# Does ladder do positive work on us when we are climbing?

A man climbs up from ground to first floor using a ladder/stair. Assume that his kinetic energy does not change appreciably. Predict the sign of work done by ladder (if any).

I think the answer should be 'positive' because the negative work done by gravity has to be countered and hence some external agent must do positive work on us.

But, there's a second thought. Since at each instant normal reaction is perpendicular to direction of motion (in case of stairs) (motion being lifting of leg) therefore the work done must be zero. But then a question arises - who countered gravity?

I'm confused between the two. Both sound promising but not perfect.

The ladder (or the stairs) don't do any work at all. The reason for the same is that the ladder (or stairs) applies the force on our feet only when our feet are right in contact with the ladder (or the stairs). Thus, the point of application of force doesn't move at all while the force is being applied. Thus, net work done by the ladder (or the stairs) is zero because there is no displacement of the point of application of the force. As soon as the displacement occurs, the force ceases to be applied instantaneously.

Now, coming to the question of "who then did the work?". It is your body who did the work through its muscular forces using the (bio)chemical energy. In the case of an escalator or an elevator lifting you up, the point of application of force moves in the direction of the force (upward) and thus, the work done required to counter the work done by gravity is done by the elevator (or the escalator). Of course, this energy comes from the electricity used to run the elevator (or the escalator) and essentially, the electricity does the work instead of your body - giving you some rest and comfort!

• Can you please elaborate more on how our body does work on itself? Commented May 3, 2017 at 4:02
• Interestingly, when you think of a real ladder there will be small displacements as you step on and off. Those displacements will slow down the leg movement a bit when pushing down; until it has enough force to support your weight. The reason this doesn't change the scenario is because when you begin to lift your foot, the bending of the ladder helps to lift it as well, so the net contribution is still 0. Just thought it's worth noting that in real life it would displace; but since it is like every step is a spring; the net work will still be 0 once a step has been completed.
– JMac
Commented May 3, 2017 at 14:59
• @JMac in real life the work done by the ladder will be marginally negative, since it is not a perfectly elastic spring. We do a tiny bit of work on the ladder, causing the ladder to heat up.
– bdsl
Commented Sep 12, 2022 at 10:45

There is no work being done by the ladder/stairs. The man exerts a force on the stairs but as long as the stairs don't move, there is no energy being transferred. Work equals force times distance and this case the distance is 0.

That would be different if the ladder would deform. Than energy would be put into the ladder as its moving. Most of it would be returned when the weight is lifted since the ladder would mainly act as a spring, but some would also be absorbed and turned into heat since there is always some amount of damping and loss.

I agree with Dvij, the ladder does no work, it is your muscles do the work when you climb up a ladder. Muscles generally do work when they contract. At each end they are attached to bones. Suppose that at a given moment the bones (to which a given muscle is attached) don't want to be drawn together. The muscle, when 'switched on' by your nerves, can generate enough tension to overcome this reluctance of the bones to move. Suppose the required tension is T, and the bones move so that the muscle shortens its length by L. Then the muscle has done work TL.

It is amazing that the body is so organized that it can get you upstairs just by contracting and relaxing muscles, in the right order. Of course when a muscle is 'switched off' - the relaxation phase - it goes slack and can be restored to its original length without the application of force (or not much).