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August 30, 2014

August 30, 2014

Posted by **martini** on Saturday, April 28, 2012 at 2:57am.

(a) What is the speed of this particle?

(b) If the kinetic energy of this particle is doubled, does its speed increase by more than, less than, or exactly a factor of 2?

(c) Explain

(d) Calculate the speed of a particle whose kinetic energy is twice its rest energy.

I got (a) and (d)

(a) .866c and (d) .943c

but I'm stuck on (b) and (c) I think it might be less than 2 but I have no idea why that would be the case, can someone please explain it to me!? Thank you!

- physics -
**Elena**, Saturday, April 28, 2012 at 7:11am(a)

KE = m(o) •c^2•[1/sqrt(1-β^2) -1],

E(o) = m(o) •c^2,

KE = E(o),

m(o) •c^2•[1/sqrt(1-β^2) -1] =

= m(o) •c^2,

1/sqrt(1-β^2) =2,

β = v/c = 0.866.

v = 0.866•c =0.866•3•10^8 =2.6•10^8 m/s.

(b),(c),(d)

KE = 2 •E(o)

m(o) •c^2•[1/sqrt(1-β^2) -1] =

=2•m(o) •c^2,

1/sqrt(1-β^2) =3,

β = v/c = 0.94.

v =0.94•c =2.82•10^8 m/s.

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