Advanced higher physics help!!

hi,
can anyone help me with this adv higher physics mechanics problem-
Calculate the speed required to to increase a protons rest mass by 50%?

please help.

Reply 1

CallumFR

You need to use the equation for relativistic mass.

m = \frac{m_{0}}{\sqrt {1- \frac{v^2}{c^2}}}

As you want the rest mass to increase by 50%, you need to replace the left hand side of the equation with 1.5m0. Sub in rest mass of a proton into m0 and then just do algebra to get v.

Reply 2

nav man

i dont know how to get v

Reply 3

nav man

CallumFR

You need to use the equation for relativistic mass.

m = \frac{m_{0}}{\sqrt {1- \frac{v^2}{c^2}}}

As you want the rest mass to increase by 50%, you need to replace the left hand side of the equation with 1.5m. Sub in rest mass of a proton into m0 and then just do algebra to get v.

how do i get v?

Reply 4

CallumFR

nav man

how do i get v?

You can simplify the equation by cancelling m0 on either side (so actually, there's no need to sub in the rest mass)

1.5 = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}

Square both sides

2.25 = \frac{1}{1-\frac{v^2}{c^2}}

1-\frac{v^2}{c^2}= \frac{1}{2.25}

1-\frac{1}{2.25}=\frac{v^2}{c^2}

c^2(1-\frac{1}{2.25}) = v^2

Unparseable latex formula:

v = \sqrt{({3*10^{8})}^2(1-\frac{1}{2.25})}}

and then just do the maths on a calculator

Reply 5

nav man

thanks a lot man, that was a big help. +rep

Reply 6

CJN

Did you do higher maths? If not then generally you should look over the course, ah physics has some higher maths in it and especially in things like rearranging equations (like above) it is very useful.