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 = 60 N/m that is unstretched R = 5 m. The particle is attached to the point O by means of a linear spring of stiffness k when the particle is at O. Assume that during the motion of P along the circle, the spring follows the circle. Let {b, by} be a reference frame attached to N = {n, ny} be a fixed reference frame as shown in the figure and let B = P so that b is tangent to the circular path and by is perpendicular to the circular path. For convenience, take g = 10 m/s 2 in this question.

Elements Of Electromagnetics
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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
= 60 N/m that is unstretched
R = 5 m. The particle is attached to the point O by means of a linear spring of stiffness k
when the particle is at O. Assume that during the motion of P along the circle, the spring follows the circle. Let
N = {n, ny} be a fixed reference frame as shown in the figure and let B = {b, 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/s
2
in this question.
1/
Dy
nx
IP
Transcribed Image Text: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 = 60 N/m that is unstretched R = 5 m. The particle is attached to the point O by means of a linear spring of stiffness k when the particle is at O. Assume that during the motion of P along the circle, the spring follows the circle. Let N = {n, ny} be a fixed reference frame as shown in the figure and let B = {b, 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/s 2 in this question. 1/ Dy nx IP
a)
Determine the Direction Cosine Matrices [C]B and BCN.
b)
Determine for P in the frame N the position vector NTP, velocity vector NP, and acceleration vector NaP.
c)
Draw a Free Body Diagram of the particle, clearly indicating all forces acting on the particle, and use the Free Bod
Diagram to determine the equation(s) of motion of the particle.
d)
What relationship between 0 and needs to be satisfied at the point where the particle leaves the circle?
1
e)
For each value of 00 between 0 and determine the value of vo for which the particle leaves the circular path at
0=00.
7
Transcribed Image Text:a) Determine the Direction Cosine Matrices [C]B and BCN. b) Determine for P in the frame N the position vector NTP, velocity vector NP, and acceleration vector NaP. c) Draw a Free Body Diagram of the particle, clearly indicating all forces acting on the particle, and use the Free Bod Diagram to determine the equation(s) of motion of the particle. d) What relationship between 0 and needs to be satisfied at the point where the particle leaves the circle? 1 e) For each value of 00 between 0 and determine the value of vo for which the particle leaves the circular path at 0=00. 7
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