### Physics Formulas#### Net Force- **Net Force Equation**: \(\vec{F}_{\text{net}} = m\vec{a}\) - Describes the relationship between the net force acting on an object, its mass (\(m\)), and its acceleration (\(\vec{a}\)).#### Friction- **Kinetic Friction Force**: \(F_{\text{fric,k}} = \mu_k N\) - Represents the force of kinetic friction, where \(\mu_k\) is the coefficient of kinetic friction and \(N\) is the normal force.- **Maximum Static Friction Force**: \(F_{\text{fric,s,max}} = \mu_s N\) - Represents the maximum force of static friction, where \(\mu_s\) is the coefficient of static friction.#### Motion- **Velocity in Circular Motion**: \(v = r\omega\) - Describes the tangential velocity (\(v\)) in circular motion, where \(r\) is the radius and \(\omega\) is the angular velocity.#### Circular Motion- **Centripetal Acceleration**: \(a_c = \frac{v^2}{r} = r\omega^2\) - Defines the centripetal acceleration (\(a_c\)) for an object moving in a circle of radius \(r\).- **Net Force in Circular Motion**: \(F_{\text{net,c}} = ma_c\) - Relates the net centripetal force required to keep an object moving in a circle to its mass and centripetal acceleration.These equations are fundamental in understanding the dynamics of objects, specifically in scenarios involving friction and circular motion. A mischievous child goes to an amusement park with his family. On one ride, after a severe scolding from his mother, he gets out of his seat and climbs to the top of the ride’s structure, which is shaped like a cone with its axis vertical and its sloped sides making an angle of \(\theta = 20^\circ\) with the horizontal as shown in the Figure. This part of the structure rotates about the vertical central axis when the ride operates. The child sits on the sloped surface at a point \(d = 5.32 \, \text{m}\) down the sloped side from the center of the cone and pouts. The coefficient of static friction between the boy and the cone is \(\mu_s = 0.7\). The ride operator does not notice that the child has slipped away from his seat and so continues to operate the ride. Calculate the speed \(v\) at which the child will start to slip off the ride. Answer: \(3.62 \, \text{m/s}\).The diagram shows:- A conical structure with a vertical central axis. - A child sitting on the sloped side of the cone.- The slope makes an angle \(\theta = 20^\circ\) with the horizontal.- The distance down the slope from the center of the cone to the child is \(d = 5.32 \, \text{m}\).- A flag on top indicates the rotation of the structure.

Answered: Image /qna-images/answer/d0be05de-86b2-41fa-bfee-bc4bd25ed153.jpg

A mischievous child goes to an amusement park with his family. On one ride, after a severe scolding from his mother, he gets out of his seat and climbs to the top of the ride's structure, which is shaped like a cone with its axis vertical and its sloped sides making an angle of 0 = 20° with the horizontal as shown in the Figure. This part of the structure rotates about the vertical central axis when the ride operates. The child sits on the sloped surface at a point d = 5.32 m down the sloped side from the center of the cone and pouts. The coefficient of static friction between the boy and the cone is μ = 0.7. The ride operator does not notice that the child has slipped away from his seat and so continues to operate the ride. Calculate the speed v at which the child will start to slip off the ride. Answer: 3.62 m/sec. 0

A mischievous child goes to an amusement park with his family. On one ride, after a severe scolding from his mother, he gets out of his seat and climbs to the top of the ride's structure, which is shaped like a cone with its axis vertical and its sloped sides making an angle of 0 = 20° with the horizontal as shown in the Figure. This part of the structure rotates about the vertical central axis when the ride operates. The child sits on the sloped surface at a point d = 5.32 m down the sloped side from the center of the cone and pouts. The coefficient of static friction between the boy and the cone is μ = 0.7. The ride operator does not notice that the child has slipped away from his seat and so continues to operate the ride. Calculate the speed v at which the child will start to slip off the ride. Answer: 3.62 m/sec. 0

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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