Explanation Work is referred to as the amount of energy that is required to perform any substantial task. If constant force is applied, then the work is simply given by the following equation W = F × d Where W = W o r k d o n e F = C o n s t a n t F o r c e d = d i s t a n c e t h r o u g h w h i c h t h e f o r c e a c t s If the force applied is not constant and changes over time, then integral equation is used to calculate the work done. W = ∫ x = a x = b f ( x ) d x Where, W = W o r k d o n e f ( x ) = f o r c e a s a f u n c t i o n o f d i s t a n c e x = d i s t a n c e t h r o u g h w h i c h t h e f o r c e a c t s Given: Distance as

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ISBN: 9781319050733

Author: Rogawski

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Chapter 6.5, Problem 4E

To determine

The work done (in Joules) required for compressing a spring from equilibrium to $4 c m$ past equilibrium.

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Chapter 6.5, Problem 3E

Chapter 6.5, Problem 5E

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A mass weighing 4 pounds is attached to a spring whose constant is 2 Ib/ft. The medium offers a damping force that is numerically equal to the instantaneous velocity. The mass is initially released from a point 1 foot above the equilibrium position with a downward velocity of 16 ft/s. Determine the time (in s) at which the mass passes through the equilibrium position. (Useg = 32 ft/s? for the acceleration due to gravity.) Find the time (in s) after the mass passes through the equilibrium position at which the mass attains its extreme displacement from the equilibrium position. What is the position (in ft) of the mass at this instant? ft

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2. A mass of 4 pounds stretches a spring 0.4 feet. The mass moves through a medium which offers a damping force that is numerically twice the value of the instantaneous velocity. a) Find the equation of motion if the mass is released from rest 1 foot below the equilibrium position. b) Find the time the mass passes through the equilibrium position for the first time. Solve using algebraic techniques. л c) Find the velocity of the mass and direction (upwards or downwards) at /==sec. 4

Chapter 6 Solutions

CALCULUS (CLOTH)

Ch. 6.1 - Prob. 1PQ Ch. 6.1 - Prob. 2PQ Ch. 6.1 - Prob. 3PQ Ch. 6.1 - Prob. 4PQ Ch. 6.1 - Prob. 5PQ Ch. 6.1 - Prob. 6PQ Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E

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The work done (in Joules) required for compressing a spring from equilibrium to 4 c m past equilibrium.

Solution Summary: The author explains that the work required to compress a spring from equilibrium to 4 c m past equilibrium is 0.64 J o u l e

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The work done (in Joules) required for compressing a spring from equilibrium to $4 c m$ past equilibrium.

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Chapter 6 Solutions

The work done (in Joules) required for compressing a spring from equilibrium to 4 c m past equilibrium.

Solution Summary: The author explains that the work required to compress a spring from equilibrium to 4 c m past equilibrium is 0.64 J o u l e

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The work done (in Joules) required for compressing a spring from equilibrium to 4 cm past equilibrium.

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Chapter 6 Solutions

The work done (in Joules) required for compressing a spring from equilibrium to $4 c m$ past equilibrium.