Why Does Work Have Positive and Negative Values?

  • Thread starter Thread starter Calpalned
  • Start date Start date
  • Tags Tags
    Scalar Work
AI Thread Summary
Work is defined as a scalar quantity, represented by the dot product of force and distance, which can have positive or negative values. The work done on a spring is positive, while the work done by the spring is negative, reflecting the transfer of energy between the two. This distinction arises from Newton's third law, where the forces involved act in opposite directions, resulting in the work being equal in magnitude but opposite in sign. Scalars do not have direction but can possess positive or negative values, similar to other scalar quantities like temperature or altitude. The discussion emphasizes that while work itself is scalar, the context of energy transfer gives it a directional aspect.
Calpalned
Messages
297
Reaction score
6

Homework Statement


Fact: Being the dot product of force and distance, work is a scalar. Fragment from my textbook: The work done on the spring is ##\frac{1}{2}kx^2##, and so the work done by the spring is ##-\frac{1}{2}kx^2##.

Homework Equations


##W = f \cdot d ##

The Attempt at a Solution


I thought scalars don't have directions. Why is the "work done on" positive, while the "work done by" is negative?
 
Physics news on Phys.org
Calpalned said:

Homework Statement


Fact: Being the dot product of force and distance, work is a scalar. Fragment from my textbook: The work done on the spring is ##\frac{1}{2}kx^2##, and so the work done by the spring is ##-\frac{1}{2}kx^2##.

Homework Equations


##W = f \cdot d ##

The Attempt at a Solution


I thought scalars don't have directions. Why is the "work done on" positive, while the "work done by" is negative?
Scalars don't have direction but they do have + or - signs!
 
rude man said:
Scalars don't have direction but they do have + or - signs!

rude man said:
Scalars don't have direction but they do have + or - signs!

I thought that scalars are magnitudes (aka absolute values)...
 
Calpalned said:
I thought that scalars are magnitudes (aka absolute values)...
It's the "aka" part of your statement that's erroneous.

The magnitude of a vector is an absolute value and scalars are often described as having magnitude, but not direction.

That's not to say that all magnitudes are absolute values.
 
Calpalned said:
I thought that scalars are magnitudes (aka absolute values)...
Not so. Temperature in Celsius for example is a scalar. It can be + or -, right? Or altitude - can be above or below sea level. Etc.
 
  • Like
Likes Calpalned
Calpalned said:

Homework Statement


Fact: Being the dot product of force and distance, work is a scalar. Fragment from my textbook: The work done on the spring is ##\frac{1}{2}kx^2##, and so the work done by the spring is ##-\frac{1}{2}kx^2##.

Homework Equations


##W = f \cdot d ##

The Attempt at a Solution


I thought scalars don't have directions. Why is the "work done on" positive, while the "work done by" is negative?
When you stretch a spring, you're doing work on the spring. According to Newton's third law, the spring exerts a force on you and therefore does work on you. The action and reaction forces point in opposite directions, but the displacement is the same in either case, so the work done on the spring by you and the work done by the spring on you are always negatives of each other.

Another way to look at it is that work is the transfer of energy. Energy goes from one thing to another, so in that sense there's a direction to work. It's like if I handed you a $1 bill. Money went from me to you, but you wouldn't say a $1 bill has a direction.
 
  • Like
Likes Calpalned
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
Thread 'Voltmeter readings for this circuit with switches'
TL;DR Summary: I would like to know the voltmeter readings on the two resistors separately in the picture in the following cases , When one of the keys is closed When both of them are opened (Knowing that the battery has negligible internal resistance) My thoughts for the first case , one of them must be 12 volt while the other is 0 The second case we'll I think both voltmeter readings should be 12 volt since they are both parallel to the battery and they involve the key within what the...
Thread 'Trying to understand the logic behind adding vectors with an angle between them'
My initial calculation was to subtract V1 from V2 to show that from the perspective of the second aircraft the first one is -300km/h. So i checked with ChatGPT and it said I cant just subtract them because I have an angle between them. So I dont understand the reasoning of it. Like why should a velocity be dependent on an angle? I was thinking about how it would look like if the planes where parallel to each other, and then how it look like if one is turning away and I dont see it. Since...
Back
Top