How can work be negative?

In summary: The textbook condition is misleading as it implies that the force and displacement have to be in the same direction for work to be done. In summary, work can be done even if the force and displacement are in opposite directions, as long as they are not directly perpendicular. In this case, the work done is negative, indicating energy extraction from the system.
  • #1
Ellipses
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0
Hello everyone.

I understand the concept of work in general, but the concept of negative work still somewhat baffles me. One of my main problems is this: according to my textbook, 3 conditions must be met in order for work to be done, and one of them is "at least part of the force must be in the same direction as the displacement."

Well, how can negative work occur if the force in displacement are going in opposite directions?

Thanks for the help!
 
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  • #2
That's a poorly worded condition. I would reword it to say that in order for work to be done, the force must not be normal to the displacement (in other words, the dot product of the force and displacement must be nonzero). It can be in the same direction as the displacement or the opposite direction, so long as it isn't directly perpendicular.
 
  • #3
Ellipses said:
Hello everyone.

I understand the concept of work in general, but the concept of negative work still somewhat baffles me. One of my main problems is this: according to my textbook, 3 conditions must be met in order for work to be done, and one of them is "at least part of the force must be in the same direction as the displacement."

Well, how can negative work occur if the force in displacement are going in opposite directions?

Thanks for the help!

As has been said, that's not correct. Imagine a force directed in a certain direction and label that direction with an arrow. If the displacement is a 90 degree angle from that arrow (perpendicular) than no work is done. However, if the displacement is, at least a little bit, pointing along OR OPPOSITE to the force arrow than work is done. In the opposite direction case that work is negative. Intuitively you can say that this force is giving energy BACK to the system.
 
  • #4
Work is done by a particular force. This can be either done by imparting energy to the system or by extracting energy from the system. The former case we say the work done is positive and the latter it is negative.
 
  • #5


I can explain how work can be negative. Work is defined as the transfer of energy from one object to another due to a force acting on the object and causing it to move in the same direction as the force. However, when the force and displacement are in opposite directions, the work done can be considered negative because the object is losing energy instead of gaining it.

For example, imagine a person lifting a heavy box off the ground and placing it on a shelf. The force applied by the person is in the upward direction, while the displacement of the box is in the same direction. This results in positive work, as the box gains energy and is lifted to a higher position.

But if the person were to drop the box from the shelf back to the ground, the force of gravity would act in the downward direction while the displacement of the box is still in the upward direction. In this case, the work done by gravity would be considered negative as the box loses energy and falls to a lower position.

In summary, negative work occurs when the force and displacement are in opposite directions, resulting in the object losing energy instead of gaining it. This concept is important in understanding various physical phenomena, such as the braking of a car or the descent of an object due to gravity. I hope this explanation helps clarify the concept of negative work.
 

What is negative work?

Negative work refers to the situation where the force applied to an object is in the opposite direction of its displacement. This results in a decrease in the object's kinetic energy.

How is negative work measured?

Negative work is measured by multiplying the magnitude of the force applied to an object by the distance over which the force is applied in the opposite direction of the object's motion. This is represented by the equation W = -F * d.

What causes negative work?

Negative work is caused by external forces that act in the opposite direction of an object's motion. This can include friction, air resistance, and drag forces.

What are some real-life examples of negative work?

Some examples of negative work include pushing a book across a table, braking a car to slow it down, or lifting an object in the opposite direction of its motion.

Is negative work always bad?

Negative work is not always bad, as it can also be used to slow down or stop an object's motion. For example, negative work is essential for braking in a car to slow down or stop at a traffic signal. However, excessive negative work can be harmful, as it can lead to wear and tear on objects or decrease efficiency.

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