Laws of Motion -05- An Object In Equilibrium

An object is in equilibrium under four concurrent forces in the directions shown in figure. Find the magnitudes of F1 and F2.

Transcript

00:00Hey guys, always try to make your Tuesday better.

00:05Trust me, the rest of your workday will automatically become interesting.

00:11Is this question interesting enough for our minds?

00:15A particle is subjected to some forces.

00:19This particle is not moving at all.

00:23Well, we are asked to get the magnitude of two unknown forces.

00:30Let's discuss this in more detail.

00:34Based on the concept of force equilibrium,

00:37an object will not move anywhere when the resultant force acting on it is zero.

00:43How about we put this system into two-dimensional Cartesian coordinates?

00:48Where the particle is right at the center of coordinates.

00:54Next, resolve all the forces to be parallel to the x-axis or parallel to the y-axis.

01:03The resultant force acting on the particle is zero.

01:07That means sigma fx is equal to zero.

01:13There are three force components there.

01:16Plus 6 root 3, plus 8 cosine 30, and minus f2 cosine 60.

01:22The positive sign means the force is going to the right or east.

01:29The cosine of 30 is half the root of 3 and the cosine of 60 degrees is half.

01:37This is an easy calculation.

01:40F2 is equal to 20 root 3 Newtons.

01:46For the resultant in the vertical direction, sigma fy is equal to zero.

01:52In this direction, there are also three components of force.

01:57Plus f1, plus 8 sine of 30 degrees, minus f2 sine of 60 degrees.

02:06We already know the value of sine of 30 degrees and sine of 60 degrees.

02:12From here, f1 is equal to 26 Newtons.

02:18This is the answer to this question.

02:22Happy learning everyone!