A particle P of mass m = 4 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 = {â, ŵy} be a fixed reference frame as shown in the figure and let B = {bæ, by } be a reference frame attached to P so that ĥ is tangent to the circular path and ɓy is perpendicular to the circular path. For convenience, take g = 10 m/s² in this question. nx a) Determine the Direction Cosine Matrices [C]B and BCN. b) Determine for P in the frame N the position vector NTP, velocity vector NVP, 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 Body Diagram to determine the equation(s) of motion of the particle.
A particle P of mass m = 4 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 = {â, ŵy} be a fixed reference frame as shown in the figure and let B = {bæ, by } be a reference frame attached to P so that ĥ is tangent to the circular path and ɓy is perpendicular to the circular path. For convenience, take g = 10 m/s² in this question. nx a) Determine the Direction Cosine Matrices [C]B and BCN. b) Determine for P in the frame N the position vector NTP, velocity vector NVP, 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 Body Diagram to determine the equation(s) of motion of the particle.
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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Question
![A particle P of mass m = 4 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
= {În, ŵy} be a fixed reference frame as shown in the figure and let B = {bx, by} be
a reference frame attached to P so that ĥ is tangent to the circular path and by is
perpendicular to the circular path. For convenience, take g =
N
=
10 m/s² in this question.
ny
nx
IP
a)
Determine the Direction Cosine Matrices N[C]B and BCN.
b)
Determine for P in the frame N the position vector NrP, velocity vector NP, and
acceleration vector NaP.
e)
For each value of
leaves the circular path at 0 = 00.
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.
d)
What relationship between 0 and needs to be satisfied at the point where the particle
leaves the circle?
between 0 and, determine the value of åå for which the particle](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F88987a03-4211-4a24-a161-6afee14c4628%2F676829d7-9b3f-4b61-aa5b-1f6e82ed9445%2Fvyc73f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A particle P of mass m = 4 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
= {În, ŵy} be a fixed reference frame as shown in the figure and let B = {bx, by} be
a reference frame attached to P so that ĥ is tangent to the circular path and by is
perpendicular to the circular path. For convenience, take g =
N
=
10 m/s² in this question.
ny
nx
IP
a)
Determine the Direction Cosine Matrices N[C]B and BCN.
b)
Determine for P in the frame N the position vector NrP, velocity vector NP, and
acceleration vector NaP.
e)
For each value of
leaves the circular path at 0 = 00.
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.
d)
What relationship between 0 and needs to be satisfied at the point where the particle
leaves the circle?
between 0 and, determine the value of åå for which the particle
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