70 \, \text{m/s})^2}{565 \, \text{N}} \]\[ r = \frac{87.0 \times 13.69}{565} \]\[ r = \frac{1191.03}{565} \]\[ r \approx 2.11 \, \text{m} \]**Answer:**The radius of the chamber is approximately $2.11 \, \text{m}$.

Solution: The force which makes the person feel pressure against his back is due to the centrifugal…

8. At an amusement park there is a ride in which cylindrically shaped chambers spin around a central axis. People sit in seats facing the axis, their backs against the outer wall. At one instant the outer wall moves at a speed of 3.70 m/s, and an 87.0-kg person feels a 565-N force pressing against his back. What is the radius of the chamber? m sf60 50 $$ sfo 60 s ssfor

8. At an amusement park there is a ride in which cylindrically shaped chambers spin around a central axis. People sit in seats facing the axis, their backs against the outer wall. At one instant the outer wall moves at a speed of 3.70 m/s, and an 87.0-kg person feels a 565-N force pressing against his back. What is the radius of the chamber? m sf60 50 $$ sfo 60 s ssfor

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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