The lever to which the force is applied is 10 feet long - from the pivot point of the boom at the top link connection on the tractor. The distance from the top link connection to the pivot point on the PHD gear box is 5 feet and even though the boom is longer and curved this straight line distance is the lever. Since the whole assembly is rigidly connected together it acts as though the PHD gear box is attached in the middle of the 10 foot lever to which the force is applied. Thus the lever is a simple second class lever as you indicated with the load in the middle and the force applied to the load is 2x the force applied to the lever. The assumption is made that the tractor is a fixed object in this problem. This is a good assumption in this case since the tractor is much heavier (5X) than the other forces being considered in the problem. You could look at the problem as a class 1 lever with the pivot point of the PHD being the fulcrum and the force being applied to the end of the lever to lift the tractor; however, it would not be an interesting problem since something would break before enough force could be applied to lift this tractor. If the tractor were smaller then it would be something to look at to determine the limit of the force that could be applied and/or how long the lever could be made before the tractor lifted. I am or rather was an engineer and although I was an electrical engineer they made us study engineering mechanics as part of the EE program at UT. This is a simple mechanics problem once you simplify the force diagram.
Digging post holes
- Thread starter centex
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wroughtn_harv
Super Member
<font color=blue>1) First Class Lever -- the effort and the load on either side of the fulcrum. Some examples would be a crowbar or a seesaw. The effort is only less than the load if the load is closer to the fulcrum. The lever then acts as a force magnifier and the mechanical advantage is greater than one. If the effort is closer to the fulcrum, then the effort is larger than the load and the mechanical advantage is less than one. In this case the lever acts as a movement magnifier.</font color=blue>
Thanks bgott.
I see it as a first class lever. We're wanting to pressure on the fulcrum, point of the auger. So the load is the back of the tractor where the weight of the tractor is picked up by the mechanism attached to the PHD. The effort would be where the suitcase weights are hanging.
So if the load is four feet from the fulcrum then to double the weight on the fulcrum we would need the weights to be four feet from the point of the auger.
There are two ways to add the multipying effect. One would be to extend the weights beyond four feet. Or two, would be to shorten the space between the load and the fulcrum.
I'm gonna have to think a bit to figure out how to do that.
Thanks bgott.
I see it as a first class lever. We're wanting to pressure on the fulcrum, point of the auger. So the load is the back of the tractor where the weight of the tractor is picked up by the mechanism attached to the PHD. The effort would be where the suitcase weights are hanging.
So if the load is four feet from the fulcrum then to double the weight on the fulcrum we would need the weights to be four feet from the point of the auger.
There are two ways to add the multipying effect. One would be to extend the weights beyond four feet. Or two, would be to shorten the space between the load and the fulcrum.
I'm gonna have to think a bit to figure out how to do that.
knucklehead
Platinum Member
bgott, you're right on, except the work thing refers to something else, like you defined it: force x distance. By the way, horsepower is force times distance divided by time (One HP = 550 ft-lb/Sec). But never mind that, because you're right about leverage.
Your explanation of types of levers is right in the bullseye, too. The post hole digger/counterweight is a "second class" lever (but we won't hold that against it). The two distances are measured from the rear axle (tire contact point with the ground), which is the fulcrum.
You usually choose the "immovable object" as the fulcrum, plus you want to know the force, or at least the amount of multiplication of force, on the bit. Centex (isn't that like C4?) is right about measuring from the top link pin bracket - similar to the axle centerline. I simplified the idea by looking at everything from the ground, where the two contact points (tires & auger bit) are located.
Measured along the ground (horizontal plane),
Axle to Weight (the center of them) = L1
Axle to bit = L2
Weight = W1
Bit force = W2
Then, relative to the fulcrum (axle)
W1 x L1 = W2 x L2, which can be simplified to
W1 x L1/L2 = W2
......O.K., so it doesn't look simplified, but the point is that the force on the bit is the weight itself multiplied by the ratio of overhang. If L1 is 12' and L2 is 8', then the ratio is 1.5, which means you are adding 150lb of bit force for every 100lb you hang on the bracket.
