A particle of fixed mass \( m \) moving vertically in a constant (downward) gravitational field has vertical acceleration \( -g \), where \( g \) is the strength of the gravitational field. The particle has:- **Kinetic Energy** \( K = \frac{1}{2} mv^2 \)- **Potential Energy** \( V = mgx \)Here \( x \) is its height at time \( t \), and \( v = \frac{dx}{dt} \) is its vertical velocity.Denote by \( E \), the total energy, so \( E = K + V \).Show that \( E \) is constant.

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A particle of fixed mass m moving vertically in a constant (downward) gravitational field has vertical acceleration -g, where g is the strength of the gravitational field. The particle has: • Kinetic Energy K = mv2 • Potential Energy V = mgx. Here x is its height at time t and v = is its vertical velocity. Denote by E, the total energy, so E = K + . Show that E is constant.

A particle of fixed mass m moving vertically in a constant (downward) gravitational field has vertical acceleration -g, where g is the strength of the gravitational field. The particle has: • Kinetic Energy K = mv2 • Potential Energy V = mgx. Here x is its height at time t and v = is its vertical velocity. Denote by E, the total energy, so E = K + . Show that E is constant.

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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