Why is Work Done When Walking Upstairs But Not Horizontally?

[kaweezah]

Homework Statement

my teacher says that there is no work done on carrying a bag walking horizontally but there is work done in walking upstairs. why?

Homework Equations

work is done with motion in the direction of the force/ with displacement.

The Attempt at a Solution

when the teacher first asked i answered there is work because it's just like pushing the bag but the difference is that the bag is elevated the other thing that lead me to that was that the force from the legs' direction is forwards and the bag moves forward too, i thought my answer made sense because the displacement was in the direction of the force. later i found out that i was wrong because they said force to be considered was the force of the arm and since the bag wasn't displaced upwards (the direction of the force of the arms); no work. so, i was wrong. i didn't quite accept that because when you illustrate it (| is the person and o is the bag) |o...|o it obviously shows that the bag was displaced from its original position and moved to the direction of the force of the legs. then someone said (i think it was my teacher or my classmate) that the point of origin was your body and since the bag didn't move away from the body..no displacement no work. that to me finally made sense. then the teacher asked if there was work done walking upstairs; i said none because the bag wasn't displaced away from the body. i was also wrong then. the reason now was that the bag moved up and the direction of the force was also up. then i got confused again because walking up, the bag doesn't move away from your body and how come walking horizontally didn't qualify as work when the bag still moved in the direction of the force!

 

[Fingolfin_Noldo]

The first thing to understand is that Work Done = Force * displacement in the direction of the force.

Well, your legs aren't lifting the bag so the arms are exerting an upward force on the bag. So when you are walking the forces exerted by the leg is perpendicular to the force on the bag, so no work done.

So yes, when you go up the stairs, since there is motion in the vertical direction, there is work done. Your confusion here is, that the bag must be displaced from the body in some fashion. That is not true. Remember first that the force must be in contact with the bag and it being displaced from the body means the force is no longer in contact! Displacement is not relative to the body but relative to a fixed point in space.

 

[kaweezah]

Fingolfin_Noldo...how about just walking? my teacher also added that walking is no work. now why is that? the force from the legs is forwards and the body moves forwards too. makes no sense to me again

 

[mgb_phys]

If you are walking on a level surface there is no work done (in a physics sense)!
Actually in walking you do move up and down slightly so some work is done each time you take a step and lift your body mass a few cm against gravity.

 

[D H]

Part of your confusion is that your muscles and physicists have different definitions of work. To illustrate, simply extend an arm straight out, palms up and supporting a book on your hand (even a little paperback will do). Your muscles can support this position for a very limited period of time. Nothing is moving, so obviously no physical work is being performed. But even with no motion involved, physiological work is being done here.

The first thing to do then is to accept that physicists use the term a bit differently than you are used to. Work to a physicist is a measure of how much some object has been made to move with respect to some force, and only the component of the motion that is directed along or against some force counts towards "work".

In the example of the grocery bag, your body is doing physiological work just to hold the bag off the ground, even when you are standing still. If the bag is heavy enough you can even feel your muscles "burn" simply from holding the bag. Your arms might even get warm to the touch. No motion, no work as far as a physicist is concerned.

Now start walking. At the end of the walk, the bag is still at the same height. The motion was perpendicular to the force of gravity. No net work was done on the bag¹. If instead you walk up a flight of stairs, some of the motion is directed against the force of gravity. What physicists call work is now being performed.

It is all a matter of definition. Why do we use this wacky definition? We use it because it works. This definition of work helps with building and operating machinery and with understanding the universe.

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¹I said the net work done on the bag is zero. Your body does do some work on the bag while walking. As you walk, your chest and the bag you are holding to your chest move up and down a bit. Every time you step forward, your chest drops a little bit. Your chest raises a bit when you bring the rear leg back underneath you, and then drops again when you bring that leg in front of the other. Every time your chest falls gravity does work on the bag. Every time your chest rises,you do work on the bag. The net work is zero, but your body has indeed done a small but non-zero amount of physical work. If instead you strap on a pair of ice skates and glide across a skating rink with a bag in hand, both the net work and your contribution to the work are zero.