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.

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- Jan 15th 2007, 06:54 PMJenny20force
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. - Jan 15th 2007, 07:03 PMThePerfectHacker
I think you mean,

"how much**work**is done".

Okay, we need to compute, the line integral,

$\displaystyle \int_C \bold{F}\cdot d\bold{R}$

Thus, I assume, the curve $\displaystyle C$ is from,

$\displaystyle (0,0)$ to $\displaystyle (10/\sqrt{2},10\sqrt{2},)$

(Because that is i+j, 10 units in length.)

The parameterized curve is,

$\displaystyle t\bold{i}+t\bold{j}, 0\leq t\leq \sqrt{10}/2$

Thus, the line integral is,

$\displaystyle \int_0^{\sqrt{10}/2} 1(t)'dt+\int_0^{\sqrt{10}/2} 2(t)'dt+\int_0^{\sqrt{10}/2} 0(0)'dt$

Thus,

$\displaystyle \frac{3\sqrt{10}}{2}$

**Physics IS NOT my thing. Do not count on the authencity of this solution**. - Jan 16th 2007, 12:38 PMJenny20
Hi perfecthacker,

Do you have a simpler way to solve this question? If yes, please teach me. :) - Jan 16th 2007, 01:09 PMCaptainBlack
- Jan 16th 2007, 01:38 PMtopsquark
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:

$\displaystyle W = \vec{F} \cdot \vec{s}$

where $\displaystyle \vec{F}$ is the force and $\displaystyle \vec{s}$ is the displacement (the directed distance over the path taken) and $\displaystyle \cdot$ 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 - Jan 16th 2007, 01:45 PMCaptainBlack
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) - Jan 16th 2007, 01:51 PMThePerfectHacker
- Jan 16th 2007, 01:57 PMCaptainBlack
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 - Jan 16th 2007, 02:07 PMtopsquark