1.As known,for a fusion reaction the fraction of mass converted to energy is about 0.007.So there is
△E=△mc²=0.007mc².
Here △E=P*△t=3.83×10^26(W)×1(s)=3.83×10^26(J),c≈3×10^8(m/s).We get
m=△E/(0.007c²)≈3.83×10^26/(0.063×10^16)≈6.08×10^11(kg).
So there are about 6.08×10^11 kilograms of protons and electrons are transformed into helium every second.
2.According to problem 1 and the presumption that about one tenth (0.1) mass of the Sun is in the core,we can calculate that the number of seconds the Sun will last is about
T=0.1M/(m/t)≈0.1×1.99×10^30kg/(6.08×10^11kg/s)≈3.27×10^17s,
which is
T≈3.27×10^17s/(31536000s/yr)≈1.04×10^10yr.
3.For the formular of the Schwarzschild radius is R=2GM/c² and here M=86kg,G=6.67×10^(-11m³/kgs²),we get
R=2GM/c²=2×6.67×10^(-11m³/kgs²)×86kg/(9×10^16m²/s²)≈1.275×10^(-25m).
So the Schwarzschild radius of a black hole made from a male who started with a mass of 86 kg is about 1.275×10^-25 meters.
4.Here an acceleration of 4.19 m/s² in one direction is like gravity of 4.19 m/s² in another direction.So we get
a/g=4.19(m/s²)/9.81(m/s²)≈0.427.
Now we know that this acceleration feel like 0.427 "g"s.
