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Finding the work done in lifting a leaking bag of cement. A bag of cement originally weighing 143 lb was lifted at a constant rate. As it rose, cement also leaked out at a constant rate. By the time the bag had been lifted to 24 ft, of the cement had leaked out. How much work was done lifting the cement this far? (Neglect the weight of the bag and lifting equipment.) Part 1. Assuming the force required to lift the cement is equal to its weight, find the force function, F(z), that acts on the cement when the bag is at a height of z ft. Hint: it will help to find the rate (in ) at which the cement leaking from the bag. F(x) = (143 – Part 2. Setup the integral that will give the work required to lift the cement 24 ft. 24 Weement = (1401.4 – 14.6x) dx ㅇ Part 3. The work done in lifting the cement 24 ft is W 29428.8 ft-lb. Note: enter your answer using values correct to three decimal places.

Finding the work done in lifting a leaking bag of cement. A bag of cement originally weighing 143 lb was lifted at a constant rate. As it rose, cement also leaked out at a constant rate. By the time the bag had been lifted to 24 ft, of the cement had leaked out. How much work was done lifting the cement this far? (Neglect the weight of the bag and lifting equipment.) Part 1. Assuming the force required to lift the cement is equal to its weight, find the force function, F(z), that acts on the cement when the bag is at a height of z ft. Hint: it will help to find the rate (in ) at which the cement leaking from the bag. F(x) = (143 – Part 2. Setup the integral that will give the work required to lift the cement 24 ft. 24 Weement = (1401.4 – 14.6x) dx ㅇ Part 3. The work done in lifting the cement 24 ft is W 29428.8 ft-lb. Note: enter your answer using values correct to three decimal places.

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.3: Getting Information From The Graph Of A Function
Problem 66E
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Finding the work done in lifting a leaking bag of cement. A bag of cement originally weighing 143 lb was lifted at a constant rate. As it rose, cement also leaked out at a constant rate. By the time the bag had been lifted to 24 ft, of the cement had leaked out. How much work was done lifting the cement this far? (Neglect the weight of the bag and lifting equipment.) Part 1. Assuming the force required to lift the cement is equal to its weight, find the force function, F(z), that acts on the cement when the bag is at a height of z ft. Hint: it will help to find the rate (in ) at which the cement leaking from the bag. F(x) = (143 – Part 2. Setup the integral that will give the work required to lift the cement 24 ft. 24 Weement = (1401.4 – 14.6x) dx ㅇ Part 3. The work done in lifting the cement 24 ft is W 29428.8 ft-lb. Note: enter your answer using values correct to three decimal places.
Transcribed Image Text:Finding the work done in lifting a leaking bag of cement. A bag of cement originally weighing 143 lb was lifted at a constant rate. As it rose, cement also leaked out at a constant rate. By the time the bag had been lifted to 24 ft, of the cement had leaked out. How much work was done lifting the cement this far? (Neglect the weight of the bag and lifting equipment.) Part 1. Assuming the force required to lift the cement is equal to its weight, find the force function, F(z), that acts on the cement when the bag is at a height of z ft. Hint: it will help to find the rate (in ) at which the cement leaking from the bag. F(x) = (143 – Part 2. Setup the integral that will give the work required to lift the cement 24 ft. 24 Weement = (1401.4 – 14.6x) dx ㅇ Part 3. The work done in lifting the cement 24 ft is W 29428.8 ft-lb. Note: enter your answer using values correct to three decimal places.
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