00:01
Okay, so here we have a question of a horizontal, here we have a question of a horizontal beam weighing 100, with the mass of 140 kilograms, and at a 320 kilogram piano rests a quarter of the way from the end.
00:20
And we are asked, what's the vertical force on the support nearest the piano? so i've labelled this part b, and then a is the support furthest from the piano.
00:31
So the first thing we need to do before we do anything else is get these masses into forces.
00:37
So in order to do that, we're going to multiply by the gravitational field strength of earth, which is 9 .81.
00:43
It's 9 .81, 9 .81.
00:44
So we know that weight is mass times the gravitational field strength.
00:48
And that will give you a force of 1 ,373 .4 neutins for the 140 kilogram beam.
00:57
And 3 ,139 .2 neutons for the 320 kilogram piano.
01:07
And then we can get some distances in here as well.
01:10
So we're going to be working out the support at point b first.
01:17
So that means that point a is going to be our point of rotation.
01:21
So this is where we're going to take moments about.
01:24
So we're going to imagine the beam, if it was allowed to rotate, the 140 kilogram mass and 320 kilogram piano, they would cause a clockwise moment around point a, and then b or the supporter b resists that and provides a counteracting anti -clockwise moment.
01:43
So given that b is a quarter of the way along, sorry, the piano is a quarter of the way along from b, that must mean it is three quarters, so three quarters l from point a, l is the entire length of the beam, and then 140 kilogram, the 140 kilogram centre of mass of the beam is obviously just half l away from a.
02:11
Okay, so then what we can do is we can express, so we have clockwise moments is equal to anti -clockwise moments.
02:23
So cwm, clockwise moments is equal to anti -clockwise moments, is the principle of consolidation of moments for equilibrium.
02:30
And this is in equilibrium here.
02:33
So part a.
02:35
Our clockwise moments come from the 140 kilogram mass and the 320 kilogram mass, or rather, their forces, multiplied by the distances to a.
02:46
So for the 140 kilogram mass, that is going to be 1373 .4, multiplied by its distance, and its distance is l over 2, plus, so that's up the first of the clockwise moments, we need the second one, plus 3139 .2...