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: 500 k g wrecking ball hanging from a 12 m cable of mass density of 15 k g / m Formula Used: The amount of work done in lifting a body to a height is given by the formula W o r k D o n e = m × g × h Where, m = mass of the object in kilograms g = acceleration due to gravity ( at the surface of the earth) h = height in meters Calculation: Let us consider a small segment of the chain of the length Δ x located at distance of meters from top end of the building. Thus, the work needed to lift the Δ x segment of cable12 m above the ground level. W j ≈ ( 15 Δ x ) ( 9.8 ) x j J W j ≈ 147 Δ x x j J Now, summing over all the segments of the cable and passing to the limit Δ x → 0 , we get the total work as W o r k R e q u i r e d = ∫ 0 12 147 x d x W o r k R e q u i r e d = 73...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 6.5, Problem 32E

To determine

The work done in lifting a $500 k g$ wrecking ball hanging from a $12 m$ cable of mass density of $15 k g / m$ attached to the crane from the ground level to $12 m$ in the air by drawing the cable.

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Chapter 6.5, Problem 31E

Chapter 6.5, Problem 33E

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a winch lifts a bag of sand of mass 12kg from the ground with a constant force of 240N until it reaches a speed of 10m/s. Then the winch provides a force to keep the bag moving at constant speed. Find the time taken to reach the height of 40m.

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The work done in lifting a 500 k g wrecking ball hanging from a 12 m cable of mass density of 15 k g / m attached to the crane from the ground level to 12 m in the air by drawing the cable.

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The work done in lifting a 500 kg wrecking ball hanging from a 12 m cable of mass density of 15 kg/m attached to the crane from the ground level to 12 m in the air by drawing the cable.

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The work done in lifting a $500 k g$ wrecking ball hanging from a $12 m$ cable of mass density of $15 k g / m$ attached to the crane from the ground level to $12 m$ in the air by drawing the cable.