Question

Problem 1: The energy E of a particle of mass m moving at speed v is given by: E2 = m2 c4 + p2 c2 (1) p=γmv (2) 1 γ = 1−v2/c2 (3) This means that if something is at rest, it’s energy is mc2. We can define a kinetic energy to be the difference between the total energy of an object given by equation (1) and the rest energy mc2. What would be the kinetic energy of a baseball moving at half the speed of light? Give your answer in Joules but also in tons of TNT equivalent. For context, the worst nuclear weapons are measured in megatons. Do you think we could ever accelerate a baseball to half the speed of light?

Problem 2: As we said in lecture, if you heat something up, it becomes more massive! Imagine you took 1 kg of water and heated it up by 50 deg C. By how much would it’s mass increase because of this heating? You might have to look up the heat capacity of water.

Answer 1

From option 1 we can see for giving baseball the velocity half of the velocity of light c, will require the huge amount of energy. If we can supply that much energy then baseball will move on the velocity of half of c.