A particle of mass m is attached to a spring, as shown below. Initially, the spring is unstretched with length lo and at rest. The spring constant is k. An impulse is applied to give an initial ve- locity vo in the direction a. The motion occurs in the horizontal plane (ignore gravity and friction). Part A: What is the angular impulse about point O required to produce this speed and direc- tion? Part B: Show that the equations of motion for the position of particle P with respect to O (in a polar frame) are as follows: Ö // -2r0 1 -k(r-lo) m Ÿ +r0², where r is the distance of P with respect to O and is the corresponding angle measured counter- clockwise from the horizontal. (Hint: Define a polar reference frame and use Newton's Second Law (angular momentum form, Mp/o = (hp/o) to find and use Newton's Second Law (standard form, Fp = mpap/o) with the polar acceleration to find r.) Values: lo=1 m, mp = 2 kg, vo = 3 m/s, a = 45 deg. (1) (2) lo m No fa P

A particle of mass m is attached to a spring, as shown below. Initially, the spring is unstretched with length lo and at rest. The spring constant is k. An impulse is applied to give an initial ve- locity vo in the direction a. The motion occurs in the horizontal plane (ignore gravity and friction). Part A: What is the angular impulse about point O required to produce this speed and direc- tion? Part B: Show that the equations of motion for the position of particle P with respect to O (in a polar frame) are as follows: Ö // -2r0 1 -k(r-lo) m Ÿ +r0², where r is the distance of P with respect to O and is the corresponding angle measured counter- clockwise from the horizontal. (Hint: Define a polar reference frame and use Newton's Second Law (angular momentum form, Mp/o = (hp/o) to find and use Newton's Second Law (standard form, Fp = mpap/o) with the polar acceleration to find r.) Values: lo=1 m, mp = 2 kg, vo = 3 m/s, a = 45 deg. (1) (2) lo m No fa 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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