# If a force is applied to a box, and the box is not displaced, no work

#### InvalidID

If a force is applied to a box, and the box is not displaced, no work is done on the box, right? But to apply the force, don't you use up calories which is a unit of energy?

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#### Khashishi

Your body wastes energy, but it doesn't accomplish any work on the box. This is because your body is inefficient in metabolizing food and generating forces.

#### Drakkith

Staff Emeritus
2018 Award
No. Consider gravity. Gravity acts upon a box sitting on the ground, applying a force that pulls it down. If we watch the box we will see that it does not move, there is no displacement. As such there is no work done on it. Also, no energy is expended by applying this force.

Now, this changes a little bit if you talk about using machines, such as your body, to apply a force. Your body is not a perfect machine and must expend energy to apply any force using its muscles. In such a case you would indeed use up calories, but this energy is used up in your body, and the work performed is on your body, not on the box.

#### InvalidID

Your body wastes energy, but it doesn't accomplish any work on the box. This is because your body is inefficient in metabolizing food and generating forces.
Where does the energy go?

No. Consider gravity. Gravity acts upon a box sitting on the ground, applying a force that pulls it down. If we watch the box we will see that it does not move, there is no displacement. As such there is no work done on it. Also, no energy is expended by applying this force.

Now, this changes a little bit if you talk about using machines, such as your body, to apply a force. Your body is not a perfect machine and must expend energy to apply any force using its muscles. In such a case you would indeed use up calories, but this energy is used up in your body, and the work performed is on your body, not on the box.
So where does the energy go?

#### Drakkith

Staff Emeritus
2018 Award
So where does the energy go?
What energy? If you mean the energy used by your body, it is turned into heat.

Oh ok. Thanks.

#### InvalidID

I'm still having trouble with work & energy.

Consider a ball that starts 1m above the ground and falls down to the ground without bouncing. All of the ball's gravitational energy is converted into kinetic energy, right? But we also know that work was done on the ball. So if all the energy is converted from gravitational energy to kinetic energy and there is no energy left to do work, then how has work been done?

#### Drakkith

Staff Emeritus
2018 Award
I'm still having trouble with work & energy.

Consider a ball that starts 1m above the ground and falls down to the ground without bouncing. All of the ball's gravitational energy is converted into kinetic energy, right? But we also know that work was done on the ball. So if all the energy is converted from gravitational energy to kinetic energy and there is no energy left to do work, then how has work been done?
Potential energy was converted to kinetic energy. That process IS work.

#### Rap

I'm still having trouble with work & energy.

Consider a ball that starts 1m above the ground and falls down to the ground without bouncing. All of the ball's gravitational energy is converted into kinetic energy, right? But we also know that work was done on the ball. So if all the energy is converted from gravitational energy to kinetic energy and there is no energy left to do work, then how has work been done?
Work is what was done as the potential energy was turned into kinetic energy. Work is force times distance. The distance was 1 meter, the force was mg where m is mass, g is the acceleration due to gravity, so the work done on the ball is 1 x mg.

The total energy of the ball is potential energy V plus kinetic energy E. V=mgh and E=mv^2/2. In this case, work is the amount of potential energy that has been converted into kinetic energy. Work is not how much energy a body has, its how much energy has been transferred to it. Keep that always in mind. Work is not an amount of energy, it is an amount of energy transferred. Work is not energy, it is a process by which energy is transferred, the amount of work done is the amount of energy transferred.

#### InvalidID

Is work the only process that energy can be transferred through? If so, then whenever energy is transferred, there will always be a force and displacement involved?

#### sophiecentaur

Gold Member
The problem with this topic is the special and general uses of the word "work". Moreover, the (useful) work done ON an object is always less than the work done BY the source of the work.
Inside your muscles, there is actual 'force times distance' mechanical work done as individual muscle fibres tighten and relax in sequence - the sum of thousands of small forces times small distances - but it may achieve no useful work if you are just standing supporting a mass and not raising it.

#### Rap

Is work the only process that energy can be transferred through? If so, then whenever energy is transferred, there will always be a force and displacement involved?
Energy can also be transferred by heating. Just like work, heat is not energy, it is the amount of energy transferred by heating. If the force is constant, the work is the force times the change in position (or the displacement in position). For heat, if the temperature is constant, the heat energy transferred is the temperature times the change in entropy. It has the same form, and temperature is sometimes referred to as a "thermodynamic force" and the entropy as a "thermodynamic displacement".

Also, you can transfer energy by moving warm material, simply moving a bunch of warm particles. This is called convection. If the chemical potential is constant, the amount of energy moved is the chemical potential times the number of particles. It also has the same form as work, and the chemical potential is sometimes called another kind of "thermodynamic force" and the change in the number of particles as another kind of "thermodynamic displacement".

These are thermodynamic ways of transferring energy. I cannot think of any other ways, and I can't think of a way that work does not involve a force acting through a distance. The work does not always wind up as kinetic energy, though. If there is friction, for example, it can be converted immediately to thermal energy. Actually, thermal energy is just the random kinetic or rotational energy of the molecules, so maybe you could say work does supply kinetic energy in one way or another.

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