# When I walk down the stairs where does my potential energy go?

When I leave my room I walk down three flights of stairs releasing about 7kJ of potential energy. Where does it go? Is it all getting dispersed into heat and sound? Is that heat being generated at the point of impact between my feet and the ground, or is it within my muscles?

Related question, how much energy do I consume by walking? Obviously there's the work I'm doing against air resistance, but I feel like that doesn't account for all the energy I use when walking.

• Speeding up the earths rotation, crazy as it sounds... Jun 13, 2021 at 16:59
• Only if you're walking to the west. Jun 13, 2021 at 20:17
• @DawoodibnKareem The effect of horizontal (tangential) motion on the Earth's rotational speed lasts only during the motion itself; there is no permanent change. Stian Yttervik was presumably talking about the effect of vertical (radial) motion, which would occur even if descending say a firefighter's pole instead of stairs. This is a genuine, permanent, but very small effect, per my comment above. Jun 13, 2021 at 23:15
• If you have another question, no matter how related you think it is, you should pose it as a separate question Jun 14, 2021 at 8:47
• @StianYttervik That's not the gravitational potential energy, though (in the case of going down stairs or a pole, etc) - that's just your angular momentum doing that (which is a form of kinetic energy, not potential). The gravitational energy is dissipated by various mechanisms.
– J...
Jun 14, 2021 at 16:47

## 9 Answers

Make it simple. If a mass of your weight fell down the height of three flights of stairs through the air, when it landed where would the kinetic energy accumulated by falling go?

1. moving the earth for conservation of momentum

2. dissipated in heat on the ground

3. deformation of the matter of the weight

4. sound

That is why humans invented the stairs, to dissipate the kinetic energy acquired in small increments, in the same but in a non-human-frame-destructive way.

• "to dissipate the kinetic energy acquired in small increments". This is the key. Jun 13, 2021 at 22:18
• Note, the energy of #1 is negligibly small compared to the others because of the huge mass of the Earth. Jun 13, 2021 at 22:39
• @nanoman sure, but I like reminding that momentum conservation is a law too. Jun 14, 2021 at 3:45
• @nanoman the huge mass of the Earth doesn't prove anything about the proportion of energy dissipated by momentum transfer. It only means that an absolutely tiny change in velocity is necessary to transfer 100% of your kinetic energy. In practice, the earth isn't nearly rigid enough for its whole mass to be relevant. Energy forms 1, 2, and 4 are essentially all localised descriptions of the same lossy momentum transfer from the impact site to the surroundings.
– Will
Jun 14, 2021 at 12:21
• @Will No, nanoman is right. What is transferred in significant quantities is momentum, which is $F*t$; the kinetic energy though is almost entirely transformed into heat because it is $F*s$, and the Earth (if we consider it an inertial system for the split second of the impact) doesn't move at all, so that the distance over which the force is applied to Earth is practically zero, and with it the transferred kinetic energy. Unfortunately anna has confused the issue by making the momentum change the first answer of the question "where does the energy go?" The two are unrelated. Jun 15, 2021 at 15:29

The heat is predominantly generated in your muscles.

More direct conversion of potential energy to heat is when a person is sliding down a pole to get to a lower floor quickly. With sufficient friction, the descent is at a constant velocity instead of accelerating.

In muscle, some structures slide along each other. Muscle contraction is those structures being made to move relative to each other, using molecular motors that act somewhat like a hand-over-hand method.

As we know, muscles can also extend in a controlled manner. If you are bending down to the ground you allow your muscles to extend while maintaining tension, so that your motion is controlled.

During that controlled extending: potential energy converts to heat in the muscles.

This conversion of potential energy is on top of the baseline heat generation because the muscle is active.

When you stand up your muscles are working against gravity, actively contracting. The energy source for that contraction is, ultimately, the food you have eaten. In the muscles, the conversion of chemical energy is not 100% efficient. A percentage is transformed to actual power output, a percentage becomes heat straightaway.

When you are allowing your muscles to extend in a controlled manner your muscles are active, so some heat is generated just because the muscle is active.

When you are walking downstairs the total heat generated in the muscles is the sum of two contributions: heat that is generated anyway because the muscle is active, and heat generated because the process of a muscle being extended against muscle tension is work being done on the muscle, and that leads to heat generation in the muscle. (That is, that heat is not generated in the muscle when a completely relaxed muscle is extended by an external force.)

In walking we use our leg muscles actively to smooth out the motion; the leg muscles are used actively to provide some level of elastic suspension.

