Mechanical Engineering: Particle Equilibrium (1 of
19) Addition of Forces - Graphically
Mechanical Engineering
Welcome to electron line and here we're beginning a new series on mechanical engineering. and first of all we're going to start off with some basics. I'm going to learn how to add some forces we're going to work on some static situations. where forces act on a single point and we're going to calculate the net force and the force on the members involved so here's turning out a simple example,
we have a hook attached to a wall we have two forces one pulling upward at an angle of 30 degrees above the horizontal another force pulling downward with an angle of 45 degrees below the horizontal notice we have a hundred-pound force and 150-pound force what will be the net force of those two acting on the hook well we can add those up in various ways one of them is graphical the other one is using components and so we're going to start out with a simple example showing how to add up forces graphically so starting at a single point we have our first force pulling upward an angle of 30 degrees above the horizontal draw a dashed line along the horizontal line and then the direction of the first force the length of the arrow represents the force or the magnitude of the force so since this force is 150 pounds and this is 100 pounds and this this line here
This arrow should be about one and a half times the length of the 100-pound force so at the tip of the first vector representing by represented by the 100-pound force we have a second vector notice again we draw a horizontal line that's our reference line and the second force is pulling an angle of 45 degrees below the horizontal so you attach the tail of the second vector the tip of the first vector in that arrangement and then you can see that the resultant vector starts at the tail of the first vector and ends at the tip of the last vector if you have more than two vectors you just keep that process going and any time at all times the resultant force will be the arrow from the tail of the first vector to the tip of the last vector and of course if you take a ruler and you measure the length of this vector they'll give you the approximate magnitude of the resultant or total force what you could also do is have both vectors drawn like this just like Avot there where both tails start at the same point and then you draw a line from the tip of the first vector which is parallel to
The second vector and you're all line from the tip of the second vector which is parallel to the first vector and where those two lines come together that's going to be the tip of the resultant vector so the resultant vector simply the vector sum of these two and that is how you do that notice again that the length of each vector represents the magnitude of each of the forces and that
The length of this force represents the magnitude of the sum of the two forces this vector and of course this vector should be equal because I drew it freehand redundant rulers and any protractors I got reasonably close but that is how we graph vectors and that is how we add vectors graphically on the next video we'll do a similar kind of problem but then we'll add the vectors by component what we will do then is we'll find the XL y component of each of the vectors add all the X components together add all the Y components together and that will give us the exact value for the resultant vector so stay tuned and I'll show you
how to do that using components of
vectors.