Solving Force Combinations: 6N + 8N = 14N, 2N, 10N

[Crusaderking1]

Homework Statement

3. Draw figures showing how you would combine a 6 N force and an 8 N force to obtain a resultant force with magnitude (a) 14 N; (b) 2 N; (c) 10 N.

Homework Equations

The Attempt at a Solution

I just don't know where to start or what equation to use.

 

[cepheid]

Do you understand how to calculate a vector sum graphically? That's all this question is really about...

 

[Crusaderking1]

Do you understand how to calculate a vector sum graphically? That's all this question is really about...

In our lab we graphed forces, but they had an angle as well.

 

[Crusaderking1]

Oh wait, like draw a straight line with 8 and 6 for 14, while drawing lines with arrows towards each other for 2?

14
-------------->------------------------->2
--------------><-------------------------

 

[cepheid]

Oh wait, like draw a straight line with 8 and 6 for 14, while drawing lines with arrows towards each other for 2?

Well, you've found two combinations that work. If the forces are in the same direction, the magnitude of the resultant is just the sum of the magnitudes of the two vectors. Likewise if they're in the exact opposite direction, the magnitude of the resultant is just the difference of their magnitudes. But the more general case is when they are not co-linear, meaning along the same line. I.e. the angle between them is something other than 0 or 180 degrees. How do you find the resultant in this case? In other words, how do vectors sum together? You should know this.

 

[Crusaderking1]

Well, you've found two combinations that work. If the forces are in the same direction, the magnitude of the resultant is just the sum of the magnitudes of the two vectors. Likewise if they're in the exact opposite direction, the magnitude of the resultant is just the difference of their magnitudes. But the more general case is when they are not co-linear, meaning along the same line. I.e. the angle between them is something other than 0 or 180 degrees. How do you find the resultant in this case? In other words, how do vectors sum together? You should know this.

Well, I can add vectors(of force) by finding components, graphing them, or using a force table.

I don't really know how to add vectors that well, but wouldn't there be a 90 degree angle between 6 and 8 to give me 10, since 8^2+6^2 square root= 10.

Thanks.

 

[cepheid]

Well, I can add vectors(of force) by finding components, graphing them, or using a force table.

I don't really know how to add vectors that well, but wouldn't there be a 90 degree angle between 6 and 8 to give me 10, since 8^2+6^2 square root= 10.

Yeah. So you figured out the answer to all three cases by trial and error or "guess and check." But the general method for finding the resultant is either to resolve each vector into components and add them component-wise, or to do it graphically by using the "parallelogram rule" for vector sums (which I can only assume you must have learned):

http://en.wikipedia.org/wiki/Euclidean_vector#Addition_and_subtraction

 

[Crusaderking1]

Yeah. So you figured out the answer to all three cases by trial and error or "guess and check." But the general method for finding the resultant is either to resolve each vector into components and add them component-wise, or to do it graphically by using the "parallelogram rule" for vector sums (which I can only assume you must have learned):

http://en.wikipedia.org/wiki/Euclidean_vector#Addition_and_subtraction

Thanks a lot.

I definitely understand what I'm suppose to do much better.