Physics Question

[jkindredpdx]

This is admittedly not boat related, but I think the explanation might relate to understanding sailing physics... so I'm asking you engineers.

When stepping up an upward moving escalator, does one expend more energy per step than walking up stationary stairs? If you are able, please provide the equation.

[trashpad]

When a body is in motion it will require an equal and opposite motion to stop it so yes it would require more effort to step up. The degree of added effort would be equal to the speed of the rise which on an escalator is minimal.

Sent from my SM-N900V using Cruisers Sailing Forum mobile app

[Claude_Marie]

Originally Posted by jkindredpdx

This is admittedly not boat related, but I think the explanation might relate to understanding sailing physics... so I'm asking you engineers.

When stepping up an upward moving escalator, does one expend more energy per step than walking up stationary stairs? If you are able, please provide the equation.

IMHO "equation" would read :
Kinetic energy of human + kinetic energy of escalator (unsignificant as said).
Possibly, in an upward motion gravity interfere...have to think about it...

[conachair]

Originally Posted by jkindredpdx

When stepping up an upward moving escalator, ...

before stepping up a step, if your eyes were closed would you know you were moving?

[Caribbeachbum]

Only for the step on and the step off. The escalator moves at a constant rate, so delta-v exists only at those two points. Walking up the escalator is no different than walking up stairs.

But if you add in the energy expended by the escalator system to maintain the constant rate against the forces applied when you walk up, then yes, walking does consume more energy than merely riding.

[Stu Jackson]

No difference once you're on it. In the small amount of time you're getting an and accelerating to its speed, yes. But once you're on you're both moving at the same speed.

This is a perfect candidate for a Google search, since it's, as you said, Physics 101.

[Claude_Marie]

Originally Posted by Stu Jackson

No difference once you're on it. In the small amount of time you're getting an and accelerating to its speed, yes. But once you're on you're both moving at the same speed.
.

When you arrive at the top of the escalator, may I call it last step.
The acceleration provided by the escalator + your first step "on firm ground" when you generate your own acceleration add on, don't they ?


just like a boat with its own acceleration + acceleration due to swell = surf.

[sailorchic34]

Hum, So in order to lift say 200 pounds up say 9 inches requires a fixed amount of energy. if the escalator is moving or stopped the net energy use would, I think, be the same. This as, the vertical component stays the same.

Just like climbing steps in your house, the steps are moving at 1000 miles per hour as the earth rotates about its axis and 60,000 miles per hour as the earth travels around the sun. But so is the house and yourself. So the net work done stays the same.

It's only when you move from one energy state, say the moving escalator to another, the floor, that there is a change in velocity and a net change in energy expended. You feel this as you step on and step off the escalator.

There is a slight difference in the forward component while on the moving escalator due to wind resistance from the forward velocity of the escalator. But it is tiny compared to the energy expended to lift the mass.

[Claude_Marie]

Originally Posted by sailorchic34

Hum, So in order to lift say 200 pounds up say 9 inches requires a fixed amount of energy. if the escalator is moving or stopped the net energy use would, I think, be the same. This as, the vertical component stays the same.

Just like climbing steps in your house, the steps are moving at 1000 miles per hour as the earth rotates about its axis and 60,000 miles per hour as the earth travels around the sun. But so is the house and yourself. So the net work done stays the same.

It's only when you move from one energy state, say the moving escalator to another, the floor, that there is a change in velocity and a net change in energy expended. You feel this as you step on and step off the escalator.

There is a slight difference in the forward component while on the moving escalator due to wind resistance from the forward velocity of the escalator. But it is tiny compared to the energy expended to lift the mass.

Nice explanation (house, earth, sun)
How reads the equation ?

