How Do You Calculate Vector Differences and Resultant Forces?

[Vaalron]

I have a couple problems.

Homework Statement

One displacement vector A has a magnitude of 2.43 km and points due north. A second displacement vector B has a magnitude of 7.74 km and also points due north. (a) find the magnitude and direction of A - B. (b) Fidn the magnitude and direction fo B - A.

vector a - 2.43 km, points north
vector b - 7.74 km, points north

Homework Equations

None

The Attempt at a Solution

I thought that A -B meant from tail a to head b, and B- A meant tail B to head A

Is this right??

http://img154.imageshack.us/img154/5466/blahqj5.png

Homework Statement

A force vector F1 points due east and has a magnitude of 200 Newtons. A second force F2 is added to F1. The resultant of the two vectors has a magnitude of 400 Newtons and points along the east/west line. Find the magnitude of direction of F2. Note that there are two answers.

Homework Equations

None

The Attempt at a Solution

I have no clue how to do this

 

[Vaalron]

A chimpanzee sitting against his favorite bananna tree gets up and walks 51m due east and 39m due south to reach a termite mound, where he east lunch. (a) what is the shortest distance btwn the tree and the termite mound? (b) what angle does the shortest distance make with respect to due east?

51m east
39m south

here is my interpretation of the problem:

http://img117.imageshack.us/img117/4750/untitledxu3.png

Do you have to use trig for (b) and the pythagorean theorem for (a)?

 

[learningphysics]

In the first problem, you have to add -B to A, to get A - B... so do the same thing you would if you were adding B to A... except now instead use -B (same magnitude as B except opposite direction)...

In the diagram you drew... if you go from the tail of A to the head of B, then that's A + B right?

Draw a different diagram... this time draw A... then draw -B with its tail at the head of A.

So going from the tail of A to the head of -B... that is A + (-B) = A - B

And do the same type of thing for B - A.

You could also, just do the math without the diagrams and get the numbers and interpret the result... depends on what is expected from you.

For the force problem... F1 is due east 200N... F2 is unknown... the sum is 400N... the sum could be 400N east, or 400N west... 400N east will give one answer for F2... 400N west will give another answer.

Use vector algebra.
$$\vec{F_1} + \vec{F_2} = \vec{F_{sum}}$$

solve for F2 in the above... then deal with the two cases, where Fsum is 400N east, and Fsum is 400N west.

For the banana problem, everything you did looks right.

 

[Vaalron]

^^ I still don't understand the F1 question... I understand 400N east will get one answer, But I can't figure out how 400N west will give another answer...

for 400N east, i used algebra to get F2 = 2N east...


this is so freaking confusing, I'm probably going to drop this course since I can't even freaking do vectors... >=/

 

[rocomath]

lol nice paint drawings, what book are you using? don't drop, we're here for you :D

you've got work ethic! you're even taking time out to draw them on your comp. to post them here, you'll make it.

 

[learningphysics]

^^ I still don't understand the F1 question... I understand 400N east will get one answer, But I can't figure out how 400N west will give another answer...

for 400N east, i used algebra to get F2 = 2N east...


this is so freaking confusing, I'm probably going to drop this course since I can't even freaking do vectors... >=/

Did you mean F2 = 200N east ?

For 400 west... do vector algebra again... what do you get for F2?

 

[learningphysics]

this is so freaking confusing, I'm probably going to drop this course since I can't even freaking do vectors... >=/

Don't drop... everything is hard at the beginning... even the things you find easy now were hard before... you just forgot how hard it was at the beginning.

It'll get easier as you gain experience.

 

[Vaalron]

I got that f2 = 200N east, because F1 starts out at 200N, and the resultant of the two is 400N, so it must be 200N East.

For the west, i was thinking it would be 400N west. I take it as a guess, but since it's going the opposite way, it seems like a logical answer.



I got the answers to the first problem and the banana problem already, by the way.

 

[rocomath]

it's like saying

your x is 50, and your hypotenuse is 125, what is y?

 

[Vaalron]

y would equal 13.23, but i don't know what that has to do with anything~

lol

i got classes tomarrow, I'll just ask my teacher to help me. thanks anyways guys.

 

[learningphysics]

I got that f2 = 200N east, because F1 starts out at 200N, and the resultant of the two is 400N, so it must be 200N East.

For the west, i was thinking it would be 400N west. I take it as a guess, but since it's going the opposite way, it seems like a logical answer.



I got the answers to the first problem and the banana problem already, by the way.

But if you add a 200N force east to a 400N force west... you get a 200N force west. You need a 400N force west as the resultant. You're almost there.

 

[learningphysics]

Vaalron, have you studied unit vectors yet... like $$\vec{i}$$ along the x-axis, and $$\vec{j}$$ along the y axis?

 

[Vaalron]

I got it! Or at least I think I do. One of the answers is 200N East, The other one is 200 N West. How Did i get this?

The sum equals 400, so 200+200= 400N east, since it's already pointing east in the first place.

When it goes west, it's different.

It starts pointing due east at 200N east, and the sum is 400N west. So you must have to subtract 400N, to get 200N west.


Correct?

 

[learningphysics]

I got it! Or at least I think I do. One of the answers is 200N East, The other one is 200 N West. How Did i get this?

The sum equals 400, so 200+200= 400N east, since it's already pointing east in the first place.

When it goes west, it's different.

It starts pointing due east at 200N east, and the sum is 400N west. So you must have to subtract 400N, to get 200N west.


Correct?

If F2 = 200N west, then you add F1 = 200N east to 200N west, and get a sum of 0N not 400N west. hint: you need to make F2 bigger than 400N west...

 

[Vaalron]

AH!

F2= 600N West
and F2 = 200N West
Thanks so much. :D

 

[learningphysics]

AH! F2= 600N west

Exactly. Here's a shortcut way to do these vector problems. If I take east as positive... west as negative... I can call

$$\vec{F_1} = 200\ihat{i}$$
$$\vec{F_{net}} = -400\ihat{i}$$

We need:

$$\vec{F_1} + \vec{F_2} = \vec{F_{net}}$$
$$\vec{F_2} = \vec{F_{net}} - \vec{F_1}$$
$$\vec{F_2} = -400\ihat{i} - 200\ihat{i}$$
$$\vec{F_2} = -600\ihat{i}$$

So this means F2 is 600N west. If this doesn't make sense now don't worry. You'll learn about it in your class.

 

[Vaalron]

Yep. For the first problem, a) is pointing south and has a magnitude of 5.31
and b) is pointing north with a magnitude of 5.31

Right?

 

[learningphysics]

Yep. For the first problem, a) is pointing south and has a magnitude of 5.31
and b) is pointing north with a magnitude of 5.31

Right?

Yup.