What is the resultant force acting on a body if two forces F1 and F2 of magnitude 5N each, inclined to each other at an angle of 60°, act on the same body?

 What is the resultant force acting on a body if two forces F1 and F2 of magnitude 5N each, inclined to each other at an angle of 60°, act on the same body?

Solution

Let's make one force 0 degrees so its traveling along the x-axis and we'll make the other 60 degrees.

We have to do some vector addition which means we need to determine the x and y coordinates for both forces.

To determine the x coordinate you find find the product of the force and the cosine of its angle. For the y coordinate you do the same thing except using sine.

X=5×Cos(0)=5

Y=5×Sin(0)=0

F1−(5,0)$F1-(5,0)$

X=5×cos(60)=2.5

Y=5×cos(60)=4.33

F2−(2.5,4.33)$F2-(2.5,4.33)$

Now you add the coordinates.

5+2.5=7.5

0+4.33=4.33

ResultantForce−(7.5,4.33)$ResultantForce-(7.5,4.33)$

To find the angle, you have to find the inverse tangent of y divided by x.

Tan−1$-1$(4.33/7.5)=29.99 degrees.

Now to find the resultant forces magnitude, you need to find the square root of x squared plus y squared.

F=4.332+7.52−−−−−−−−−−√=8.66N$F=\sqrt{{4.33}^2+{7.5}^2}=8.66N$

So, the resultant force has a magnitude of 8.66N at a 29.99 degree angle.