A worker on scaffolding 75 ft above the ground needs to lift a 410 lb bucket of cement from the ground to a point 25 feet above the ground by pulling on a rope weighing 5 lb/ft. How much work is required
To calculate the work required, we need to determine the total weight that needs to be lifted and then multiply it by the distance it is lifted.
First, let's calculate the weight of the bucket of cement. The bucket itself weighs 410 lb.
Next, let's calculate the weight of the rope. We need to find the length of the rope in feet, which is the distance from the ground to the lifting point (25 ft), plus the height of the scaffolding (75 ft). So the total length of the rope is 25 ft + 75 ft = 100 ft.
The weight of the rope is given as 5 lb/ft, so we can multiply the length (100 ft) by the weight per foot (5 lb/ft) to get 500 lb.
Now, let's calculate the total weight that needs to be lifted. We add the weight of the bucket (410 lb) to the weight of the rope (500 lb) to get 910 lb.
Finally, we multiply the total weight (910 lb) by the distance lifted (25 ft) to get the work required:
Work = Weight * Distance = 910 lb * 25 ft = 22,750 ft-lb.
Therefore, 22,750 ft-lb of work is required to lift the bucket of cement.