Question

A particle of mass $m_{0}$
moves with speed c/2. Calculate it's mass, momentum, total energy and kinetic energy.

Answer 1

Thanks for the question.

Here, given quantity is v= c/2

Mass (m)= ?
Total Energy (E) = ?
Momentum (p) = ?
Kinetic Energy (K.E) = ?

Thus, m= $\frac{m_{0} }{ \sqrt{1 - \frac{v ^{2} }{u^{2} } } }$ = $\frac{m_{0}}{ \sqrt{1 - \frac{1}{4} } } =\boxed{\frac{2m_{0}}{ \sqrt{3} }}$

In agreement of this, Apparently

p = mv = $\frac{2m_{0}}{ \sqrt{3} } . \: \frac{c}{2} = \boxed {\frac{m_{0}{c}}{ \sqrt{3} }}$

Total energy, E = $m {c}^{2} = \boxed{ \frac{2m_{0}(c^{2} )}{ \sqrt{3} } }$

So,

K.E. = Total Energy- Rest mass energy

= $m {c}^{2} - m_{0} {c}^{2} = \frac{2m_{0}{c}^{2} }{ \sqrt{3} } - m_{0} {c}^{2}$

Thus, K.E. = $\boxed{( \frac{2}{ \sqrt{3} } - 1)m_{0} {c}^{2}}$

Regards
Vickysky
@Brainly (India)