# Problem understanding the definition of mechanical work

In summary: All the work done was done in that initial acceleration.In summary, the conversation discusses the concept of work done and its relationship to displacement, force, and energy. It also explores different scenarios and questions related to the conservation of energy in various systems. The main points are that work done is defined as the product of force and displacement, and energy can be converted into different forms such as heat or kinetic energy.
Hi guys,

I know that the simple definition of work done is just Work=Force X Displacement.
If this is the case, there are 2 scenarios which I don't really understand.

1. If say the force applied on a car moving at constant velocity at 5m/s is 500N for a distance of 10m (therefore 2 sec), and the friction work done on the car which is also 500N- hence the constant velocity,the work done on the car by definition is 5000J. What happens to the 5000J of energy if the car does not gain it in KE (velocity is constant)? If say another car was acted on by the same forces and same amount of time but was not moving at all- started at 0 velocity did not accelerate due to friction, then by definition no work is done on the car as there was no displacement. I can't get how this could be possible. In both cases you must have used the same effort. Can someone explain this to me please?

2. If the heat of reaction of a chemical reaction forming an expandable gas is measured in a system of which you forced to have constant volume, then does the mechanical work done- expansion of the gas, get converted into heat energy?(therefore increase of temp) if it does not, what happens to the mechanical energy?

Thank you very much again for answering my newbie questions.

Hi guys,

I know that the simple definition of work done is just Work=Force X Displacement.
If this is the case, there are 2 scenarios which I don't really understand.

1. If say the force applied on a car moving at constant velocity at 5m/s is 500N for a distance of 10m (therefore 2 sec), and the friction work done on the car which is also 500N- hence the constant velocity,the work done on the car by definition is 5000J. What happens to the 5000J of energy if the car does not gain it in KE (velocity is constant)? If say another car was acted on by the same forces and same amount of time but was not moving at all- started at 0 velocity did not accelerate due to friction, then by definition no work is done on the car as there was no displacement. I can't get how this could be possible. In both cases you must have used the same effort. Can someone explain this to me please?

No displacement means no work done on the car. In a real system, of course, objects can be compressed and warped and bent. (I.e., there is displacement, just not a lot). If you're talking about effort, then it's likely whatever is applying the force is doing so through internal force of it's own that generate heat as a byproduct. Your cells, for instance, have little pumps in them that act on ions over a distance. Work is being done internally. It's just that no work is being done on the object you're trying to move.

2. If the heat of reaction of a chemical reaction forming an expandable gas is measured in a system of which you forced to have constant volume, then does the mechanical work done- expansion of the gas, get converted into heat energy?(therefore increase of temp) if it does not, what happens to the mechanical energy?

Yes, the particles will have more kinetic energy which means more heat.

Pythagorean said:
No displacement means no work done on the car. In a real system, of course, objects can be compressed and warped and bent. (I.e., there is displacement, just not a lot). If you're talking about effort, then it's likely whatever is applying the force is doing so through internal force of it's own that generate heat as a byproduct. Your cells, for instance, have little pumps in them that act on ions over a distance. Work is being done internally. It's just that no work is being done on the object you're trying to move.

Thanks for your answer good sir. If I apply a force, and the object moves at constant speed due to opposing forces, am I still doing work on the object? If not, where has the energy gone?

1. If say the force applied on a car moving at constant velocity at 5m/s is 500N for a distance of 10m (therefore 2 sec), and the friction work done on the car which is also 500N- hence the constant velocity,the work done on the car by definition is 5000J. What happens to the 5000J of energy if the car does not gain it in KE (velocity is constant)?

converted to heat at the point of friction

Pythagorean said:
No displacement means no work done on the car. In a real system, of course, objects can be compressed and warped and bent. (I.e., there is displacement, just not a lot). If you're talking about effort, then it's likely whatever is applying the force is doing so through internal force of it's own that generate heat as a byproduct. Your cells, for instance, have little pumps in them that act on ions over a distance. Work is being done internally. It's just that no work is being done on the object you're trying to move.

Thanks for your answer good sir. If I apply a force, and the object moves at constant speed due to opposing forces, am I still doing work on the object? If not, where has the energy gone?

Yes, you're doing work against the opposing forces. But you knew this, from your first question:

If say the force applied on a car moving at constant velocity at 5m/s is 500N for a distance of 10m (therefore 2 sec), and the friction work done on the car which is also 500N- hence the constant velocity,the work done on the car by definition is 5000J.

That 5000J is spent working against friction. No other work is needed since you're not considering the car when it accelerated from 0 to 5m/s. The object would "continue on it's path" of 5m/s if not "acted upon by another force."

