Question

A particle of mass m0 moves with a speed c/2. Calculate its mass, momentum, total energy and kinetic energy.

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Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

According to special theory of relativity, the mass of a body varies with the velocity v, it's mass is given by :

${\bold{\sf{⟼ \: \: \: \: \: \: \: \: \: \: \: m \: = \: \frac{m_0}{\sqrt{1 \: - \: \Big(\frac{v²}{c²}\Big)}}}}}$

${\bold{\sf{⟼ \: \: \: \: \: \: \: \: \: \: Where \: m_0 \: is \: the \: rest \: mass \: of \: the \: body \: and \: c \: is \: the \: velocity \: of \: light}}}$

${\bold{\sf{ \: \: \: \: \: \: \: \: \: \: \: \: ∴ \: \: \: \: \: m \: = \: \frac{m_0}{\sqrt{1 \: - \: \Big(\frac{v²}{c²}\Big)}} \: = \: \frac{2}{\sqrt{3}} \: m_0}}}$

${\bold{\sf{⟼ \: \: \: \: \: \: \: \: \: \: Momentum, \: p \: = \: mv}}}$

${\bold{\sf{⟼ \: \: \: \: \: \: \: \: \: \: \frac{2}{\sqrt{3}} \: m_0 \: \: × \: \: \frac{c}{2}}}}$

${\bold{\sf{⟼ \: \: \: \: \: \: \: \: \: \: \frac{1}{\sqrt{3}} \: m_0 \: c}}}$

${\large \: \: \: \: \: \: \: \: \: \: \: {\boxed{\rm{\red{ Total \: Energy, \: E \: \: = \: mc²}}}}}$

${\bold{\sf{⟼ \: \: \: \: \: \: \: \: \: \: \frac{2}{\sqrt{3}} \: m_0 \: c²}}}$

${\bold{\rm{Kinetic \: energy \: = \: total \: energy \: (E) \: \: - \: \: rest energy \: (E_0) }}}$

${\bold{\sf{⟼ \: \: \: \: \: \: \: \: \: \: \: \frac{2}{\sqrt{3}}m_0 \: c² \: - \: m_0 \: c²}}}$

${\bold{\sf{⟼ \: \: \: \: \: \: \: \: \: \: \: \: \Big(\frac{2}{\sqrt{3}} \: - \: 1\Big) m_0 \: c² }}}$