Question

Using E = mc², we found that 1 kg of mass has the energy equivalent of 20 megatons. Estimate how many megatons of energy would be required to accelerate a spaceship with a mass of one million kg to a speed of 0.99c. What does this suggest to you regarding the practicality of space travel at relativistic speeds?

Answer 1

at relativistic speed, the mass energy relation takes the form

where,

at non-relativistic speeds, v<<c or v/c<<1 and hence this factor equals 1

now for the given case, m = 1 million kg = 10⁶ kg

v = 0.99 c

thus, we get

in terms of tons,

we know that

this is the huge amount of energy, which is quite impossible. Thus, we can say that travelling at such relativistic speeds is very much difficult.