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2) A heavy rope, 50 ft long, weighs 0.5 lb/ft and hangs over the edge of a building 120 ft high. (a) How much work is done (in ft-lb) in pulling the rope to the top of the building? work done = ( ) ft lb (b) How much work is done (in ft-lb) in pulling half the rope to the top of the building? work done= ( ) ft lb A bucket that weighs 4 lb and a rope of negligible weight are used to draw water from a well that is 80 ft deep. The bucket starts with 40 lb of water and is pulled up at a rate of 2 ft/s, but water leaks out of a hole in the bucket at a rate of 0.2 lb/s. Find the work done (in ft-lb) in pulling the bucket to the top of the well. work done = ( ) ft lb

          2) 
A heavy rope, 50 ft long, weighs 0.5 lb/ft and hangs over the
edge of a building 120 ft high.
(a) How much work is done (in ft-lb) in pulling the rope to the
top of the building?
work done = ( ) ft lb
(b) How much work is done (in ft-lb) in pulling half the rope to
the top of the building?
work done= ( ) ft lb
A bucket that weighs 4 lb and a rope of negligible weight are
used to draw water from a well that is 80 ft deep. The bucket
starts with 40 lb of water and is pulled up at a rate of 2 ft/s,
but water leaks out of a hole in the bucket at a rate of 0.2 lb/s.
Find the work done (in ft-lb) in pulling the bucket to the top of
the well.
work done = ( ) ft lb
        
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Added by Edward T.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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2) A heavy rope, 50 ft long, weighs 0.5 lb/ft and hangs over the edge of a building 120 ft high. (a) How much work is done (in ft-lb) in pulling the rope to the top of the building? work done = ( ) ft lb (b) How much work is done (in ft-lb) in pulling half the rope to the top of the building? work done= ( ) ft lb A bucket that weighs 4 lb and a rope of negligible weight are used to draw water from a well that is 80 ft deep. The bucket starts with 40 lb of water and is pulled up at a rate of 2 ft/s, but water leaks out of a hole in the bucket at a rate of 0.2 lb/s. Find the work done (in ft-lb) in pulling the bucket to the top of the well. work done = ( ) ft lb
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Finding the work done in lifting a bucket: A 6 lb bucket attached to a rope is lifted from the ground into the air by pulling in 20 ft of rope at a constant speed. If the rope weighs 1.1 lb/ft, how much work is done lifting the bucket and rope? Part 1. Find the work done in lifting the bucket (without the rope) 20 ft. W_bucket = ft-lb Part 2. Assuming the force required to lift the rope is equal to its weight, find the force function, F(x), that acts on the rope when the bucket is at a height of x ft. F(x) = Part 3. Setup the integral that will give the work required to lift the rope 20 ft. W_rope = Part 4. The total amount of work done in lifting the bucket and rope is W = ft-lb. Note: enter your answer using values correct to three decimal places.

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Transcript

-
00:01 Okay, so for part a, let's think about it like this.
00:05 So we have the center of mass of the rope is going to be 25 feet down.
00:11 So the weight is going to be equal to 0 .5 pounds per foot times 50 feet.
00:21 So we know that's going to be 25 pounds.
00:26 So we know we need to center of mass to go up 25 feet.
00:31 So work, work is going to be equal to force times the distance.
00:43 Well, in a force in this case, would just be 25 pounds.
00:46 Then the distance is 25 feet...
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