Question

a 170 lb man carries a 25 lb can of paint up a helical staircase that encircles a silo with radius 25 ft. if the silo is 60 ft high and the man makes exactly three complete revolutions, how much work is done by the man against gravity in climbing to the top?

Answer 1

The work done by the man in carrying the 25 lb can of paint up to the top of the 60 ft high silo is 11,700 foot-pounds. ​​

How to find work done?

The total weight the man is carrying (including himself and the paint can) is the sum of his weight and the weight of the paint can:

`\[ \text{Total Weight} = \text{Man's Weight} + \text{Paint Can's Weight} \\= 170 \, \text{lb} + 25 \, \text{lb} \]`

`\[ \text{Total Weight} = 195 \, \text{lb} \]`

The vertical distance climbed by the man is the height of the silo:

`\[ \text{Height} = 60 \, \text{ft} \]`

Work done against gravity is calculated as the product of the force (in this case, the weight) and the distance (height) moved in the direction of the force:

`\[ \text{Work} = \text{Total Weight} * \text{Height} \]`

`\[ \text{Work} = 195 \, \text{lb} * 60 \, \text{ft} \]`

`\[ \text{Work} = 11700 \, \text{foot-pounds} \]`

Therefore, the work done by the man in climbing to the top of the silo is 11,700 foot-pounds.