So after all the dubbing around, if you keep everything the same, you'll always know you're increasing the force by the ratio of the distances. If you forget which one to divide the other by, just remember that you intuitively know that it's gonna be heavier, so your ratio will be greater than 1.
Your explanation of types of levers is right in the bullseye, too. The post hole digger/counterweight is a "second class" lever (but we won't hold that against it). The two distances are measured from the rear axle (tire contact point with the ground), which is the fulcrum.
You usually choose the "immovable object" as the fulcrum, plus you want to know the force, or at least the amount of multiplication of force, on the bit. Centex (isn't that like C4?) is right about measuring from the top link pin bracket - similar to the axle centerline. I simplified the idea by looking at everything from the ground, where the two contact points (tires & auger bit) are located.
Measured along the ground (horizontal plane),
Axle to Weight (the center of them) = L1
Axle to bit = L2
Weight = W1
Bit force = W2
Then, relative to the fulcrum (axle)
W1 x L1 = W2 x L2, which can be simplified to
W1 x L1/L2 = W2
......O.K., so it doesn't look simplified, but the point is that the force on the bit is the weight itself multiplied by the ratio of overhang. If L1 is 12' and L2 is 8', then the ratio is 1.5, which means you are adding 150lb of bit force for every 100lb you hang on the bracket.
So after all the dubbing around, if you keep everything the same, you'll always know you're increasing the force by the ratio of the distances. If you forget which one to divide the other by, just remember that you intuitively know that it's gonna be heavier, so your ratio will be greater than 1.
bgott
Veteran Member
I need to go back through those websites I hit. There was one or two that had pictures of some kind of pulley arraingment on the end of the lever to multiply force. I didn't spend much time on them because it wasn't what I was looking for. Oh well, as long as I know it's somewhere I'll find it! 
wroughtn_harv
Super Member
You know I thought I had this all figured out last night in the shower. Now we have three saying it's obviously a two when in my mind I can't get over it being a one.
I can understand where ya'll are coming from. I just don't thing you're correct, completely correct, ya'll are just partly wrong.
The reason is ya'll are looking at the fulcrum, auger point, from a lifting or leverage up perspective. But it isn't about the lifting up but the pushing down.
Well on second thought. If I stood on my head and I saw the weights as handles on a wheelbarrow then I could see where one could see it as a two.
But I'm not standing on my head.
It goes back to the weights attempting to lift the back of the tractor off the ground. It just happens to be incidental that in the act of attempting to life the back of the tractor with the auger point being the fulcrum there is more weight exerted upon the fulcrum.
So it's a number one plain and simple. I'm also having a bit of trouble seeing where the point to measure the tractor being the center of it's rear axle.
As I see it the point we need to see as the L1 would be where the three point attaches to the TPD assembly.
If don wasn't so darn far away and I didn't have so much to do.....maybe I can duplicate this at the shop on a smaller scale............
I know I'm rowing against the flow but then you gotta figure the good Lord didn't give me that extra oar and not expect me to use it.
I can understand where ya'll are coming from. I just don't thing you're correct, completely correct, ya'll are just partly wrong.
The reason is ya'll are looking at the fulcrum, auger point, from a lifting or leverage up perspective. But it isn't about the lifting up but the pushing down.
Well on second thought. If I stood on my head and I saw the weights as handles on a wheelbarrow then I could see where one could see it as a two.
But I'm not standing on my head.
It goes back to the weights attempting to lift the back of the tractor off the ground. It just happens to be incidental that in the act of attempting to life the back of the tractor with the auger point being the fulcrum there is more weight exerted upon the fulcrum.
So it's a number one plain and simple. I'm also having a bit of trouble seeing where the point to measure the tractor being the center of it's rear axle.
As I see it the point we need to see as the L1 would be where the three point attaches to the TPD assembly.
If don wasn't so darn far away and I didn't have so much to do.....maybe I can duplicate this at the shop on a smaller scale............
I know I'm rowing against the flow but then you gotta figure the good Lord didn't give me that extra oar and not expect me to use it.
bgott
Veteran Member
I'm finding all sorts of neat stuff I didn't know, or never thought about. I figured a screwdriver worked just because the fat handle let you get a grip on it.
