Answer to Question #220087 in Physics for Alex

Question

(c) The speed of a particle relative to an observer on the Earth is 0.80c, and the

speed of another particle relative to her is -0.90c. What is the speed of the

particles with respect to each other?

(d) A particle of rest mass 1.0 kg has an initial speed of 1.0x10⁸ ms^-1 A constant

relativistic force of magnitude 5.0 x 10⁶N is exerted on the particle in the same

direction as the initial relativistic momentum for 100 s. Calculate the magnitudes

of the initial and final relativistic linear momenta of the particle.

(e) Calculate the linear momentum, kinetic energy and total energy (in J and MeV) of

a particle travelling with speed 0.90c given that its rest mass is and 1.68 x10^-27kg and 1MeV =1.6 x10^-13 J

Answer 1

c)

$$u=\frac{0.8c+0.9c}{1+0.8(0.9)}=0.988c$$

d)

$$p=\frac{10^8}{\sqrt{1-\frac{1}{3^2}}}=1.1\cdot10^8\frac{N}{s}\\p'=1.1\cdot10^8+(100)5\cdot10^6=6.1\cdot10^8\frac{N}{s}$$

e)

$$p=\frac{(1.68\cdot10^{-27})(0.9)3\cdot10^8}{\sqrt{1-0.9^2}}=1.04\cdot10^{-18}\frac{N}{s}$$