00:01
In this question, we're looking at a starship which combines matter and antimatter to accelerate.
00:06
When this happens, the total rest energy is converted to other forms.
00:10
So we're told we have a starship of mass 2 times 10 to 5 kilograms and it accelerates to 0 .35c from rest.
00:20
We want to find out how much matter and antimatter must be converted into kinetic energy for this to be able to occur.
00:27
So what we know is einstein's mass energy equivalence formula that equals mc squared.
00:33
We also know the relativistic gamma factor, which is equal to one over the square root of one minus the velocity it's traveling at over the speed of light squared.
00:44
So what we want to do is we say that the matter and antimatter, which is converted to the kinetic energy of the spaceship, will be noted by small m.
00:53
So it will have an energy of mc squared.
01:00
Now we want to find the kinetic energy of the spaceship.
01:05
So we're going to label this one, k, and we're going to say it's equal to capital m, c squared.
01:13
However, because it's travelling relativistically, we must multiply it by the gamma factor minus 1.
01:21
And now we know that the energy of the matter and antimatter, this, is going to be converted to the kinetic energy of the spaceship...