Continuous Levers: Screwdrivers
A screwdriver is actually a form of lever where a handle with a large radius provides a mechanical advantage in turning a blade with a smaller radius. All sorts of circular devices make use of this form of mechanical advantage. Circular water valve handles, tire irons, socket wrenches, monkey wrenches, and many other items utilize this time of circular lever.
Measure the radius of the handle on a screwdriver and then measure the radius of the blade. Calculate the mechanical advantage from de/dr.
Note that the mechanical advantage to a circular device is de/dr while the mech. adv. for a lever was Fr/Fe. Note that the seeming "flip-flop" of the fraction is not a mistake.
Consider that Fe × de = Fr × dr. Cross dividing by Fe and dr yields:
de = Fr
-- -- = mechanical advantage
dr Fe
Continuous Levers: Screwdrivers
A screwdriver is actually a form of lever where a handle with a large radius provides a mechanical advantage in turning a blade with a smaller radius. All sorts of circular devices make use of this form of mechanical advantage. Circular water valve handles, tire irons, socket wrenches, monkey wrenches, and many other items utilize this time of circular lever.
Measure the radius of the handle on a screwdriver and then measure the radius of the blade. Calculate the mechanical advantage from de/dr.
Note that the mechanical advantage to a circular device is de/dr while the mech. adv. for a lever was Fr/Fe. Note that the seeming "flip-flop" of the fraction is not a mistake.
Consider that Fe × de = Fr × dr. Cross dividing by Fe and dr yields:
de = Fr
-- -- = mechanical advantage
dr Fe
knucklehead
Platinum Member
The good Lord gave you a lot more than an extra oar, Harv! Does that mean you have three arms? No wonder you're so good at bending stuff! /w3tcompact/icons/grin.gif I always have to draw a picture, myself, but the paper gets wet in the shower. What is it about the shower, anyway....relaxing?
We're all heading in the same direction, so this is only for fun, from my perspective /w3tcompact/icons/smile.gif. The easiest way to get this all settled is to get the auger on a scale while attached to the tractor, and see what a known weight on the bracket is multipied into at the auger bit. But I'll try to explain where I'm coming from.
<font color=orange>2) Second Class Lever -- the load is between the fulcrum and the effort. An example is a nutcracker or a wheelbarrow. This type of lever always acts as a force magnifier and its mechanical advantage is greater than one.</font color=orange>
The lever is a second class, from bgott's good definition above. The key is to identify the three things we are talking about: fulcrum, load, & effort. Jam that wheelbarrow tire under the bumper of a car, Harv, push down on the handles, and pretend the legs are the auger. That's what we are talking about. The load (legs) is between the fulcrum (tire pushing up against the bumper) and the effort (you pushing down). The PHD auger down-pressure is the load, the tractor is the fulcrum, and the weights are the effort. I should stop right here, but this is fun, so let's make it worse.
Centex mentioned simplifying the force diagram, and that's the key - what's all this stuff pushing/pulling on?. The ground and the tractor weight. If you wanted to get really technical, we should use the center of mass of the tractor, probably somewhere ahead of the rear axle /w3tcompact/icons/eyes.gif.
The auger frame movement at the ends of the lift arms is limited by the top link, and doesn't hinge there when you load the tool (only hinges when you lift/lower the tool, and only in a very constrained motion). Take off the top link and you can use that point as your fulcrum, because now the arms are just like the car bumper, a hunk of iron holding something down (picture them raised when you do this). That top link changes things.
Again, Centex's reminder to simplifiy is key. Sometimes the exact, measured location of the fulcrum is hard to find, but the load and effort are pretty much obvious, as in this case. If you are still getting heart burn about the axle being the fulcrum, remember the top link locks things up and makes the PHD and 3-pt one solid part of the lever.
By the way, Harv, I really liked the post you made about breaking rock, and cleaning the concrete off the fence posts. I could feel it myself when you described it. It's amazing how that little bit of give that something has when it's cracked can be felt all the way up though the hammer head and handle in the split second it hits. Ain't we designed well!
