00:01
So in this question we're told that we have a frictionless horizontal plane, and we have a spring of constant k, attached to a block at x equals zero.
00:16
So this is a position a.
00:18
This gets stretched out to position b, which is x equals 0 .2 meters, and then projected with speed 1 metre per second in towards the centre of the system.
00:39
And when it reaches the equilibrium point, its speed is v equals 2 metres per second.
00:50
So first of all, let's get the total mechanical energy.
00:54
That's going to be the kinetic energy at the equilibrium point.
00:56
Because at the equilibrium point, the spring energy is zero.
01:00
So that's, and the mass, by the way, m is 0 .5 kilograms.
01:06
So the energy is going to be a half m v squared, which is v squared is 4, so that's just going to be 2m, so this is 1 jule.
01:17
We need to get the spring constant now.
01:19
So the energy at b is going to be equal to the energy at a...