work sign convention

[wblack]

A man pushes a crate to distance D with a frictional force opposing the motion of the crate. Thus the work done by friction is -Wa. He then adds more mass to the crate and pushes the heavy crate to distance D. This time, the work done by friction is -Wb. Which of the following is true?
a) Wa<Wb
b)Wa=Wb
c)Wa>Wb

Since the frictional force does negative work and since B does more negative work, shouldn't the answer be C. In PR it says A because the work done by friction for Wb is more. Is this because the answer choices do not have the negative sign in the front?

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[MedPR]

A man pushes a crate to distance D with a frictional force opposing the motion of the crate. Thus the work done by friction is -Wa. He then adds more mass to the crate and pushes the heavy crate to distance D. This time, the work done by friction is -Wb. Which of the following is true?
a) Wa<Wb
b)Wa=Wb
c)Wa>Wb

Since the frictional force does negative work and since B does more negative work, shouldn't the answer be C. In PR it says A because the work done by friction for Wb is more. Is this because the answer choices do not have the negative sign in the front?

Even if it had the negative sign, the answer would still be A. Workb does more work than Worka.

The sign convention just indicates whether work is being done on or by the system and it is purely arbitrary who you assign the sign to (unless they do it for you, as in this problem). If friction is doing negative work, that means it is opposing the work done in the "positive" direction, which is just about always the case with friction. If you imagine the man pushing the crate to the right, then the frictional force, and thus the work done by friction, is pointing to the left (the negative direction).

Since workb and worka are both going in the same direction, they have the same sign so you can choose to keep it or cancel it out. It doesn't change your answer though.

You could have completely ignored the signs and thought about it more conceptually. Friction is dependent on the weight of the object and the coefficient of friction. Since the objects are pushed on the same surface, the coefficient of friction is the same. Since block b is heavier than block a, the frictional force (and thus the work) done on b must be greater than on a. So Work B > Work A.

 

[SaintJude]

Even if it had the negative sign, the answer would still be A. Workb does more work than Worka.

The sign convention just indicates whether work is being done on or by the system and it is purely arbitrary who you assign the sign to (unless they do it for you, as in this problem). If friction is doing negative work, that means it is opposing the work done in the "positive" direction, which is just about always the case with friction. If you imagine the man pushing the crate to the right, then the frictional force, and thus the work done by friction, is pointing to the left (the negative direction).

Since workb and worka are both going in the same direction, they have the same sign so you can choose to keep it or cancel it out. It doesn't change your answer though.

You could have completely ignored the signs and thought about it more conceptually. Friction is dependent on the weight of the object and the coefficient of friction. Since the objects are pushed on the same surface, the coefficient of friction is the same. Since block b is heavier than block a, the frictional force (and thus the work) done on b must be greater than on a. So Work B > Work A.

Hmm, very interesting MedPr. Thanks for that answer.

 

[milski]

It's a poorly worded question with a poor answer. It is correct that the magnitude of Wb will be larger than Wa. You cannot tell which one is larger without knowing the sign. In very simple terms, 5 > 3 but -5 < -3.

 

[MedPR]

It's a poorly worded question with a poor answer. It is correct that the magnitude of Wb will be larger than Wa. You cannot tell which one is larger without knowing the sign. In very simple terms, 5 > 3 but -5 < -3.

But either way doesn't Wb do more work even if you are considering them both to be negative work?

A higher value of negative work just means it did more work in the negative direction...?

 

[milski]

But either way doesn't Wb do more work even if you are considering them both to be negative work?

A higher value of negative work just means it did more work in the negative direction...?

Yes, it is more work and if they had asked about that I would have no problem with the answer. |Wb|>|Wa| would have been acceptable as well. They are asking for Wb>Wa which is not the same thing. The sign '>' for numbers has a very well defined meaning. While we can agree about things like 'more work' and 'more displacement', writing things like -5>-3 is outright wrong.

That said, I think it's not such a poor question and I might have complained too early. The work done by the friction force is negative and they also say that it is -Wb. That means that Wb is positive and it's ok to write Wb > Wa.