Assuming gravitational field force is 9. You consider the weight of the aluminium beam to act through its centre of mass 2. Its actually the same situation as a wheelbarrow described further down the page! Q5 The diagram on the right shows downward forces N and N acting on a concrete beam that is held in position by a wall at P - effectively acting as a pivot point. Calculate the force F that this 2nd wall needs to be able to withstand to produce a structurally stable balanced equilibrium situation.
Many of the examples described below involve a lever , which is a means of increasing the rotational effect of a force. You push down on one end of a lever, and the rotation about the pivot point can cause the other end to rise with a greater force. F is the force involved N and d m is the shortest perpendicular distance from the pivot point to the point where the force is applied OR generated.
When balanced, i. Therefore by making d1 much bigger than d2 you can produce a much bigger output force compared to the original input force. Generally speaking you make the distance d1 much bigger than distance d2 - you can see this using scissors, levering a lid off a can and its a very similar situation when using a fork to lift deep tough roots out of the soil or moving a heavy stone with a pole.
So, levers are very useful because they make lifting and moving things much easier by reducing the input force necessary to perform the task. Example of a lever question. Suppose a heavy manhole cover requires a force of N to open it. Imagine you have a steel bar 1 metre long pivoted at a point 0. If you press down with a force of 20 N, will the upward force you generate be enough to lift the manhole cover?
The output force N exceeds the N force required, so the manhole cover can be lifted. A hole punch of some description. This machine can punch holes in a material. The pivot point turning point is on the left. We can analyse this situation in terms of turning forces. Therefore by making d2 'long' and d1 'short' you considerably multiply the force F1 compared to F2.
So you are able to easily punch holes in a strong material e. For example, suppose d2 is 0. So the force you manually apply is multiplied 10 ten times, not bad for a little effort! In other words you need less force to get the same moment.
When you press the scissor hands together you create a powerful turning force effect close to the pivot point. That's why you apply the blades to whatever you are cutting as near as possible to the pivot point. You don't cut using the ends of the scissor blades where you gain little mechanical advantage i. Its the same principle as described in the whole punch machine described in a above. Levering the lid of a can.
You can use a broad bladed screwdriver to get the lid off a can of paint. The pivot point is the rim of the can. The length of the screwdriver to the pivot point d2 is much greater than tip of the screwdriver beyond the rim d1.
Another example of needing less force to get the same moment to do the job of opening the can. The relatively long handle of a spanner. Spanners have long handles to give a strong turning force effect.
Generally speaking, the larger the nut to be tightened, the longer the spanner. Spanners were discussed in detail at the start of the page. A cork screw. The radius of the handle is much greater than the boring rod. The great difference in radius gives you a much greater torque turning force effect to bore into the cork stopper of a wine bottle.
The screw driver. The argument for a screwdriver is the same as for the corkscrew above. The greater the diameter of the screwdriver 'handle' compared to the diameter of the screw head, the greater the force torque you can apply to drive a screw into wood.
A wheelbarrow. The handles of the wheelbarrow are much further away from the wheel axis than the centre of gravity of the full wheelbarrow shown by the yellow blob! The wheel axis is the pivot point about which you calculate the two moments involved. F1 is the weight of the loaded wheelbarrow acting from its centre of mass centre of gravity.
The 'weight' moment F1 x d1, is a small moment to manage the weight of the wheelbarrow. However the 'lift' moment is F2 x d2 and so a smaller force F2 is needed operating at the longer perpendicular distance d2 to lift up the wheelbarrow and its load. The magnitude of the lifting force F2 is much less than the weight of the load, so you can lift the barrow and move it along.
The latter case is much more common situation in structural design problems. A moment is expressed in units of foot-pounds, kip-feet, newton-meters, or kilonewton-meters. A moment also has a sense; A clockwise rotation about the center of moments will be considered a positive moment; while a counter-clockwise rotation about the center of moments will be considered negative. The most common way to express a moment is.
The example shows a wrench being applied to a nut. A pound force is applied to it at point C, the center of the nut. The force is applied at an x- distance of 12 inches from the nut. The center of moments could be point C, but could also be points A or B or D. Moment about C The moment arm for calculating the moment around point C is 12 inches. The magnitude of the moment about point C is 12 inches multiplied by the force of lbs to give a total moment of inch-lbs or ft-lbs.
