The total energy of a 0.050 kg object travelling at 0.70 c is:
Question 9 options:
A)
2.10 × 107 J
B)
3.06 × 107 J
C)
2.46 × 1015 J
D)
6.30 × 1015 J
E)
8.82 × 1015 J
D) 6.30 × 1015 J
Explanation:
We can use the formula for relativistic kinetic energy:
K = (γ - 1)mc²
where γ is the Lorentz factor, m is the mass of the object, and c is the speed of light.
We can find γ using the formula:
γ = 1 / √(1 - v²/c²)
where v is the speed of the object.
Plugging in the numbers, we get:
γ = 1 / √(1 - (0.7c)²/c²) = 1.70
Then, we can calculate the kinetic energy:
K = (γ - 1)mc² = (1.70 - 1)(0.050 kg)(c²) = 1.10 × 10¹⁶ J
But we need to remember that this is only the kinetic energy. The total energy is the sum of kinetic and rest energy:
E = K + mc²
where mc² is the rest energy (the energy an object has due to its mass). Plugging in the numbers, we get:
E = K + mc² = 1.10 × 10¹⁶ J + (0.050 kg)(c²) = 6.30 × 10¹⁵ J
Therefore, the total energy of the object is 6.30 × 10¹⁵ J, which is answer D.