By comparison, kangaroos are known to have Achilles tendons that are optimized to store elastic energy. The jumping form of travelling that kangaroos can do is quite energy-efficient. The power needed for the next jump is mostly from elastic energy stored in the tendon on coming down.

Human walking doesn't have that level of efficiency. Muscle power is used actively both when the centre of mass of the body comes down and when the centre of mass of the body comes back up again. So there is the generation of heat from that power output.

• As a child I felt it really unfair that walking downstairs costs effort. I thought it ought to be giving you more energy, making you less tired. There must be a better way. :-) Jun 14, 2021 at 5:47
• @RedSonja while I can't claim going down a long fast slide gives you physical energy, it certainly brightens up your day for some metaphorical energy. All tall buildings should have them Jun 14, 2021 at 8:48
• @ChrisH The artist Carsten Höller might agree with you.
– bdsl
Jun 14, 2021 at 10:51
• @RedSonja to this day it annoys me greatly that basically all electrified mountainbikes fail to make use of the possibility of regerative braking (unlike electric cars, which use this to significantly extend their range in mountainous trips). Jun 14, 2021 at 17:38
• @leftaroundabout Link to: bicycle stackexchange Why are regenerative brakes uncommon on e-bikes? Jun 14, 2021 at 17:51

Yes, once you are standing still at the bottom of the stairs then all of the potential energy you had at the top of the stairs has been transformed into heat (due to friction and heat produced by your body) and sound waves. And even the energy in the sound waves ends up as heat once it has been absorbed by the walls, floor, ceiling etc.

The potential energy of your body starting at a height is gradually lost with each step.

Your body is transferring this potential energy into the stretching and flexing of your muscles, and the heat created by this. Some of the energy is also lost due to friction from your feet or shoes in contact with the stairs, some is lost to air resistance and sound.

Basically, a majority of the potential energy is gradually lost to biological and biochemical processes (generating heat).

As you take a step, you accelerate for a short while, before coming to rest again. Then you step down further. This way you cyclically reduce yourself from a higher level(energy or otherwise) to a lower one in steps, no pun intended.

At the end of each step, you come to an abrupt stop. That's because you suffer an inelastic collision with the step. The step exerts a force on you upon contact, stopping you. Since you don't bounce, the collision is inelastic.

The resulting energy loss could be to the ground (stiff stairs) or be shock absorbed and dissipated in your legs (steep stairs), go into silent deformation (soft stairs), be eaten up by friction (wide & rough stairs) or be lost as expletives (thorny stairs)!.

As mentioned in other answers, if you are the system, the earth is the surroundings. So if you lose energy, the earth gains it.

how much energy do I consume by walking?

You rightly conjectured that at a walking pace, the loss to air drag is negligible. So what is the work being done against? It's actually to again accelerate you forth. As one walks, one pushes against the ground gaining energy, then losses some on re-impact on the following step. There's definitely energy being lost, so it must be supplied. The exact kinematics or biomechanics aren't easy to model. As a rough estimate, if you are moving with speed $$v$$ and in each step, you generate, again grossly speaking, an average force of $$F$$, then your walking is dissipating energy at the rate $$Fv$$.

Footnote: The above discussion of energy loss via inelastic collision is, like many other answers, a simplified view. As I remarked the actual biomechanics of walking or going down steps are more refined and evolved. In particular, in the case of stepping downstairs, our body has learned to slow itself right before landing. We step gently not abruptly. To achieve this, our muscles do work by extending/contracting to exert control - that takes a lot of work too. See Cleonis's answer above for that perspective.

• What you're describing here is stomping down a stairset. It is not advisable – very loud, especially on wooden stairs, and quite bad for the joints. A proper way to descent actually involves “braking”, both before you hit the next step, and while setting down the foot (toes first, then softly put down the heel). Jun 15, 2021 at 12:17
• @leftaroundabout yeah I had thought about, mentitoning that but I made the cow to be a sphere Jun 15, 2021 at 17:31
• @leftaroundabout A proper way to descent... i think its the natural way ;-) Jun 15, 2021 at 17:32

There is a nice answer by @annav, I would like to add something none of the answers mention, that is atmospheric pressure.

However small the atmospheric pressure is changing when you walk down the stars, it does change, and it means that as you descend, your body must take more pressure.

At low altitudes above sea level, the pressure decreases by about 1.2 kPa (12 hPa) for every 100 metres.

https://en.wikipedia.org/wiki/Atmospheric_pressure

As the atmospheric pressure rises (when you walk down the stairs), your body needs to act against it (so your body needs to adjust accordingly), and this needs energy from the body.