A moment causes a rotation about a point or axis. If the moment is to be taken about a point due to a force F, then in order for a moment to develop, the line of action cannot pass through that point. If the line of action does go through that point, the moment is zero because the magnitude of the moment arm is zero.
Such was the case for point D in the previous wrench poblem. A textbook definition: A turning effect is called Moment in static situations with no motion. In dynamics applications with movement a turning effect is called Torque. So a spinning motor shaft has torque, but a lever has moment. This is the textbook definition, but in practice the two terms are often used interchangeably. Otherwise it will accelerate in rotation, angular acceleration.
Mathematically this is very simple - add the clockwise moments and subtract the anticlockwise ones. For equilibrium of moments; "Taking clockwise as positive, the sum of all moments about point A is zero" These calculations are very simple.
The most common mistake is not getting the perpendicular shortest distance between pivot and force. Force Couples Two equal forces of opposite direction, with a distance d between them will cause a moment, where; A special case of moments is a couple. A couple consists of two parallel forces that are equal in magnitude, opposite in sense and do not share a line of action.
It does not produce any translation, only rotation. The resultant force of a couple is zero, but it produces a pure moment. A tap wrench is an example of a couple. The two hand forces are equal but opposite direction. Example of a couple: Wheel brace using two hands pushing opposite directions.
This is very handy when doing calculations. Demonstration of Varignon's Theorem. Video Lesson Description and Link. Moments can be Anywhere. And if anything, I didn't cover some of the most basic moment to force problems that you see in your standards physics class, especially physics classes that aren't focused on calculus or going to make you a mechanical engineer the very next year. So we did that with-- why did I write down the word "mechanical?
If you do a search for mechanical advantage, I cover some things on moments and also on torque. So what is moment of force? Well, it essentially is the same thing as torque. It's just another word for it. And it's essentially force times the distance to your axis of rotation.
What do I mean by that? Let me take a simple example. Let's say that I have a pivot point here. Let's say I have some type of seesaw or whatever.
There's a seesaw. And let's say that I were to apply some force here and the forces that we care about-- this was the exact same case with torque, because there's essentially the same thing. The forces we care about are the forces that are perpendicular to the distance from our axis of rotation. So, in this case, if we're here, the distance from our axis of rotation is this.
That's our distance from our axis of rotation. So we care about a perpendicular force, either a force going up like that or a force going down like that.
Let's say I have a force going up like that. Let's call that F, F1, d1. So essentially, the moment of force created by this force is equal to F1 times d1, or the perpendicular force times the moment arm distance. This is the moment arm distance. That's also often called the lever arm, if you're talking about a simple machine, and I think that's the term I used when I did a video on torque: moment arm.
And why is this interesting? Well, first of all, this force times distance, or this moment of force, or this torque, if it has nothing balancing it or no offsetting moment or torque, it's going to cause this seesaw in this example to rotate clockwise, right?
This whole thing, since it's pivoting here, is going to rotate clockwise. The only way that it's not going to rotate clockwise is if I have something keep-- so right now, this end is going to want go down like that, and the only way that I can keep it from happening is if I exert some upward force here.
So let's say that I exert some upward force here that perfectly counterbalances, that keeps this whole seesaw from rotating. F2, and it is a distance d2 away from our axis of rotation, but it's going in a counterclockwise direction, so it wants to go like that.
So the Law of Moments essentially tells us, and we learned this when we talked about the net torque, that this force times this distance is equal to this force times this distance. So F1 d1 is equal to F2 d2, or if you subtract this from both sides, you could get F2 d2 minus F1 d1 is equal to 0.
And actually, this is how we dealt with it when we talked about torque. Because just the convention with torque is if we have a counterclockwise rotation, it's positive, and this is a counterclockwise rotation in the example that I've drawn here. And if we have a clockwise rotation, it has a negative torque, and that's just the convention we did, and that's because torque is a pseudovector, but I don't want to confuse right now.
What you'll see is that these moment problems are actually quite, quite straightforward. So let's do a couple. It always becomes a lot easier when you do a problem, except when you try to erase things with green. So let's say that -- let me plug in real numbers for these values.
Let me erase all of this. Let me just erase everything. There you go. All right, let me draw a lever arm again.
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