# Work Definition: Force x Distance vs. Force x Displacement

• Fizziks_Fan
In summary, the concept of work is often defined as the dot product of the force and displacement vectors, but another way to think about it is force multiplied by distance. This raises the question of whether someone lifting a weight and then bringing it back down is actually doing work, since the displacement is zero. However, it can be argued that they are doing work against gravity. Additionally, if the weight is slowly lowered to the floor, the net work done is zero. This is because the direction of the displacement is opposite to that of the force, resulting in a negative work done. The feeling of tiredness in this scenario is due to the muscles continuously doing work, but the net work done is technically negative.
Fizziks_Fan
Hi I always thought work was defined as the dot product of the force and displacement vectors.

W = F parallel to D

However, my physics teacher told me that it's force x DISTANCE.

Does that mean that whenever someone lifts a weight and brings it back down is actually doing work? (displacement is zero...)

I've always known work as $$W = \vec {F} \cdot \vec {D}$$ or $$W = |F||D|cos\theta$$ theta being the angle between the force and displacement vectors.

The person does no net work when moving the block up and then back down. As you noted, the displacement is 0. You could also argue that it takes say 100 joules of work to move it up, and -100 joules of work to bring it down. However you slice it, it all adds up to nothing.

Distance that you are referring to is the distance moved the DIRECTION of the force. The person did do work: against gravity. When he let's go, it is actually gravity that does work, not him.

QuantumCrash said:
Distance that you are referring to is the distance moved the DIRECTION of the force. The person did do work: against gravity. When he let's go, it is actually gravity that does work, not him.
]But if he doesn't let go, and slowly lowers the weight to the floor, he still does work, but the net work he does in both directions is zip.
He might be tired and claim he did a lot of work, but he really didn't do any. Depends on what you mean by "work".

Well, if you put it that way yes. His total work against is technically negative since the direction of movement when the net work is 0. Since while he lowers down the weight, the direction of the displacement is opposite that of the force. Hence, work done is actually negative.

Note: The man feels tired because his muscles are actually doing work by continously stretching and compressing. I won't delve further since we are already touching biology.

## 1. What is the difference between force x distance and force x displacement?

Force x distance and force x displacement are two ways of measuring the work done by a force. Force x distance is calculated by multiplying the magnitude of the force by the distance the object moves in the direction of the force. Force x displacement, on the other hand, is calculated by multiplying the magnitude of the force by the displacement vector, which takes into account both the magnitude and direction of the displacement. In other words, force x displacement takes into account the direction in which the force is applied while force x distance does not.

## 2. How do you calculate work using force x distance and force x displacement?

To calculate work using force x distance, you simply multiply the magnitude of the force by the distance the object moves in the direction of the force, as shown by the formula W = F x d. To calculate work using force x displacement, you multiply the magnitude of the force by the displacement vector, which takes into account both the magnitude and direction of the displacement, as shown by the formula W = F x s.

## 3. Which method of calculating work is more accurate?

Force x displacement is considered to be more accurate because it takes into account the direction of the force and displacement, which can greatly affect the amount of work done. Force x distance only considers the distance moved in the direction of the force, which may not accurately represent the actual work done.

## 4. Can you use force x distance and force x displacement interchangeably?

No, force x distance and force x displacement cannot be used interchangeably. They are two different methods of calculating work and will result in different values. Force x distance is used when the direction of the force is not important, while force x displacement is used when the direction of the force is important.

## 5. In what situations would you use force x distance and force x displacement?

Force x distance is typically used when calculating work done by a constant force, such as lifting an object straight up. Force x displacement is used when the direction of the force is changing, such as pushing an object up a ramp. It is also used for calculating work done by a variable force, as it takes into account the varying direction of the force.

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