please help?

Question

you have been given the task of moving a huge box of baseball to a shelf that is 1meter above the floor ther are three ramps available for you to use they all have height of 1meter however the first one is 1meter long the second is 2meter and the third is 3meter long which ramp will make you task easiest?why

Answer 1

The 3 metre ramp will make your task easier, the gradient is less on this ramp so you have a larger mechanical advantege.

The amount of work done is the same whichever ramp you choose, but the longest ramp means you do less work per step you take (although you will have to take more steps) - so the work done is always the same.

i.e. Work done is path independant.

Answer 2

Well, the longest ramp is obviously going to be the least steap. If you want to prove that mathematically, use the following:
Sin x = o/l, where x is the angle the ramp makes with the floor, o is the height (1 metre), l is the length of the ramp (1,2 or 3 metres).
Rearrange: x = inverse sine (o/l).
x is a smaller angle when h is a bigger number. Thus the ramp is less steap.

Now, the total work done in getting the box up a height of one metre is always going to be the same:
= mgh, where m is the mass of the box, g is acceleration due to gravity (9.8 ms^-2), and h is the height (1 metre).
This change in energy is the 'work done', and is constant whichever ramp you use.

Work done = force x distance moved.
Now, 'work done' is constant, but 'distance moved' can be 1,2 or 3 metres, depending on the length of the ramp.
Rearranging the equation gives:
Force = (work done)/(distance moved).
So you see, the longer the ramp, the greater the magnitude of 'distance moved', and hence the smaller the force that must be applied to get it up the ramp.

Answer 3

The 3m ramp... it has the highest Mechanical Advantage (3/1 vs 2/1 or 1/1).

Answer 4

The 3 meter ramp will spread the work out more.