A particle P of mass m = 3 kg arrives at point O with a horizontal velocity and starts rollingdown a circle with radius R = 1.5 m. The particle is attached to the point O by means of a linearspring of stiffness k = 50 N/m that is unstretched when the particle is at O. Assume that duringthe motion of P along the circle, the spring follows the circle. Let N = {x, ây} be a fixedreference frame as shown in the figure and let B = {bx, by} be a reference frame attached to Pso that b is tangent to the circular path and by is perpendicular to the circular path. Forconvenience, take g = 10 m/s² in this question.nyĤTIP e)For each value of 0 between 0 and, determine the value of vo for which the particle leavesthe circular path at 0 = 00.

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 = 1.5 m. The particle is attached to the point O by means of a linear spring of stiffness k = 50 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 = {x,y} be a fixed reference frame as shown in the figure and let B = {bx, by} be a reference frame attached to P so that by 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 ÎT P

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 = 1.5 m. The particle is attached to the point O by means of a linear spring of stiffness k = 50 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 = {x,y} be a fixed reference frame as shown in the figure and let B = {bx, by} be a reference frame attached to P so that by 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 ÎT P

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 and starts rolling
down a circle with radius R = 1.5 m. The particle is attached to the point O by means of a linear
spring of stiffness k = 50 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 = {x, ây} be a fixed
reference frame as shown in the figure and let B = {bx, 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.
ny
ĤT
IP

e)
For each value of 0 between 0 and, determine the value of vo for which the particle leaves
the circular path at 0 = 00.

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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 = 1.5 m. The particle is attached to the point O by means of a linear spring of stiffness k = 50 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 = {x, ây} be a fixed reference frame as shown in the figure and let B = {bx, 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. ny ĤT IP
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