Three men are pulling on ropes attached to a tree the ﬁrst man exerts a force of 6.0 N north, the second a force of 35 N east, and the third 40 N to south. What is the magnitude of the resultant force on the tree?

Question

7500 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-12-01T23:44:02

$48.8 N$ $48.8"N"$ on a bearing of ${134.2}^{\circ}$ $134.2^@$

First we can find the resultant force of the men pulling in the north and south directions:

$F = 40 - 6 = 34 N$ $F=40-6=34"N"$ due south (180)

Now we can find the resultant of this force and the man pulling east.

Using Pythagoras:

$R^{2} = 34^{2} + 35^{2} = 2381$ $R^2=34^2+35^2=2381$

$:.R=sqrt(2381)=44.8"N"$

The angle $theta$ from the vertical is given by:

$tantheta=35/34=1.0294$

$:.theta=45.8^@$

Taking N as zero degrees this is on a bearing of $134.2^@$