force

**Jenny20** · January 15th 2007, 06:54 PM

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.

**ThePerfectHacker** · January 15th 2007, 07:03 PM

Originally Posted by Jenny20

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,
$\int_C \bold{F}\cdot d\bold{R}$
Thus, I assume, the curve $C$ is from,
$(0,0)$ to $(10/\sqrt{2},10\sqrt{2},)$
(Because that is i+j, 10 units in length.)
The parameterized curve is,
$t\bold{i}+t\bold{j}, 0\leq t\leq \sqrt{10}/2$
Thus, the line integral is,
$\int_0^{\sqrt{10}/2} 1(t)'dt+\int_0^{\sqrt{10}/2} 2(t)'dt+\int_0^{\sqrt{10}/2} 0(0)'dt$
Thus,
$\frac{3\sqrt{10}}{2}$

Physics IS NOT my thing. Do not count on the authencity of this solution.

**Jenny20** · January 16th 2007, 12:38 PM

Hi perfecthacker,

Do you have a simpler way to solve this question? If yes, please teach me.

**CaptainBlack** · January 16th 2007, 01:09 PM

Originally Posted by Jenny20

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.

Find the component of F parallel to i+j.

A unit vector parallel to i+j is (i+j)/sqrt(2).

The component of F in the direction we want is then:

F.(i+j)/sqrt(2)=(1+2)/sqrt(2)=3/sqrt(2).

This moves 10m, so the work done is: 10 (3/sqrt(2)=30/sqrt(2).

RonL

**topsquark** · January 16th 2007, 01:38 PM

Originally Posted by Jenny20

Hi perfecthacker,

Do you have a simpler way to solve this question? If yes, please teach me.

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:
$W = \vec{F} \cdot \vec{s}$
where $\vec{F}$ is the force and $\vec{s}$ is the displacement (the directed distance over the path taken) and $\cdot$ 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

**CaptainBlack** · January 16th 2007, 01:45 PM

Originally Posted by topsquark

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.

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)

**ThePerfectHacker** · January 16th 2007, 01:51 PM

Originally Posted by CaptainBlack

One of my pet hates about Physics taught in the Maths department is -
where did the meaning go?

I do not understand.

---
Where did I make a mistake?
I was sure I was doing it right.

**CaptainBlack** · January 16th 2007, 01:57 PM

Originally Posted by ThePerfectHacker

I do not understand.

---
Where did I make a mistake?
I was sure I was doing it right.

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

**topsquark** · January 16th 2007, 02:07 PM

Originally Posted by CaptainBlack

(Referring to TPH)
That is you seem more interested in the machinery than in what
it is used for.

No! Never!

-Dan

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