Astrophysics 14 Use Newton's second law, F = dp/dt, and the formula for relativistic momentum, Eq. ( 44), to show that the acceleration vector a = dv/dt produced by a force F acting on a particle of mass m is F (F • v), ymc² ym where F · v is the vector dot product between the force F and the particle velocity v. Thus the acceleration depends on the particle's velocity and is not in general in the same direction as the force. my = ymv (44) VI - v²/c² 1 –
Astrophysics 14 Use Newton's second law, F = dp/dt, and the formula for relativistic momentum, Eq. ( 44), to show that the acceleration vector a = dv/dt produced by a force F acting on a particle of mass m is F (F • v), ymc² ym where F · v is the vector dot product between the force F and the particle velocity v. Thus the acceleration depends on the particle's velocity and is not in general in the same direction as the force. my = ymv (44) VI - v²/c² 1 –
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Transcribed Image Text:Astrophysics
14 Use Newton's second law, F = dp/dt, and the formula for relativistic momentum, Eq. ( 44),
to show that the acceleration vector a = dv/dt produced by a force F acting on a particle of
mass m is
F
(F. v),
ymc²
Ym
where F· v is the vector dot product between the force F and the particle velocity v. Thus the
acceleration depends on the particle's velocity and is not in general in the same direction as the
force.
mv
p =
/1 – v²/c²
= ymv
(44)
VI -
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