Question 1. A tube rotates in the horizontal ry plane with a constant angular velocity w about the z-axis. A particle of mass m is released from a radial distance R when the tube is in the position shown. This problem is based on problem 3.2 in the text. R m 2R Figure 1 x a) Draw a free body diagram of the particle if the tube is frictionless. b) Draw a free body diagram of the particle if the coefficient of friction between the sides of the tube and the particle is = k = p. c) For the case where the tube is frictionless, what is the radial speed at which the particle leaves the tube? d) For the case where there is friction, derive a differential equation that would allow you to solve for the radius of the particle as a function of time. I'm only looking for the differential equation. DO NOT solve it. 1 e) If there is no friction, what is the angle of the tube when the particle exits? • Hint: You may need to solve a differential equation for the last part. The "potentially useful formulas" may be useful if you are rusty on your differential equations.
Question 1. A tube rotates in the horizontal ry plane with a constant angular velocity w about the z-axis. A particle of mass m is released from a radial distance R when the tube is in the position shown. This problem is based on problem 3.2 in the text. R m 2R Figure 1 x a) Draw a free body diagram of the particle if the tube is frictionless. b) Draw a free body diagram of the particle if the coefficient of friction between the sides of the tube and the particle is = k = p. c) For the case where the tube is frictionless, what is the radial speed at which the particle leaves the tube? d) For the case where there is friction, derive a differential equation that would allow you to solve for the radius of the particle as a function of time. I'm only looking for the differential equation. DO NOT solve it. 1 e) If there is no friction, what is the angle of the tube when the particle exits? • Hint: You may need to solve a differential equation for the last part. The "potentially useful formulas" may be useful if you are rusty on your differential equations.
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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
Transcribed Image Text:Question 1.
A tube rotates in the horizontal ry plane with a constant angular velocity w about the z-axis. A
particle of mass m is released from a radial distance R when the tube is in the position shown.
This problem is based on problem 3.2 in the text.
R
m
2R
Figure 1
x
a) Draw a free body diagram of the particle if the tube is frictionless.
b) Draw a free body diagram of the particle if the coefficient of friction between the sides of the
tube and the particle is = k = p.
c) For the case where the tube is frictionless, what is the radial speed at which the particle
leaves the tube?
d) For the case where there is friction, derive a differential equation that would allow you to
solve for the radius of the particle as a function of time. I'm only looking for the differential
equation. DO NOT solve it.
1
e) If there is no friction, what is the angle of the tube when the particle exits?
• Hint: You may need to solve a differential equation for the last part. The "potentially
useful formulas" may be useful if you are rusty on your differential equations.
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