Magnitude and Direction

• Apr 6th 2011, 01:58 PM
masters
Magnitude and Direction
Hey guys,

This is more for the Physics forum, but there's noone over there.

Three workers are pulling on ropes attached to a tree stump (S) as shown in the diagram.
Find the magnitude and direction of the resultant force on the stump.

Diagram is attached at the bottom.

A force of 60 Newtons North, a force of 35 Newtons East and a force of 40 Newtons 60 degrees South of East is applied.

I know the answer is 61 Newtons at a direction of 23 degrees North of East, but I'll be danged if I can get there.

A little nudge in the right direction would be helpful.

Attachment 21385
• Apr 6th 2011, 02:08 PM
derdack
Make a polygon of the forces and then use the trigonometric functions to solve the distance.
• Apr 6th 2011, 02:51 PM
masters
Revised drawing:

Attachment 21387

I have two resultant vectors with two different magnitudes with 2 different directions.

I need these two forces to combine to 61 Newtons somehow. Do I combine those two vectors and find the resultant of these two forces?

"My mind's going, Dave. I can feel it."
• Apr 6th 2011, 04:02 PM
NOX Andrew
Decompose the force vectors into each of their x- and y-components, then sum the x-components and sum the y-components. The resulting x- and y-components are the components of the resultant force.

Note the x- and y-components of a force vector $\displaystyle \vec A$ is given by

$\displaystyle x = |\vec A|\cos \theta$
$\displaystyle y = |\vec A|\sin \theta$

where $\displaystyle |\vec A|$ is the magnitude of the force vector and $\displaystyle \theta$ is the angle between the force vector and the x-axis.
• Apr 6th 2011, 10:23 PM
derdack
It is not need to make two result vectors and then find final resultant. Just make a polygon of vectors and use trigonometric. Find what is a polygon of the vectors. This way is better because when you will get 10, 15 vectors, It is not need two make resultant for each two vectors.

Kind regards
• Apr 7th 2011, 12:31 AM
earboth
Quote:

Originally Posted by masters
Revised drawing:

Attachment 21387

I have two resultant vectors with two different magnitudes with 2 different directions.

...

If you want to use both resultant forces you would have used the force of 35 N twice!

Quote:

Originally Posted by masters
Hey guys,

Three workers are pulling on ropes attached to a tree stump (S) as shown in the diagram.
Find the magnitude and direction of the resultant force on the stump.

Diagram is attached at the bottom.

...

I assume that you are looking for a more geometric way to solve this question:

1. I've attached a (nearly exact) drawing. Scale is 1 cm correspond to 10 N.

2. Calculate the green resultant first using Pythagorean theorem ($\displaystyle \sqrt{4825}$)

2. Calculate the green angle: $\displaystyle \tan^{-1}\left(\frac{60}{35}\right)\approx 59.744^\circ$

3. Use the greyed triangle and the Cosine rule to calculate the final (red) resultant:

$\displaystyle R = \sqrt{4825 + 1600 - 2 \cdot \sqrt{4825} \cdot 40 \cdot \cos(60.256^\circ)}$

I've got $\displaystyle R \approx 60.565\ N$

4. Use Sine rule or Cosine rule to calculate the missing angle.