00:01
All right, so let's say a child is pulled on a swing, and they're pulled back an angle of 45 degrees.
00:07
So let's say this is the swing.
00:10
This is the child.
00:13
This is, i don't know, this is kind of a crude depiction of what's going on.
00:17
But we're told the swing has a length of 2 .4 meters, and the child has a mass of 21 kilograms.
00:29
And we want to know if they're pulled back this distance, what is the potential energy relative to the potential energy at the bottom of the swing? so let's say this is zero at the bottom of the spring.
00:42
And then the potential energy at their initial location is just mg times their location y.
00:49
And so what is that going to be? it's their change in height above the ground.
00:54
So this is going to be like mg times l times one minus.
01:00
The cosine of the angle they're pulled back by because the l times the cosine of the angle they're pulled back by tells you what this distance is right this is l cosine so if we do l minus that that tells us what the change in height is and so if we plug in our numbers it's 21 kilograms times 9 .8 meters per second squared times 2 .4 meters times one minus the square root of 2 over 2.
01:30
This is the cosine of 45...