[KHJackson]

Look at total energy Kinetic energy 1/2m V^2plus gravitational potential (mgh)

Total energy = 1/2 m V^2 + mgh
(moving escalator)= 1/2 m*V1^2 + mgh
(walking up)=1/2m*V2^2 +mgh

V1= V(walking) + Ve(escalator)
V2= V(walking)
Obviously
V1>V2

Better to analyze this problem in terms of the energy expended per unit time (or power). In terms of the escalator the total energy is larger because V1 is greater than V2. Also the amount of time required to traverse the same distance using escalator is less. This is important because the energy per step you expend per step is the same but the time you are doing so is less because of the motion of escalator. So overall the escalator reduces the amount of energy you have to expend over walking up steps alone. This reduction in energy is considerable because it depends on V^2.

[denverd0n]

Originally Posted by sailorchic34

Just like climbing steps in your house, the steps are moving at 1000 miles per hour as the earth rotates about its axis and 60,000 miles per hour as the earth travels around the sun. But so is the house and yourself. So the net work done stays the same.

You forgot to mention that our solar system is moving within its galaxy, and our galaxy is moving within the universe.

So, short answer, no. One step up is one step up, regardless of whether or not the steps themselves are moving at the time (which they always are).

[sailorchic34]

Originally Posted by KHJackson

Look at total energy Kinetic energy 1/2m V^2plus gravitational potential (mgh)

Total energy = 1/2 m V^2 + mgh
(moving escalator)= 1/2 m*V1^2 + mgh
(walking up)=1/2m*V2^2 +mgh

V1= V(walking) + Ve(escalator)
V2= V(walking)
Obviously
V1>V2

Better to analyze this problem in terms of the energy expended per unit time (or power). In terms of the escalator the total energy is larger because V1 is greater than V2. Also the amount of time required to traverse the same distance using escalator is less. This is important because the energy per step you expend per step is the same but the time you are doing so is less because of the motion of escalator. So overall the escalator reduces the amount of energy you have to expend over walking up steps alone. This reduction in energy is considerable because it depends on V^2.

You are correct that the total energy expended from man and machine is larger then just a man walking up steps, also correct that the energy expended by the man to move from one floor to another is less as the escalator has a forward velocity.

But the question was only does a man use more energy climbing a step on a moving escalator or on fixed stairs. Not the total energy used to traverse from one level to the next.

The forward velocity does not effect the energy expended in moving one step up. With the escalator and man at the same velocity, the man uses the same energy climbing a step. From an outside observer the man uses less energy per unit time, but from the man's frame reference it's the same energy expended.

Welcome to general relativity.

• Gmn = -(8pG/c2)Tmn
  
  
  

[sailorchic34]

Originally Posted by denverd0n

You forgot to mention that our solar system is moving within its galaxy, and our galaxy is moving within the universe.

.

I oddly would never forget that. We are moving about 240,000 MPH about the galaxy. Alas I've not worked out the velocity of the milkyway across the universe. Slacker I know.

We could even extend that to universe motion across membranes, but then my brain explodes and it gets messy.

[KHJackson]

Originally Posted by denverd0n

You forgot to mention that our solar system is moving within its galaxy, and our galaxy is moving within the universe.

So, short answer, no. One step up is one step up, regardless of whether or not the steps themselves are moving at the time (which they always are).

One step up is one step up, correct. The total energy expended by you depends on how many steps you take. Say with the escalator stopped it would take 10 steps to reach top. The motion of the escalator reduces the number of steps you take therefore you may take 5 steps instead of the 10 required with the escalator stopped. In fact you can reduce your energy expenditure to almost zero by not taking any steps at all and letting escalator do all the work.http://www.cruisersforum.com/images/smilies/thumb.gif

[sailorchic34]

Originally Posted by KHJackson

One step up is one step up, correct. The total energy expended by you depends on how many steps you take. Say with the escalator stopped it would take 10 steps to reach top. The motion of the escalator reduces the number of steps you take therefore you may take 5 steps instead of the 10 required with the escalator stopped. In fact you can reduce your energy expenditure to almost zero by not taking any steps at all and letting escalator do all the work.http://www.cruisersforum.com/images/smilies/thumb.gif

We are in complete agreement!