- #1
fawk3s
- 342
- 1
I think I am misunderstanding something. Because I had this strain of thought and it doesn't really want to logically up. By my logic anyways.
Ok, here it is:
Let us have a standard lever/seesaw and a fulcrum at a point. Let us apply a force to the very end of the lever (which is the farthest away from the fulcrum).
Now let's look at the other half of the lever. Let's observe a point on it closer to the fulcrum than the force we applied. Since torque
M = F*l
we see that the point closer to the fulcrum has to have a higher force applied to it (since its closer to the fulcrum) in order to have the same moment, the moment the whole lever has.
So we got that a point closer to the fulcrum has a higher force applied to it.
Now let's look at the movement of the lever, we can tell its circular motion, where fulcrum is the centerpoint. Say the force we applied was perpendicular to the lever at that moment. As force results in an acceleration by Newton's second law, we get that an acceleration perpendicular to the lever, aka tangential acceleration, is higher closer to the fulcrum than away from it.
And this is the part that I don't understand... As the lever has an angular acceleration, we can tell that the tangential acceleration of a point would get higher as we move farther away from the fulcrum. So why do we get a higher force closer to the fulcrum?
P.S. At this point, I am only interested in the forces. Please do NOT bring in the conservation of mechanical energy/work, saying something like "the farther you are from the fulcrum the longer distance you have to travel, ergo closer to the fulcrum point there has to be higher force" or likewise. I do not care about that at this moment. I am only interested in how these forces are created and how they balance each other out.
Thanks in advance
Ok, here it is:
Let us have a standard lever/seesaw and a fulcrum at a point. Let us apply a force to the very end of the lever (which is the farthest away from the fulcrum).
Now let's look at the other half of the lever. Let's observe a point on it closer to the fulcrum than the force we applied. Since torque
M = F*l
we see that the point closer to the fulcrum has to have a higher force applied to it (since its closer to the fulcrum) in order to have the same moment, the moment the whole lever has.
So we got that a point closer to the fulcrum has a higher force applied to it.
Now let's look at the movement of the lever, we can tell its circular motion, where fulcrum is the centerpoint. Say the force we applied was perpendicular to the lever at that moment. As force results in an acceleration by Newton's second law, we get that an acceleration perpendicular to the lever, aka tangential acceleration, is higher closer to the fulcrum than away from it.
And this is the part that I don't understand... As the lever has an angular acceleration, we can tell that the tangential acceleration of a point would get higher as we move farther away from the fulcrum. So why do we get a higher force closer to the fulcrum?
P.S. At this point, I am only interested in the forces. Please do NOT bring in the conservation of mechanical energy/work, saying something like "the farther you are from the fulcrum the longer distance you have to travel, ergo closer to the fulcrum point there has to be higher force" or likewise. I do not care about that at this moment. I am only interested in how these forces are created and how they balance each other out.
Thanks in advance