A particle P of mass m = 3 kg arrives at point O with a horizontal velocity and starts rolling down a circle with radius R = 3.5 m. The particle is attached to the point O by means of a linear spring of stiffness k = 60 N/m that is unstretched when the particle is at O. Assume that during the motion of P along the circle, the spring follows the circle. Let N = {î, îy} be a fixed reference frame as shown in the figure and let B = {b₁, by} be a reference frame attached to P so that b is tangent to the circular path and by is perpendicular to the circular path. For convenience, take g = 10 m/s² in this question.

A particle P of mass m = 3 kg arrives at point O with a horizontal velocity and starts rolling down a circle with radius R = 3.5 m. The particle is attached to the point O by means of a linear spring of stiffness k = 60 N/m that is unstretched when the particle is at O. Assume that during the motion of P along the circle, the spring follows the circle. Let N = {î, îy} be a fixed reference frame as shown in the figure and let B = {b₁, by} be a reference frame attached to P so that b is tangent to the circular path and by is perpendicular to the circular path. For convenience, take g = 10 m/s² in this question.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be created or destroyed — only transformed.

Question

A particle P of mass m = 3 kg arrives at point O with a horizontal velocity vo and starts rolling
down a circle with radius R = 3.5 m. The particle is attached to the point O by means of a linear
spring of stiffness k = 60 N/m that is unstretched when the particle is at O. Assume that during the
motion of P along the circle, the spring follows the circle. Let N = {î, îy} be a fixed reference
frame as shown in the figure and let B = {b, by} be a reference frame attached to P so that ba
is tangent to the circular path and by is perpendicular to the circular path. For convenience, take
g = 10 m/s² in this question.
ny
nx
IP

Draw a Free Body Diagram of the particle, clearly indicating all forces acting on the particle, and
use the Free Body Diagram to determine the equation(s) of motion of the particle.

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