Moments 1

[00:00:01]Moments question one.

[00:00:03]A seesaw is modeled by a uniform rigid rod AB of mass 45 kg and length 3 m resting on a smooth support at the center of the rod.

[00:00:13]An adult of mass 64 kg sits at end A and a child of mass 40 kg sits at end B.

[00:00:20]When another child of mass M kg sits in a position 0.3 from B, the seesaw is in equilibrium.

[00:00:29]Right, okay. So, we have I'm going to diagram, so that's the first thing we're going to do.

[00:00:33]Okay, so we need our seesaw in equilibrium horizontally.

[00:00:40]We've got a smooth support at the center.

[00:00:45]And we're going to have a reaction force there.

[00:00:54]Let's call that end A and that end B.

[00:00:59]Okay, so when you're drawing the diagram, you've just got to make sure you've got every scrap of information onto your diagram.

[00:01:07]So, you've got the weight of the rod itself, which is 45 kg, and because it says it's uniform, we've got the mass acting exactly at the center.

[00:01:20]Okay, so we'll put a downwards force of 45 G there.

[00:01:26]We've got an adult of mass 64 G at this end.

[00:01:32]We've got a child of mass 40 at the other end.

[00:01:38]And it says we've got a child of mass M 0.3 m from B.

[00:01:45]Okay, so let's put some lengths in. If the whole thing is 3 m, then that's 1.5, and then that is 1.5 there. So, 0.3 from B, let's draw it about there.

[00:01:59]That's M kilograms, so that's MG downwards.

[00:02:04]That's 0.3 and that's 1.2.

[00:02:09]Okay, so we've got everything onto our diagram.

[00:02:14]So, we don't have any unknowns except the mass of the child there.

[00:02:21]And actually the size of the support.

[00:02:25]There.

[00:02:26]Okay?

[00:02:28]So, once you're happy you've got your diagram with everything labeled, you're going to think about the two things that you do with moments, which are you can resolve vertically and you can take moments about a chosen pivot point.

[00:02:45]Okay. So, because question A is asking me to find the value of M and it's not asking me to find the reaction until part B, I'm going to choose my pivot point at the center, okay?

[00:02:59]Which is the obvious place to take it because that's the tipping position.

[00:03:04]Okay?

[00:03:05]So, if I pivot at point C, then the two forces acting at point C aren't going to come into this equation that we're going to write down.

[00:03:18]Okay? So, what we're thinking of is if you've got a pivot point there and you have forces pushing down on that side and you have forces pushing down on that side, you're basically saying that they are equal.

[00:03:31]Okay?

[00:03:33]So, your moment is your force times your distance.

[00:03:38]So, we're going to say on the left-hand side we've got 64 G multiplied by a distance of 1.5.

[00:03:46]And balancing that, we've got MG times a distance of 1.2 and 40g times a distance of 1.5. So, these distances are distances from the pivot.

[00:04:01]So, M is 1.2 away and 40 is 1.5 away.

[00:04:08]Okay. So, I don't need to include the 45 and I don't need to include the R because they are zero distance.

[00:04:16]Okay, and now we just need to work this out. We can actually cancel the G out, but if you're happier put it in as 9.8.

[00:04:26]Okay, so I'll say 64 * 1.5.

[00:04:32]That's equal to 1.2 M plus 60.

[00:04:37]Hop that across and then divide by 1.2.

[00:04:45]And our M is 30.

[00:04:49]Okay.

[00:04:51]We don't need to worry about 9.8. It was in every term and it canceled out. If you put it in as a number, that's fine.

[00:04:58]You'll still get M is 30. So, that is 30 kg for the mass of the child.

[00:05:04]Okay.

[00:05:05]And then for part B, because now we only have one unknown and it's a force, we can then say we can do our resolving vertically.

[00:05:19]Sometimes that's the first thing you do when you do a moment's question or sometimes it is the second thing or sometimes you don't do it at all.

[00:05:27]If I resolve vertically here, I've got one force upwards, R, and that will equal 64g plus 45g plus M, which we now know is 30g and 40g on the end. So, you include all the downward forces.

[00:05:46]So, I need to work out 64 add 45 add 30 add 40 and then times everything by 9.8.

[00:05:55]Okay?

[00:05:57]And that gives me 1754.2.

[00:06:03]So, that's a fairly standard moments question where you're choosing a pivot point and you're taking the force times the distance as the moment of the force and you're working out which forces are going to make your object spin in which direction.

[00:06:22]Okay?

[00:06:25]And resolving vertically is the other thing that you can do with moments questions. So, just the forces up are balanced by the forces down and there's no distances coming into that equation, notice.