What takes more energy; a 100 lb. weight moving on a level plain 20 ft. versus a 100 lb. weight on a 30 % grade moving 20 ft.

Question

A 100 pound gate moving on a level grade a distance of 20 feet. A 100 pound gate moving up a 30% slope a distance of 20 feet. Which one takes more power/energy?

Answer 1

The only thing I have to add here is something that is probably not a big deal in the problem... but, in physics terms, is worth mentioning.  At the last of the question you posted, it asked which one takes more "power/energy."  I know those were probably meant to me synonymous, but there is actually an important physical distinction that affects the answer.

 

For energy (and work), Arturo and Michael covered the answer very well.  However, power is work done (energy changed) per unit time.   This means, it would take more work to push the weight up the grade (assuming it is a grade above the horizontal); but, if you did that work much more slowly, it would be possible to exert less power in pushing it up the grade.

 

To be sure to be able to compare power as you would energy, you would have to specify that the work in each case was performed in the same time.

Answer 2

If you are moving up the 30% grade, you must do work against gravity, whereas when moving on a level plain, you do not have to do work against gravity.  So without having to do any calculations, you can conclude that more work is required to move up the grade.

Answer 3

In both cases, the weight and distance moving are the same.  So we don't need to solve any equations here.  Use common sense and logic.

 

It's much harder to push something up a hill (30% slope) than it is to push something on a leveled surface.  On a slope, more weight is added.  So it will take more power and energy for a 30% slope.