Question

2A. How much mass-energy is there in a 130 g sandwich? 2B. If said sandwich was travelling at a speed of 0.6c, how much kinetic energy does it have? 2C. Protons in the LHC are accelerated until their mass-energy is 8TeV (8 x 10^ 12 eV). If protons have a rest mass of 938MeV/c^2 (9.38 x 10 ^8 ev/c^2), how fast are they going in terms of c? Your answer should include three digits that are not 9

Answer 1

(a) We know that mass energy is E = m₀c² where c is the speed of light , m_ois the rest mass of sanwich
E₁ = (130*10^-3)(3*10⁸)² = 1.17*10¹⁶ J
(b) when the velocity is 0.6C then the energy will be E = mc²
where m is the relativistic massSo
m = m_o / (1-(v/c)²) = 1.25m₀
Therefore energy E₂ = 1.25m_oc²
Kinetic energy = E₂ - E₁ = m_oc²(1.25 -1) = 0.25*1.17*10¹⁶   = 2.925*10¹⁵ J
(c) So we know that E = mc²
and accelerated energy = 8*10¹² eV = mC²
m = (8*10¹² eV)/c²
and the varaible massm = m_o / (1-(v/c)²) and m_o = (9.38*(10⁸)eV)c²
Therefore
(8*10¹² eV)/c² =(9.38*(10⁸)eV)c²  / (1-(v/c)²)
8*10¹² = (9.38*10⁸) / (1-(v/c)²)
V = 2.999*10⁸ m/s