# No work done and no energy spent?

• Mesmerized
In summary, when applying an opposite force to an object, no work is done on the object unless there is displacement. This means that it is the same whether you do nothing or try to hold the object from moving by applying an equal force in the opposite direction. However, if you are the one applying the force, your muscles are converting energy internally and you may get tired. This internal energy dissipates as heat and does not transfer to the object. Additionally, if the object is not rigid, there may be deformation and energy stored in the object. This is relevant in engineering and material strength.
Mesmerized
Imagine there's some body and a force F trying to move that body. In that case the force will do a work and the body will start to accelerate (obtain a kinetic energy). Now also imagine that I'm applying a force -F right in the opposite direction of the existing force, when the body is still standing. Then it will remain standing as long as the 2 opposite forces are applied and cancel each other.

Question: Do I do some work or spent some energy while applying that force -F? If yes, then is there a formula for it, if no, then does that mean, that it's the same whether I do nothing or try to hold the body from moving by applying an equal force to the existing one but in opposite direction?

No, if there is no displacement, there is no work done by either force (assuming the body is rigid). No energy is transferred. All you're doing is not allowing the energy to be transferred from the first object applying that force.

If the object is not rigid, and can deform (like all objects on this earth) you would be transferring some of the energy into deforming the object and would be doing work.

Mesmerized said:
Imagine there's some body and a force F trying to move that body. In that case the force will do a work and the body will start to accelerate (obtain a kinetic energy). Now also imagine that I'm applying a force -F right in the opposite direction of the existing force, when the body is still standing. Then it will remain standing as long as the 2 opposite forces are applied and cancel each other.

Question: Do I do some work or spent some energy while applying that force -F? If yes, then is there a formula for it, if no, then does that mean, that it's the same whether I do nothing or try to hold the body from moving by applying an equal force to the existing one but in opposite direction?

There is no work done if there is no motion. So yes, your scenario is the same as doing nothing. You are performing no work on the body...unless, of course, the forces you are using are so great that you end up crushing the thing. Then you did do some work on it.

Also, you're not doing any work on the body, but if you're the one applying the force, then obviosuly you will get tired and have expended some work, on some level deep within your muscles. Unfortunately you got tired for nothing and all your work will have been wasted. But, that's just a limitation of the human body...

A more efficient way to accomplish the same thing is to simply put a clamp around the body, and let it squeeze it. You can then go watch 25 consecutive episodes of the Simpsons while applying your opposite forces without getting anyone tired.

Mesmerized said:
Question: Do I do some work or spent some energy while applying that force -F? If yes, then is there a formula for it, if no, then does that mean, that it's the same whether I do nothing or try to hold the body from moving by applying an equal force to the existing one but in opposite direction?
There is no work done by you on the object. Instead of your muscles you could just as well use two walls to apply that opposite forces to the object: no energy transfer, no work done. However, if you use your muscles, you convert energy internally to produce the force. But this energy doesn't go into the object, but dissipates as heat. Therefore no work is done on the object.

Think of a helicopter hovering at constant height. The engine uses energy but does no work on the helicopter chassis. Yet it still creates a force upward on the helicopter chassis.

Lsos said:
TYou can then go watch 25 consecutive episodes of the Simpsons while applying your opposite forces without getting anyone tired.
And while watching and flicking through the adds, you are putting a downwards force on your settee and could even fall asleep doing all this downward forcing.

thanks to all for detailed replies, got it :)

As mentioned above, if the body is not rigid, there is some deformation of its shape, so it stores energy like a spring when deformed by external forces. These types of work are relevant in structural engineering, architecture, and strengths of materials.

thanks SystemTheory

## 1. What does "no work done" mean in physics?

In physics, work is defined as the product of a force and the distance through which that force acts. When no force is applied or when the force is applied in a direction perpendicular to the displacement, no work is done. This means that there is no transfer of energy from one form to another.

## 2. Can work be done without spending any energy?

No, work and energy are closely related concepts. Work is defined as the transfer of energy from one form to another, so if no energy is spent, no work can be done. However, in some cases, it may appear that no work is done because the energy is being transferred internally within a system.

## 3. How is "no work done" different from "zero work done"?

In physics, "no work done" means that there is no transfer of energy between forms, while "zero work done" means that the work done is exactly equal to zero. In other words, "no work done" indicates that there is no change in energy, while "zero work done" indicates that there is no transfer of energy.

## 4. What are some examples of situations where no work is done?

One example is when an object is held stationary above the ground. In this case, the force of gravity is acting on the object, but because the displacement is zero, no work is done. Another example is when a person is carrying a heavy object and walking at a constant speed. The force applied by the person is equal to the force of gravity, therefore no work is done.

## 5. Is it possible for no work to be done but energy to be spent?

Yes, this is possible in cases where the energy is being transferred internally within a system. For example, in a closed system where there is no external force acting, no work is done, but the energy may still be spent due to internal forces such as friction or heat transfer.

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