**Physics Problem on Inclined Planes****Problem Statement:**A 6.0 kg package in an Amazon sorting room slides 3.0 m down a plane inclined 60 degrees below the horizontal. The coefficient of kinetic friction between the package and the plane is \( \mu_k = 0.35 \). Calculate the work done on the package by (a) friction; (b) gravity; (c) the normal force. If the package starts with velocity \( v = 2.0 \, \text{m/s} \), what is its final velocity?**Solution Overview:**To solve this problem, we'll break it down into several steps:1. **Determine the Forces:** - Gravitational Force (Component along the incline). - Frictional Force. - Normal Force.2. **Calculate the Work Done:** - By friction. - By gravity. - By the normal force.3. **Apply Energy Principles:** - Use work-energy theorem to find the final velocity of the package.### Detailed Steps:**1. Gravitational Force (Component along the incline):** - The gravitational force acting down the incline is given by: \[ F_{\text{gravity, parallel}} = mg \sin \theta \] - Where \( m = 6.0 \, \text{kg} \), \( g = 9.8 \, \text{m/s}^2 \), and \( \theta = 60^\circ \).**2. Frictional Force:** - The frictional force acting up the incline is calculated as: \[ F_{\text{friction}} = \mu_k F_{\text{normal}} \] - Where \( F_{\text{normal}} = mg \cos \theta \).**3. Work Calculation:** - **Work done by friction** \( W_{\text{friction}} \): \[ W_{\text{friction}} = F_{\text{friction}} \times d \times \cos 180^\circ \] - **Work done by gravity** \( W_{\text{gravity}} \): \[ W_{\text{gravity}} = F_{\text{gravity, parallel}} \times d \times \cos 0^\circ \] - **Work done by normal force** \( W_{\text{

Name: **Physics Problem on Inclined Planes****Problem Statement:**A 6.0 kg
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Description: **Physics Problem on Inclined Planes****Problem Statement:**A 6.0 kg package in an Amazon sorting room slides 3.0 m down a plane inclined 60 degrees below the horizontal. The coefficient of kinetic friction between the package and the plane is \( \m

In the given question, Mass of the package (m) = 6 kg Distance moved down the plane (d) = 3m Angle…

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[9.] A 6.0 kg package in an Amazon sorting room slides 3.0 m down a plane inclined 60 degrees below the horizontal. The coefficient of kinetic friction between the package and the plane is k = 0.35. Calculate the work done on the package by (a) friction; (b) gravity; (c) the normal force. If the package starts with velocity v = 2.0 m/s, what is its final velocity?

[9.] A 6.0 kg package in an Amazon sorting room slides 3.0 m down a plane inclined 60 degrees below the horizontal. The coefficient of kinetic friction between the package and the plane is k = 0.35. Calculate the work done on the package by (a) friction; (b) gravity; (c) the normal force. If the package starts with velocity v = 2.0 m/s, what is its final velocity?

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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