Potential energy and kinetic energy constantly convert between each other. The conversion is not perfect as some energy is dissipated into friction and deformation of materials.

When going down stairs, your brain has learnt to let your body fall in a controlled manner. How? If you move your body horizontally beyond the edge of the step, you can decrease the force you apply in the leg still in contact with the ground and gravity will accelerate your body downwards. Your potential energy is almost entirely converted to kinetic energy during that acceleration. As your forward foot reaches the step below, it must slow down your body, ie generate a force opposite to gravity. This uses energy stored in our cells. If you stop on that next step, then you've had to dissipate the kinetic energy you've converted from potential energy. It dissipates into your body almost entirely, with very small amount in friction between floor and feet. The dissipation is in heat and friction. The friction causes heat but also atoms to get dislodged ie nanoscopic damage to your tissues, and some of the energy goes there. Your tissues heal in due course.

That's why bigger steps are uncomfortable, the energy to dissipate increases quickly with step height. And that's why going down a thousand steps in a controlled manner is actually very demanding on your body, you've caused a noticeable amount of wear on your body and heat in your muscles. If you get rest, you will convert energy from food into repairing your tissues (muscles, cartilage, ligaments etc) so they are ready for the next flight of stairs - and most likely to go up it!).

Our brains learn how to optimize the motion when we go down many steps in sequence, so we have less energy to dissipate: we don't need to completely stop our body at each step, so we apply just enough force for the net acceleration to be zero, and our motion is as near constant speed down the flight of stairs as we are able. We've learnt to change this counter force constantly as we move down from one step to the next.

Go ahead, try going down a flight of steps but completely stop your body at each step. Remember to alternate which foot goes down at each step.

This is easily tested experimentally. If you walked down a longer staircase, such as subway escalator, as fast as possible, you would feel that most of the energy have been be dissipated as heat in shin muscles and tendons. Then it rapidly moves with blood flow into the rest of your body.

Energy consumption for 5km/h walking is 4 calories per kilometer per kilogram of weight.

• I have never noticed my legs being hot after descending a long staircase. Even dissipating 10kJ of energy entirely as heat, you'd only warm 10kg of water (a reasonable approximation of two legs from the knee down) by about a tenth of a degree C. This isn't something you'd notice experimentally without specialized equipment. Jun 15, 2021 at 14:07
• @NuclearHoagie That's if you imply that it warms up uniformly, but it doesn't. Most of the heat goes into back lower part. Jun 16, 2021 at 7:59
• @NuclearHoagie muscles aren't perfectly efficient, nor is walking (not all of the energy expended in walking down stairs is attributable to the person's loss of potential energy). Jun 16, 2021 at 13:58

### Into the motion of your body.

When you go down the stairs, your muscles take the vertical motion down the stairs and add a horizontal component to it. As you travel down the stairs, you will be accelerated vertically by gravity, as your potential energy is converted into kinetic energy. The faster you go vertically, the faster you go horizontally, so unless you deliberately slow yourself down, you're going a lot faster horizontally at the bottom of the stairs than you were at the top of them. As a result, in addition to the conversions into heat and sound energy covered by other answers, a portion of the potential energy you possessed at the top of the stairs has been converted into kinetic energy.

• People often stand still for a moment after descending a flight of stairs - I think it's best to assume that that's the situation. It's certainly not typical to continuously accelerate while descending stairs - that would be known as falling rather than descending.
– bdsl
Jun 14, 2021 at 10:55
• @bdsl Have you ever gone down a flight of stairs without slowing yourself down? You do continuously accelerate unless your legs are exerting a force to slow yourself down. Jun 14, 2021 at 11:15
• When you did that descending a series of 12 steps you reached the bottom at some typical speed. If you descended 24 steps in the same way did you end up going twice as fast? I think that's very unlikely, and you were in fact absorbing the energy within your legs as you went, albeit rapidly.
– bdsl
Jun 14, 2021 at 11:50
• You might move faster on the stairs than level walking, but you certainly aren't constantly accelerated, or you'd continually speed up every step. You probably reach a new faster speed after a few steps, then its back to cushioning against gravity to maintain constant (ish) speed. At the bottom you return to.level walking - probably similar gait as before, so you bleed off that kinetic energy in a few steps as well, back to low level heat. Technically whether you see that as part of descending the steps, or separate, is a personal choice. Jun 14, 2021 at 12:40
• @bdsl at a constant acceleration, velocity is proportional to the square root of the distance, so after descending 24 steps under constant acceleration one would be going just over 40% faster than one was at the 12th step. Jun 16, 2021 at 14:01