Physics: At what speed is a particle s momentum 2.5 times more than its newtonian value?

At what speed is a particle s momentum 2.5 times

Ответ:

goly9453

14.03.2022

The relativistic momentum of a particle moving with speed v is equal to:
$p=\gamma m_0 v$
where
m_0

is the rest mass of the particle
$\gamma= \frac{1}{ \sqrt{1- \frac{v^2}{c^2} } }$ is the relativistic factor, with c being the speed of light.

The Newtonian momentum is instead
p=m_0 v

For the particle in our problem, the relativistic momentum is 2.5 times the Newtonian momentum: this means $\gamma=2.5$ . If we re-arrange the formula of $\gamma$ , we get:
$v=c \sqrt{1- \frac{1}{\gamma^2} }$
and by using $\gamma=2.5$ , we find the particle velocity:
$v=(3 \cdot 10^8 m/s) \sqrt{1- \frac{1}{(2.5)^2}} =0.917 c = 2.75 \cdot 10^8 m/s$

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Ответ:

kutsarver

31.01.2020

Physics

It basically means that the gravitational pull on earth is measured as 9.8. For the moon it’s completely different

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At what speed is a particle's momentum 2.5 times more than its newtonian value?

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