**Physics Problem: Frictionless Ramp Motion****Problem Statement:**Consider an object sliding down a frictionless ramp that is inclined at an angle θ above the horizontal. What should the acceleration down the ramp \( a_x \) be when the angle θ becomes zero?**Diagram Explanation:**The provided diagram shows a setup with an inclined ramp and an object placed on it. The important elements include:- A solid block (representing the object) resting on the inclined plane.- The angle of inclination, represented by θ.- The force of gravity acting on the object, denoted by 'mg' directed downwards.- A coordinate system with the x-axis parallel to the ramp and the y-axis perpendicular to the ramp.### Analyzing the ForcesWhen analyzing the forces acting on the object on the inclined plane:1. The gravitational force \( F_g = mg \) acts vertically downwards.2. This force can be decomposed into two components: - Parallel to the inclined plane: \( F_{\parallel} = mg \sin(θ) \) - Perpendicular to the inclined plane: \( F_{\perp} = mg \cos(θ) \)### Acceleration CalculationSince there is no friction, the only force causing the block to accelerate down the plane is \( F_{\parallel} \).Using Newton's Second Law along the inclined plane:\[ F_{\parallel} = ma_x \]\[ mg \sin(θ) = ma_x \]\[ a_x = g \sin(θ) \]### Special Case: θ = 0When the angle θ becomes zero, the plane becomes horizontal. Substituting \( θ = 0 \) in the formula for acceleration:\[ a_x = g \sin((0)) \]\[ a_x = g \cdot 0 \]\[ a_x = 0 \]Therefore, the acceleration down the ramp \( a_x \) becomes zero when the angle θ is zero.

m= mass of objectg= gravitational accelerationF=forceθ=incline angle

Answered: 0 above Consider an object sliding down…

0 above Consider an object sliding down a frictionless ramp that is inclined an angle the horizontal. What should the acceleration down the ramp ar be when the angle becomes zero? 0 mg

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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