Explanation Given: m = 3 kg . k = 1200 N/m . l o = 0.5 m . Let position 1 be the initial position. r 1 = 0.3 m ( v r ) 1 = 0 ( v θ ) 1 = 2 m / s v 1 = 2 m / s x = r 1 − l o = 0.3 − 0.5 = − 0.2 m T 1 = 1 2 m v 2 = 1 2 ( 3 ) ( 2 ) 2 = 6 J V 1 = 1 2 k x 1 2 = 1 2 ( 1200 ) ( − 0.2 ) 2 = 24 J Let position 2 be when r is maximum. ( v r ) 2 = 0 r 2 = r m x 2 = ( r m − 0.5 ) T 2 = 1 2 m v 2 2 = 1 2 ( 3 ) ( v θ ) 2 2 = 1.5 ( v θ ) 2 2 V 2 = 1 2 k x 2 2 = 1 2 ( 1200 ) ( r m − 0 To determine (b) The corresponding speed.

Vector Mechanics for Engineers: Dynamics

11th Edition

ISBN: 9780077687342

Author: Ferdinand P. Beer, E. Russell Johnston Jr., Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 13.2, Problem 13.94P

To determine

(a)

Maximum distance between origin and collar.

To determine

(b)

The corresponding speed.

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Chapter 13.2, Problem 13.93P

Chapter 13.2, Problem 13.95P

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Collar A has a mass of 3 kg and is attached to a spring of constant 1200 N/m and of undeformed length equal to 0.5 m. The system is set in motion with r = 0.3 m, v0 = 2 m/s, and vr = 0. Neglecting the mass of the rod and the effect of friction, determine (a) the maximum distance between the origin and the collar, (b) the corresponding speed. (Hint: Solve the equation obtained for rby trial and error.)

Q.1. A block of mass m = 0.5 kg is pushed against a horizontal spring of spring constant k = 450 N/m and negligible mass. The spring is compressed a distance x from equilibrium, and then released from rest. The block travels along a frictionless horizontal surface and reaches point B with a speed vg = 12 m/s. Take g = 10 m/s2. The compression of the spring is: a. x = 0.16 m b. x = 0.467 m c. x = 0.533 m B. d. x = 0.4 m

Collar A has a mass of 3 kg and is attached to a spring of constant 1200 N/m and of undeformed length equal to 0.5 m. The system is set in motion with r= 0.3 m, v0 = 2 m/s, and vr = 0. Neglecting the mass of the rod and the effect of friction, determine the radial and transverse components of the velocity of the collar when r= 0.6 m.

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Vector Mechanics for Engineers: Dynamics

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(a) Maximum distance between origin and collar.

Solution Summary: The author explains the maximum distance between origin and collar.