More energy is needed to walk down stairs than to walk horizontally

[Tabe]

Ok, here is my problem: Explain why more energy is needed to walk down stairs than to walk horizontally at the same speed?
I don't get it, its against logic isn't it.
Is it because of the height, that causes the energy walking down the stairs to be greater? That's the only explanation that I can think of. Can anybody help explain this to me a little better

 

[Diane_]

Think about what it's like to walk down stairs. Every time you take a step, your foot and leg have to absorb the impact of your foot on the ground. When you're walking on the level, that impact is basically the same every time.

When you're walking down stairs, the impact is greater each time than it would be on the level. (Think energy, and answer the question why?.) It takes some work in your body to absorb that impact. (Again - why?. Think about how your muscles have to move in that case. That motion takes energy.)

Sufficient?

 

[Tabe]

Ok, now that I have that solved, I have one more question about energy.
Can the kinetic energy of an object be negative? I know that you can have a negative acceleration, but can you technically have a negative energy, or is it merely directional? If you have a negative acceleration, you would have a negative force, which in turn could produce a negative kinetic energy, but how can the object have negative energy, especially when its moving?

 

[Diane_]

Remember, there is a difference between vector quantities (like acceleration and velocity) and scalar quantities (like speed or energy). You can have a "negative" acceleration because direction is a part of it, and the direction is being carried by a negative sign. All the negative means is that the acceleration is opposite in direction to your arbitrarily-defined positive.

A negative kinetic energy, though, would be another kettle of worms all together. Remember, kinetic energy is the energy of motion. What would it mean if the kinetic energy were negative? It wouldn't mean that the object was moving in the opposite direction - the kinetic energy of an object is the amount of work it takes to get it up to speed. The direction is totally irrelevant.

Perhaps that's a better way to look at it. When I say that an object has a kinetic energy of 10J, that just means that I'll have to do 10J of work on it to take it from rest to whatever speed it has. A kinetic energy of "-10J" would seem to mean that I'll have to remove 10J of energy from it to get it from rest to that speed. If it isn't moving, though, how do I take kinetic energy out of it? There isn't any there to start with.

Basically, when you talk about negative energy of any type, you're comparing it to some arbitrary reference. You can, for instance, have a negative gravitational potential energy. All this means is that you're below your reference position. It means that you'd have to remove that amount of potential energy from the object to lower it from the reference to the position of interest. Note here that direction matters - it makes a difference whether you're lifting something up or lowering it down. With speed, there is no difference. Making it go faster from rest takes the same amount of work whatever direction you're going.

*sigh* This is hard to explain in text messages. Does that make any sense at all?

 

[Tabe]

Yes, actually it does, I think I can explain it now. Thanks for the help. I can solve the problems, but I can't master the concepts, quite interesting.