Calculating Work Done for Constant Force Acting on an Object in Space

[yazz912]

1. The problem statement, all variables and given/known

A constant Force= <2,4,1> (in Newtons) moves an object in space from (0,0,0) to (2,4,5) ( distance is measured in meters) Calculate the Work done. 2. Homework Equations

W= || proj of F onto pq|| ||PQ||

W= F• vector PQ 3. The Attempt at a Solution
Well I'm guessing for starters I'd have to make a vector component from (0,0,0) to (2,4,5)
So I know PQ would be =< 2,4,5>

I am stuck on what my next step would be. W= F•d when the force is acting in line of motion with the object. But that is not the case.

 

[Ray Vickson]

1. The problem statement, all variables and given/known

A constant Force= <2,4,1> (in Newtons) moves an object in space from (0,0,0) to (2,4,5) ( distance is measured in meters) Calculate the Work done.











2. Homework Equations

W= || proj of F onto pq|| ||PQ||

W= F• vector PQ








3. The Attempt at a Solution
Well I'm guessing for starters I'd have to make a vector component from (0,0,0) to (2,4,5)
So I know PQ would be =< 2,4,5>

I am stuck on what my next step would be. W= F•d when the force is acting in line of motion with the object. But that is not the case.

The way you have written it is correct, whether or not W acts along d (assuming that W and d are both vectors).

 

[yazz912]

So if I have two different vectors being displacement and force.
I dot them to calculate work? Would it really be that simple?

 

[tiny-tim]

yup!

work done = force "dot" displacement

 

[Ray Vickson]

So if I have two different vectors being displacement and force.
I dot them to calculate work? Would it really be that simple?

Yup. That's what your textbook will tell you.

 

[yazz912]

Wow. I really assumed i needed to do more "work" to solve it. ;)

Therefore W should = 25 Nm

 

[yazz912]

Would I not have to find || PQ|| and ||F|| and then dot?

 

[Ray Vickson]

Would I not have to find || PQ|| and ||F|| and then dot?

Why would you do that? How would you compute the dot product if you could do that? Would you not need the angle between the two vectors? How would you get that?

I am amazed that you are even asking the question---you are taking something simple and making it hard.

 

[yazz912]

I guess I probably over think the problem, considering this is part of my take home test I assume it isn't going to be as easy as it seems..

Reason I asked was bc on all my notes and in the book it shows W= ||F|| ||PQ||

 

[tiny-tim]

(just got up :zzz:)

both formulas are correct (and give the same result)

which you use depends on what information you're given

in this case, you're given the coordinates, so it's easier to use b₁c₁ + b₂c₂ + b₃c₃

but if instead you were given the magnitudes and the directions, it would be easier to use ||b|| ||c|| cosθ

 

[yazz912]

(just got up :zzz:)
both formulas are correct (and give the same result)
which you use depends on what information you're given
in this case, you're given the coordinates, so it's easier to use b₁c₁ + b₂c₂ + b₃c₃
but if instead you were given the magnitudes and the directions, it would be easier to use ||b|| ||c|| cosθ

Ohhh ok that answers my question thank you so much tiny-tim! more or so for not making me feel like an idiot for asking that last question lol :)