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Problem: A uniform rod of mass M = 0.5 kg and length L = 0.5 m is hung vertically and pivoted at its upper end (point P). It is free to rotate in a vertical plane about a horizontal axis which passes through the pivot point. A small particle of mass m = 0.05 kg is shot at the rod with initial speed v₁ = 3 m/s, at 40° below the horizontal, immediately sticking to the lower end of the rod upon hitting it. a. Consider the rod and the particle as one system, is the mechanical energy of the system conserved? What about the linear momentum and the angular momentum? Give simple justifications. b. What is the moment of inertia of the rod about point P. c. What is the angular speed of the rod immediately after the collision? d. Through what angle with the vertical the rod-particle system will rotate after the collision? E M E L Vi 40°

Problem: A uniform rod of mass M = 0.5 kg and length L = 0.5 m is hung vertically and pivoted at its upper end (point P). It is free to rotate in a vertical plane about a horizontal axis which passes through the pivot point. A small particle of mass m = 0.05 kg is shot at the rod with initial speed v₁ = 3 m/s, at 40° below the horizontal, immediately sticking to the lower end of the rod upon hitting it. a. Consider the rod and the particle as one system, is the mechanical energy of the system conserved? What about the linear momentum and the angular momentum? Give simple justifications. b. What is the moment of inertia of the rod about point P. c. What is the angular speed of the rod immediately after the collision? d. Through what angle with the vertical the rod-particle system will rotate after the collision? E M E L Vi 40°

Elements Of Electromagnetics
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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Problem: A uniform rod of mass M = 0.5 kg and length L = 0.5 m is hung vertically and pivoted at its upper end (point P). It is free to rotate in a vertical plane about a horizontal axis which passes through the pivot point. A small particle of mass m = 0.05 kg is shot at the rod with initial speed v₁ = 3 m/s, at 40° below the horizontal, immediately sticking to the lower end of the rod upon hitting it. a. Consider the rod and the particle as one system, is the mechanical energy of the system conserved? What about the linear momentum and the angular momentum? Give simple justifications. b. What is the moment of inertia of the rod about point P. c. What is the angular speed of the rod immediately after the collision? d. Through what angle with the vertical the rod-particle system will rotate after the collision? E M E L Vi 40°
Transcribed Image Text:Problem: A uniform rod of mass M = 0.5 kg and length L = 0.5 m is hung vertically and pivoted at its upper end (point P). It is free to rotate in a vertical plane about a horizontal axis which passes through the pivot point. A small particle of mass m = 0.05 kg is shot at the rod with initial speed v₁ = 3 m/s, at 40° below the horizontal, immediately sticking to the lower end of the rod upon hitting it. a. Consider the rod and the particle as one system, is the mechanical energy of the system conserved? What about the linear momentum and the angular momentum? Give simple justifications. b. What is the moment of inertia of the rod about point P. c. What is the angular speed of the rod immediately after the collision? d. Through what angle with the vertical the rod-particle system will rotate after the collision? E M E L Vi 40°
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