# Resultant Force

• September 30th 2008, 08:39 PM
magentarita
Resultant Force
One force of 20 pounds and one force of 15 pounds act on a body atthe same point so that the resultant force is 19 pounds. Find, to the nearest degree, the angle between the two original forces.

What exactly is the resultant force anyway?

My teacher stated that this question can be solved without the use of vectors.

Can someone explain this in detail?
• September 30th 2008, 09:07 PM
Chris L T521
Quote:

Originally Posted by magentarita
One force of 20 pounds and one force of 15 pounds act on a body atthe same point so that the resultant force is 19 pounds. Find, to the nearest degree, the angle between the two original forces. To solve this, we would need to apply the Law of Cosines. We can set up a triangle that is not a right triangle, where all three sides are given.

What exactly is the resultant force anyway? A resultant force is a single force that can be used to represent a number of different forces acting at the same point on an object. Resultant forces are used in engineering and physics [mechanics] to simplify calculations when analyzing forces using free body diagrams [force analysis diagrams].

My teacher stated that this question can be solved without the use of vectors.

Can someone explain this in detail?

If you set up the problem as such, where the forces act at a same point P:

http://img.photobucket.com/albums/v4...scan0001-1.jpg
you can use law of cosines to find $\alpha$, $\beta$, and then ultimately find $\varphi=\alpha + \beta$

Do you recall how to use the law of cosines?

--Chris
• October 1st 2008, 04:02 PM
magentarita
Quote:

Originally Posted by Chris L T521
If you set up the problem as such, where the forces act at a same point P:

http://img.photobucket.com/albums/v4...scan0001-1.jpg
you can use law of cosines to find $\alpha$, $\beta$, and then ultimately find $\varphi=\alpha + \beta$

Do you recall how to use the law of cosines?

--Chris

I have two questions:

How does one use the Law of Cosines when no angle is given?

What do math textbooks and math test prep books mean by "Not Drawn to Scale."

Thanks
• October 1st 2008, 06:55 PM
Chris L T521
Quote:

Originally Posted by magentarita
I have two questions:

How does one use the Law of Cosines when no angle is given? The Law of Cosines is used when we have 3 given sides, and no given angles. In this case, we know the sides.

Note that there are 3 different variations of the law of cosines for sides A, B, C, and the respective opposite angles $\alpha$ $\beta$, and $\gamma$ :

$A^2=B^2+C^2-2BC\cos\alpha$
$B^2=A^2+C^2-2AC\cos\beta$
$C^2=A^2+B^2-2AB\cos\gamma$

What do math textbooks and math test prep books mean by "Not Drawn to Scale." They mean that the measurements in the diagram they gave you aren't portrayed properly [most likely because they need to fit this into a tiny section of the page allotted for the question]. For example, in the diagram I drew, the 19 lb resultant force was a bit larger than the 20 lb force. It would look better if the resultant force was a tad smaller than the 20 lb force. In other diagrams, you may see lengths like 100 ft and 20 ft appearing to be the same size.

Thanks

--Chris
• November 5th 2008, 01:01 AM
ryan88
resultant force
How does one figure out the resultant force if only the 2 forces are given? eg 20lbs and 15lbs, how does one figure out the resultant of 19lbs?