help with newton's and or resultant force?

[garygnu]

Could someone please help me with a question that goes something like this: given two forces and their directions, be able to tell where the resultant force direction will be and how much that force will be? I searched all over the web looking for formulas but the closest I came to was a formula for newton's first law, however I can't see how it applies to the aforementioned equation. Could someone tell me the correct formula or perhaps set up a sample equation? Thanks

 

[chelu55]

Okay,
I hope that I dont confuse you. The resultant force is the result of the two forces on an object. For example, say you through a baseball in one direction (force 1) but there is a gust of wind blowing(force2)from east to west. Because of the wind blowing perpendicular, the ball is not going in a straight line. The resultant force is the net direction of of the ball. The ball will go in a straight line to the left of where you threw it.
As far as a formula, all I know is the stuff in physic books.(sin and cos).
Hope it helps.

 

[jaerose]

Take a look at this link...it should help. If it doesn't, then PM, or email me and I'll try to help...maybe some online chat. I've got a Physics degree.

http://oldsci.eiu.edu/physics/DDavis/3050/Ch05Nwtn3rdLaw/ForceVectors.html

JR

 

[Daedalus]

Although Jaerose is definitely the person to ask, I thought i'd give it a try, let me know if i get it right.
Newtons are the standard SI units that goes with force.
Force = Mass * Acceleration
Units:
Force (Newtons) = Mass (grams) * Acceleration (Meters/Seconds^2) [that is meters per second squared)]

So if you have something with a mass of say 10 grams with an acceleration of 9.8 ms^2 than the force is 10* 9.8 = 98 newtons

If the forces are in the same line it is very easy if you have a force of 98 newtons going to the right and 10 newtons going left than the resultant force is just 98-10= 78

It is different if the forces are in two or three dimensions.

One way to do it is through trig. If you are adding forces one going up (90 degrees) of 10 Newtons and one going right 20 newtons (0 degrees) the resultant force would be the hypotenuse sp?, so you can find out by (10 ^2 + 20 ^2)^-1 sorry if the symbols are odd. It’s the square root (^-1) of the sum of the squares. Which is (500)^-1 = 22.36 newtons (force)
The direction can be found by arctan of y/x or tan^-1 of 10/20 or 26.56 degrees

Summary: the resultant force of 10 newtons up and 20 newtons right is 22.36 newtons in the direction of 22.66 degrees.

Subtraction and multiplication to follow

 

[Daedalus]

Subtraction:
For subtraction (can also be done with addition) I will explain with components (if I can)

It is the easiest way. Each vector has a x and y component. In the case of the 10 newtons at 90 degrees, it’s components are: Y: (10sin 90) = 10 and X: (10 cos 90) = 0 (since it is going straight up it’s force is all in the Y direction. For the 20 Newtons to the right Y: (20sin 0) = 0 and X: (20cos 0) = 20 (because the force is going right the Y value is 0)

To subtract:

Force Y X
10 N 10 0
20N - 0 20
10 20

= Same as addition ?


To show when the vectors have both x and Y components:

Take a 10 N force going at 80 degrees and a 20 N force at 30 degrees

Force Y component X component
10N80deg 10 sin 80 10cos80
=9.84 =1.73

20N30deg 20sin30 20cos30
=10 17.32

Resultant 9.84 1.73
-10 -17.32
-.16 -15.59

Square root of( .16^2 + 15.59^2) = 15.5908
Arctan .16/15.59 = .58

Cross product multiplication = AB Sin angle

Dot product multiplication = AB Cos Angle

 

[vegita1220]

Jaerose's link is perfect. Pretty much a physics textbook w/out the clutter.

 

[jaerose]

Daedalus, don't forget your mass has to be in KILOGRAMS, not grams...so your first example is off by a factor of 10. Also, I think trying to explain it in typeset without diagrams will just be more confusing, which is why I posted the link. It's much, much easier if you can see what you're talking about and triangles/right angles will be your best friends in Physics.

JR

 

[shipwreck]

Gary
Don't get bogged down with Newton's Laws. From your discription, this sound more like a trigonometry problem. The Arco Study guide should help you with the equations you need.

 

[jaerose]

Yes, it's trig...hence the triangles, but if you understand the laws, which are easy and straight forward, then the problem is that much easier...IMHO.

JR