A force of F = i +2j-3k is applied to a particle that moves 10 meters in the direction of i+j.
How much is done?
Please teach me how to solve this question. Thank you very much.
I think you mean,
"how much work is done".
Okay, we need to compute, the line integral,
Thus, I assume, the curve is from,
to
(Because that is i+j, 10 units in length.)
The parameterized curve is,
Thus, the line integral is,
Thus,
Physics IS NOT my thing. Do not count on the authencity of this solution.
Specifically, to add to CaptainBlack's (typically excellent answer) I will say that if the force is constant and the direction of motion does not vary then the work done will simply be:
where is the force and is the displacement (the directed distance over the path taken) and is the "dot product" between the two vectors. This is the case for your problem.
If the force is varying or the direction of motion changing then we need to use ThePerfectHacker's method.
I would guess that you are in a Math class by the way the question was worded. If this were a Physics class I would tell you that we usually don't make a student use the integral form in an Introductory class. (There are exceptions but they are usually dealt with during class time, not homework.) What a Math class will throw at you I can't say.
-Dan
One of my pet hates about Physics taught in the Maths department is -
where did the meaning go?
RonL
(From one who has sat through a Maths departments idea of courses on
QM, GR, EM&SR and would still be wondering what they were about if it
was not for a lot a reading and a higher degree in Astrophysics)
Nowhere (well it must have gone wrong somewhere), but you are
using a lot a machinery to solve a problem which can be done in a
line or two by knowing what the concepts mean, and how they
relate to one another.
That is you seem more interested in the machinery than in what
it is used for.
RonL