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

A particle has a kinetic energy equal to its rest energy.

(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.

## Answer this Question

## Related Questions

- Physics - A 245 g particle is released from rest at point A inside a smooth ...
- physics kinetic energy - a) if a particle's speed decreases by a factor of four...
- physics - A 278 g particle is released from rest at point A inside an smooth ...
- Physics - The kinetic energy of a massive particle is equal to the energy of a ...
- Physics - A single conservative force F(x) acts on a 1.6 kg particle that moves ...
- Physics - A single conservative force acts on a 5.00 kg particle. The equation ...
- physics - (Requires calculus) Prove the relativistic work-energy theorem in one ...
- Physics 2 - A particle moves along a line where the potential energy of its ...
- physics - a particle of mass m moving with a speed v meters per second strikes a...
- physic - please help, I really appriciate you help alot. Question:A 0.34 kg ...