# Physics

posted by .

Determine the ratio of the relativistic kinetic energy to the nonrelativistic kinetic energy (1/2mv2) when a particle has a speed of (a) 2.12 x 10-3c. and (b) 0.959c.

• Physics -

Relativistic kinetic energy is mₒc²{[1/√(1-β²)] – 1},
nonrelativistic kinetic energy is m v²/2 = 0.5mₒv²
(a) β=v/c=2.12•10^-3•c/c=2.12•10^-3
1/√(1-β²) =1.00000224
1/√(1-β²)] – 1 = 0.00000224=2.24 •10^-6
Relativistic kinetic energy is 2.24 •10^-6•mₒc²
The ratio is 2.24 •10^-6•mₒc²/[0.5•mₒ•(2.12•10^-3)² • c² ]=
=2.24 •10^-6/2.2472•10^-6 = 0.996796.

(b) β=v/c=0.959•c/c= 0.959
1/√(1-β²) = 3.5285,
1/√(1-β²)] – 1 =2.5285
Relativistic kinetic energy is 2.5285 •mₒc²
The ratio is 2.5285 •mₒc² /[0.5•mₒ•( 0.959)² • c² ]=5.499

## Similar Questions

1. ### physics kinetic energy

a) if a particle's speed decreases by a factor of four, by what factor does its kinetic energy change?
2. ### physics

(Requires calculus) Prove the relativistic work-energy theorem in one dimension. The force exerted on a particle is given not by F=ma, but F=dp/dt. Using the expression for the relativistic momentum of a particle p=γmv, integrate …
3. ### Physics kinetic energy

Okay the equation for kinetic energy is = 1/2mv^2 so how would i figure this out?
4. ### Physics

A single conservative force F(x) acts on a 1.6 kg particle that moves along an x axis. The potential energy U(x) associated with F(x) is given by U(x) = -2.9xe-x/3 where x is in meters. At x = 3.4 m the particle has a kinetic energy …
5. ### Physics

A 245 g particle is released from rest at point A inside a smooth hemispherical bowl of radius 35.0 cm, as shown in Figure 5-21. (a) Calculate the gravitational potential energy at A relative to B. 1 . (b) Calculate the particle's …
6. ### physics

A particle has a kinetic energy equal to its rest energy. (a) What is the speed of this particle?
7. ### Physics

The kinetic energy of a massive particle is equal to the energy of a photon.  The massive particle moves at 1.49 % the speed of light.     What is the ratio of the photon wavelength to the de Broglie wavelength of the particle?
8. ### physics

A 278 g particle is released from rest at point A inside an smooth hemispherical bowl of radius 36.5 cm, as shown below. (a) Calculate the gravitational potential energy at A relative to B. J (b) Calculate the particle's kinetic energy …
9. ### Physics

Determine the ratio of the relativistic kinetic energy to the nonrelativistic kinetic energy (1/2mv2) when a particle has a speed of (a) 2.60 × 10-3c. and (b) 0.972c
10. ### Physics

The kinetic energy of a particle is equal to the energy of a photon. The particle moves at 6.9% of the speed of light. Find the ratio of the photon wavelength to the de Broglie wavelength of the particle. Take the speed to be non-relativistic.

More Similar Questions