Question

You are planning a deep space exploration and want to take your cat with you. If your spacecraft achieves a maximum speed of 87% of the speed of light, how much additional energy is required to bring your cat (during the acceleration only)? Express this quantity in units of Petajoules (1015).Assume you start from zero velocity and your magical cat does not require additional food or litter. The cat weighs 8.5 lbf. Use LaTeX: 3\times10^8 3 × 10 8 m/s for the speed of light.

Answer 1

E = 1.7 10² PJ

Step-by-step explanation:

Let's use the special relativity relations, specifically the energy of a body is

E = γ mc²

γ =
`\sqrt{ 1 - (v^2)/(c^2) }`

where m is the rest mass

for that case they tell us that the speed of the body is 87% of the speed of light

= 0.87

let's calculate

γ =
`√(1 - 0.87^2)`

γ = 0.49305

let's reduce the mass of the jack to SI units

W = 8.5 lb (4.448 N / 1lb) = 37.808 N

W = mg

m = W / g

m = 37.808 / 9.8

m = 3.86 kg

let's look for energy

E = 3.86 (3 10⁸ )² 0.49305

E = 1.7 10¹⁷ J

let's reduce to take PJ

E = 1.7 10¹⁷ J (
`( 1 PJ)/(10^(15) J)` )

E = 1.7 10² PJ