A worker on scaffolding 65 ft above the ground needs to lift a 390 lb bucket of cement from the ground to a point 20 feet above the ground by pulling on a rope weighing 5 lb/ft. How much work is required?
To determine the work required, we need to calculate the total weight being lifted and multiplied by the distance it is being lifted.
First, let's calculate the weight of the bucket plus the weight of the rope:
Weight of bucket = 390 lb
Weight of the rope = 5 lb/ft * 20 ft = 100 lb
Total weight being lifted = Weight of bucket + Weight of rope
Total weight being lifted = 390 lb + 100 lb
Total weight being lifted = 490 lb
Next, let's calculate the distance it is being lifted:
Distance = 65 ft - 20 ft = 45 ft
Finally, let's calculate the work required:
Work = Total weight being lifted * Distance
Work = 490 lb * 45 ft
Work = 22,050 ft-lb
Therefore, the work required to lift the bucket of cement is 22,050 ft-lb.
To calculate the work required, we need to consider the following:
1. Work is defined as the amount of force applied over a distance.
2. The worker needs to lift the bucket from the ground to a point 20 feet above the ground.
3. The bucket of cement weighs 390 lb.
4. The rope itself weighs 5 lb/ft.
To determine the work required, we need to break down the problem into two parts:
1. The work required to lift the bucket from the ground to the worker's level.
2. The work required to lift the bucket from the worker's level to a point 20 feet above the ground.
Let's calculate each part separately:
1. The work required to lift the bucket from the ground to the worker's level:
- The bucket weighs 390 lb, and the worker needs to lift it 65 ft.
- Therefore, the work required to lift the bucket from the ground to the worker's level is:
Work = Weight x Distance
= 390 lb x 65 ft
2. The work required to lift the bucket from the worker's level to a point 20 feet above the ground:
- The bucket now needs to be lifted an additional 20 ft.
- The rope weighs 5 lb/ft, and we need to consider its weight as well.
- The total weight to be lifted is now 390 lb + (5 lb/ft x 20 ft).
- Therefore, the work required to lift the bucket from the worker's level to a point 20 feet above the ground is:
Work = Weight x Distance
= (390 lb + (5 lb/ft x 20 ft)) x 20 ft
Now, to find the total work required, we sum up the work required for each part:
Total Work = Work to lift the bucket from the ground to the worker's level + Work to lift the bucket from the worker's level to a point 20 feet above the ground
Once you plug in the values for the weight of the bucket and the distances involved, you can calculate the total work required by solving the equation.