We're all heading in the same direction, so this is only for fun, from my perspective /w3tcompact/icons/smile.gif. The easiest way to get this all settled is to get the auger on a scale while attached to the tractor, and see what a known weight on the bracket is multipied into at the auger bit. But I'll try to explain where I'm coming from.
<font color=orange>2) Second Class Lever -- the load is between the fulcrum and the effort. An example is a nutcracker or a wheelbarrow. This type of lever always acts as a force magnifier and its mechanical advantage is greater than one.</font color=orange>
The lever is a second class, from bgott's good definition above. The key is to identify the three things we are talking about: fulcrum, load, & effort. Jam that wheelbarrow tire under the bumper of a car, Harv, push down on the handles, and pretend the legs are the auger. That's what we are talking about. The load (legs) is between the fulcrum (tire pushing up against the bumper) and the effort (you pushing down). The PHD auger down-pressure is the load, the tractor is the fulcrum, and the weights are the effort. I should stop right here, but this is fun, so let's make it worse.
Centex mentioned simplifying the force diagram, and that's the key - what's all this stuff pushing/pulling on?. The ground and the tractor weight. If you wanted to get really technical, we should use the center of mass of the tractor, probably somewhere ahead of the rear axle /w3tcompact/icons/eyes.gif.
The auger frame movement at the ends of the lift arms is limited by the top link, and doesn't hinge there when you load the tool (only hinges when you lift/lower the tool, and only in a very constrained motion). Take off the top link and you can use that point as your fulcrum, because now the arms are just like the car bumper, a hunk of iron holding something down (picture them raised when you do this). That top link changes things.
Again, Centex's reminder to simplifiy is key. Sometimes the exact, measured location of the fulcrum is hard to find, but the load and effort are pretty much obvious, as in this case. If you are still getting heart burn about the axle being the fulcrum, remember the top link locks things up and makes the PHD and 3-pt one solid part of the lever.
By the way, Harv, I really liked the post you made about breaking rock, and cleaning the concrete off the fence posts. I could feel it myself when you described it. It's amazing how that little bit of give that something has when it's cracked can be felt all the way up though the hammer head and handle in the split second it hits. Ain't we designed well!
I just happen to have a handy dandy little trailer tongue weight scale in my truck and if I can remember to do it I will put it under an auger and then put 8 42# weights (336# total) on the contraption and see how much the scale reading changes. It should be somewhere in the neighborhood of 650# but we'll see. That little scale sure came in handy when I had to trailer my tractor to keep me from severely overloading my hitch.
knucklehead
Platinum Member
That'll do it, and then if you divide the scale weight by the weights you hung, you'll know the force multiplier. Getting the length of the lever, which you now don't care about, would be easy from there.
wroughtn_harv
Super Member
Morning don,
I've running late. I'm doing a couple of aluminum projects this morning plus Ron is coming by today hopefully to try out the arc fit notcher. We'll take photos.
I'll bite the bullet and admit that from some perspectives it's obvious that we're talking about a class two lever. Folks that don't say I'll admit I'm wrong if I'm wrong are wrong. Almost.
One of the things about me being me is I accepted a long time ago that it's like I'm sitting on a different hill looking down life's path than everyone else. So I do have a different perspective on things.
I am very very interested about the ratio of weight to leverage on your set up.
The one thing I'm having a hard time with is the point referred to as L1. I'll get it straight in my mind but your input will help. I just don't see the rear wheels being it but yet I can see where that is possible.
I guess I have too much clutter in the attic to see the obvious.
I've running late. I'm doing a couple of aluminum projects this morning plus Ron is coming by today hopefully to try out the arc fit notcher. We'll take photos.
I'll bite the bullet and admit that from some perspectives it's obvious that we're talking about a class two lever. Folks that don't say I'll admit I'm wrong if I'm wrong are wrong. Almost.
One of the things about me being me is I accepted a long time ago that it's like I'm sitting on a different hill looking down life's path than everyone else. So I do have a different perspective on things.
I am very very interested about the ratio of weight to leverage on your set up.
The one thing I'm having a hard time with is the point referred to as L1. I'll get it straight in my mind but your input will help. I just don't see the rear wheels being it but yet I can see where that is possible.
I guess I have too much clutter in the attic to see the obvious.