Can anyone help me with this question 4. The compound disk pulley consists of a hub and attached outer rim. If the disk has a mass of3 kg and a radius of gyration kg = 0.045 m. Block A has a mass of 2 kg, and the spring is un-stretched when A is at rest (at 1) and the spring constant is 150 N/m. Neglect the mass of thecord and the spring.Determine the stretched length of the spring after A descends 0.3 m.a.b.Determine the speed of block A after A descends 0.3 m from rest.ww 001150 N/m0.3 m

To obtain the correct solution to the above question, the Work energy theorem must be applied. The potential energy possessed by the hanging mass at point A is equal to the sum of the kinetic energy of the hanging mass at point B, the energy lost in overcoming the inertial resistance of the pulley, and the energy consumed in stretching the spring. Thus, Potential energy of A at point 1= Kinetic energy of body A at point 2 + Energy consumed by the inertia of pulley + Energy consumed in stretching the spring. The expression for the kinetic energy of a body is- K.E.=12mv2 where m is the mass of the body v is the velocity of the mass The expression for the energy spent in compressing the spring is- E=12kx2 where k is the spring constant of the spring x is the distance by which spring is compressed Writing all the relevant data given in the question as- The mass of body A, m=2kg The mass of pulley, M=3kg the radius of gyration of the pulley, k=0.045m The spring constant of the spring, K=150 Nm Since we know that the angle turned by the pulley is the same. Thus, θ=constant∆xr=∆yR∆x30=0.3100 ∆x=0.09m Thus, the spring is stretched to a distance of 0.09m. Now, to determine the velocity of mass A at point 2, using the work-energy theorem as- The potential energy of mass A at point 1= Kinetic energy of mass A at point 2+ energy consumed by the inertia of pulley + Energy consumed in stretching of spring. mgh1-h2=12mv2+12Iω2+12Kx22×9.81×0.3=12mv2+Mk2×v2r2+Kx2 4×9.81×0.3=2v2+3×0.0452×v20.12+150×0.092 11.772=2v2+0.6075v2+1.215 10.557=2.6075v2 v=2.012 ms 1. The spring is stretched by a distance of 0.09m. 2. The velocity of mass A at point 2 be 2.012 m/s.

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4. The compound disk pulley consists of a hub and attached outer rim. If the disk has a mass of 3 kg and a radius of gyration ko stretched when A is at rest (at 1) and the spring constant is 150 N/m. Neglect the mass of the cord and the spring. 0.045 m. Block A has a mass of 2 kg, and the spring is un- %3D Determine the stretched length of the spring after A descends 0.3 m. b. Determine the speed of block A after A descends 0.3 m from rest. a. 100 mm 150 N/m 1. 0.3 m 2.

4. The compound disk pulley consists of a hub and attached outer rim. If the disk has a mass of 3 kg and a radius of gyration ko stretched when A is at rest (at 1) and the spring constant is 150 N/m. Neglect the mass of the cord and the spring. 0.045 m. Block A has a mass of 2 kg, and the spring is un- %3D Determine the stretched length of the spring after A descends 0.3 m. b. Determine the speed of block A after A descends 0.3 m from rest. a. 100 mm 150 N/m 1. 0.3 m 2.

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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Can anyone help me with this question

4. The compound disk pulley consists of a hub and attached outer rim. If the disk has a mass of
3 kg and a radius of gyration kg = 0.045 m. Block A has a mass of 2 kg, and the spring is un-
stretched when A is at rest (at 1) and the spring constant is 150 N/m. Neglect the mass of the
cord and the spring.
Determine the stretched length of the spring after A descends 0.3 m.
a.
b.
Determine the speed of block A after A descends 0.3 m from rest.
ww 001
150 N/m
0.3 m

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