Final answer:
The work done lifting 800 lb of coal with a cable that weighs 2 lb/ft over a distance of 500 ft is approximately 900,000 lb-ft. The calculation assumes the total weight of the cable contributes to the force over the entire distance.
Step-by-step explanation:
To calculate the work done in lifting 800 lb of coal using a cable that weighs 2 lb/ft for a distance of 500 ft, we start with the definition of work. Work is defined as the force multiplied by the distance over which the force acts, in the direction of the force. In this case, the force is the weight of the coal and the cable, and the distance is the depth of the mine shaft.
Step-by-Step Calculation
- First, calculate the total weight of the cable: 2 lb/ft × 500 ft = 1000 lb.
- Then, add the weight of the coal to get the total weight lifted: 1000 lb + 800 lb = 1800 lb.
- The formula for the work done is W = force × distance, so here it will be W = 1800 lb × 500 ft.
- Thus, the total work done is 900,000 lb-ft.