00:01
Okay, so this is the situation we've got.
00:01
We've got a box at the top of a slope.
00:04
This curved bit is frictionless and it's going to slide down the slope to here, to position 2, where it's going to have energy e2.
00:12
And then it's going to go up a slope with friction until it ends at this position here, where its energy is e3.
00:19
So we're going to employ the conservation of energy to find out this height y max.
00:23
So the first thing to note is that since there's no friction on the curved bit, e1 is just going to equal e2.
00:30
Now e1 is just the gravitational potential energy the box has, because it's at rest initially.
00:37
And that is going to be just m, the mass of the block, times the gravitational acceleration constant g, times the height h.
00:47
And e2, it's relative to point 1, it has zero gravitational potential energy because it's lost all that height h.
00:56
So the only energy it has left is kinetic, and its kinetic energy is a half m v squared.
01:11
Now, basically what this is telling us is that the energy at point 2 is equal to mgh, the same as the energy at point 1.
01:22
Now, the energy at point 3, e3, when it's got to its max height, is going to be equal to this energy at point 2, minus the work done by friction.
01:39
Now, the work done by friction, which i'll just call w, is equal to the frictional force f times the distance moved against that frictional force...