Pythagorean said:
Yes, you're doing work against the opposing forces. But you knew this, from your first question:

That 5000J is spent working against friction. No other work is needed since you're not considering the car when it accelerated from 0 to 5m/s. The object would "continue on it's path" of 5m/s if not "acted upon by another force."

ahh i see. I've got one thing I am not sure of though. If 500N of force was applied on a stationary object (not moving at all) with an opposing force of 500N applied on it, does that mean all the work is converted straight into heat- therefore the object does not move? Or do the forces cancel each other out in opposite directions and therefore the work/energy is canceled out? Is there anyway to work out the work done on an object which is not displaced?

Thanks again for your swift and quality responses

ahh i see. I've got one thing I am not sure of though. If 500N of force was applied on a stationary object (not moving at all) with an opposing force of 500N applied on it, does that mean all the work is converted straight into heat- therefore the object does not move? Or do the forces cancel each other out in opposite directions and therefore the work/energy is canceled out? Is there anyway to work out the work done on an object which is not displaced?
If the object doesn't move, no work is done. No mechanical energy is converted to 'heat' or anything else.

Consistent with what Doc Al is saying, if the object is compressible, it will be converted to heat (and/or kinetic energy). But the object will have "moved" (that is, its constituents will have all compressed more tightly together). So there will be a force applied over a distance for each constituent (say, molecules or atoms) of the material, but the object as a whole will not have had any displacement (since we define it's displacement by it's center, which hasn't moved) but all the atoms making up the material are squeezed into a tighter area, so they have all moved through a displacement from the applied forces.

Doc Al said:
If the object doesn't move, no work is done. No mechanical energy is converted to 'heat' or anything else.

Does that mean that when something uses energy to apply a force, as long as the object the force is applied on doesn't move (due to opposing force), it can keep applying that force as it never runs out of energy due to no work done? or is it the work done in one direction is totally canceled by the work done in the opposite direction therefore work is still done and energy is still used?

I know this a very simple concept, but I find it exceedingly difficult to grasp.

Pythagorean said:
Consistent with what Doc Al is saying, if the object is compressible, it will be converted to heat (and/or kinetic energy). But the object will have "moved" (that is, its constituents will have all compressed more tightly together). So there will be a force applied over a distance for each constituent (say, molecules or atoms) of the material, but the object as a whole will not have had any displacement (since we define it's displacement by it's center, which hasn't moved) but all the atoms making up the material are squeezed into a tighter area, so they have all moved through a displacement from the applied forces.

Assuming if something is incompressible, does the energy working in opposite directions cancel each other out? or will no energy ever be used if there was no movement?

You can either do work against friction (losses), in which case the energy will end up as thermal, or against an 'energy storing' system, like a spring or by accelerating an object. If an object is "incompressible" then no work can be done in changing its shape - but of course, you can still accelerate it.

Your idea of energies "cancelling out" would apply in the second case where the energy lost by pushing was gained by the object. In an ideal case, the same amount ot total energy (mechanical, and therefore retrievable) would be there at the end as at the start.

I think you have to be rigorous in any arguments about work and energy, remembering that you need a force and a distance moved (in that direction) by (a part of) the object.

Does that mean that when something uses energy to apply a force, as long as the object the force is applied on doesn't move (due to opposing force), it can keep applying that force as it never runs out of energy due to no work done?
Obviously not. By your own stipulation, you are using energy to provide the force. (That depends on how you are generating the force.) That's got nothing to do with the mechanical work done by the force.
or is it the work done in one direction is totally canceled by the work done in the opposite direction therefore work is still done and energy is still used?
No, there is no mechanical work being done on the object if it doesn't move.

I know this a very simple concept, but I find it exceedingly difficult to grasp.
You are mixing up the energy required to generate a force with the mechanical work done by that force. Two different things.

Example: I hold my hand out and support a 5 kg mass. I am using a biological system (me and my arm) to generate the force, which requires energy. Nonetheless, I do no work on the mass, since it doesn't move. I could have just put the 5 kg mass on a shelf, then the shelf would provide the support force without requiring any energy input. Again, no work is being done on the mass.

## 1. What is the definition of mechanical work?

The definition of mechanical work is the amount of force applied to an object multiplied by the distance the object moves in the direction of the force. It is a measure of the energy transferred to an object by a force acting on it.

## 2. How is mechanical work different from other types of work?

Mechanical work specifically refers to the work done by a force on an object, whereas other types of work can include physical or mental effort, or the transformation of energy from one form to another.

## 3. What units are used to measure mechanical work?

Mechanical work is typically measured in joules (J) in the International System of Units (SI). In some cases, it may also be measured in foot-pounds (ft-lb) in the imperial system.

## 4. What is the relationship between mechanical work and power?

Mechanical work and power are related in that power is the rate at which work is done. In other words, power is the amount of work done per unit of time. The unit of power is the watt (W), which is equal to one joule per second (J/s).

## 5. How is mechanical work calculated?

Mechanical work can be calculated by multiplying the force applied to an object by the distance the object moves in the direction of the force. The formula for calculating work is W = F x d, where W is work, F is force, and d is distance.

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