Comparing Work: Lifting vs. Pushing a Box

[dragon513]

In which of the following would a person do the least amount of work?
A. Lifting a 10 kg box a vertical height of 1.2 m.
B. Lifting a 10 kg box a vertical height of 1.2 m using a ramp.
C. Pushing a 10 kg box along a smooth floor a distance of 1.2 m.
D. Dragging a 10 kg box along a rough floor a distance of 1.2 m.

By the way the answer is C.

The work needed for choice A. and B. are different right?
Choice B requires more work since the box moves horizontal and vertically while in Choice A the box only moves vertically...or am I wrong +_+??

As well how do you know the work required to push the box along a smooth floor is less than the work needed to lift the box vertically??

Thank you

Regards,

 

[thenewbosco]

a and b are the same since the work (i.e. change in grav. potential energy is independent of the path taken) both result in some amount of work done. moving something horizontally results in no work, however in d. there is friction (from the rough floor) therefore some work must be done. In assuming the floor in c is smooth (and therefore no friction) no work is done in moving it some distance. Since all the others involve doing some work, c which involves doing no work is the least

 

[mezarashi]

As well how do you know the work required to push the box along a smooth floor is less than the work needed to lift the box vertically??

Work is applying a force over a distance. If the floor is smooth (approaching infinitely smooth), consider standing on a frozen lake. Just a small jab at the box will send it moving across the lake a relatively far distance. Newton's first law says that unless acted on by a force, an object continues moving forever. Gravity can only act vertically. If not for friction, moving something horizontally requires no work.