THE WORKING AND ANSWERS FOR THE FOLLOWING QUESTIONS QUESTIONS (15-26)
Question
Problem 15: Suppose an asteroid with a mass of 0.95 × 109 kg is heading
... [Show More] towards the Earth at 25 km/s.
Randomized Variablesm = 0.95 × 109 kg
v = 25 km/s
Part (a) Find the relativistic momentum of the asteroid in kilogram meters per second.
Numeric : A numeric value is expected and not an expression.
p = __________________________________________
Part (b) Find the fractional change of this momentum, (p - pnr) / pnr, relative to the non-relativistic momentum pnr.
Numeric : A numeric value is expected and not an expression.
(p - pnr) / pnr = __________________________________________
Problem 16: Suppose a satellite has a mass of 2100 kg and is orbiting at 6.6 km/s. Use the approximation that γ ≈ 1+(1/2)(v2/c2) at low velocities.
Randomized Variablesm = 2100 kg
v = 6.6 km/s
Part (a) What is the relativistic momentum of the satellite in kilogram meters per second?
Numeric : A numeric value is expected and not an expression.
p = __________________________________________
Part (b) Find the fractional difference between the relativistic and non-relativistic momenta, (p - pnr)/pnr.
Numeric : A numeric value is expected and not an expression.
(p - pnr)/pnr = __________________________________________
Problem 17: Suppose a 1.15-μg speck of dust has the same momentum as a proton moving at 0.999c.
Calculate the speed, in meters per second, of this speck of dust.
Numeric : A numeric value is expected and not an expression.
v = __________________________________________
Problem 18: The mass of an electron is 9.11 × 10-31 kg.
Part (a) Find the rest energy of an electron. Give your answer in joules.
Numeric : A numeric value is expected and not an expression.
E0 = __________________________________________
Part (b) Find the rest energy of an electron. Give your answer in MeV.
Numeric : A numeric value is expected and not an expression.
E0 = __________________________________________
Problem 19: The mass of a proton is 1.67 × 10-27 kg.
Part (a) Find the rest energy in joules.
Numeric : A numeric value is expected and not an expression.
E0 = __________________________________________
Part (b) Find the rest energy in mega-electron volts.
Numeric : A numeric value is expected and not an expression.
E0 = __________________________________________
Problem 20: The Big Bang that began the universe is estimated to have released 1068 J of energy.
Randomized Variablesm = 4.4 • 1030 kg
How many stars could half this energy create, assuming the average star's mass is 4.4 × 1030 kg ?
Numeric : A numeric value is expected and not an expression.
N = __________________________________________
Problem 21: A supernova explosion of a 1.2 × 1031 kg star produces 1.85 × 1044 J of energy.
Randomized Variablesm = 1.2 × 1031 kg
E = 1.85 × 1044
Part (a) How many kilograms of mass are converted to energy in the explosion?
Numeric : A numeric value is expected and not an expression.
Δm = __________________________________________
Part (b) What is the ratio Δm / m of mass destroyed to the original mass of the star?
Numeric : A numeric value is expected and not an expression.
Δm / m = __________________________________________
Problem 22: The fission of 1 kg of uranium produces 8.0 × 1013 J of energy.
Part (a) Calculate the mass, in grams, converted to energy by the fission of 0.95 kg of uranium.
Numeric : A numeric value is expected and not an expression.
Δm = __________________________________________
Part (b) What is the ratio of the converted mass to the original mass?
Numeric : A numeric value is expected and not an expression.
Δm / m = __________________________________________
Problem 23: Consider a 1050 kg car moving at 31 m/s.
Part (a) Calculate the relativistic kinetic energy of the car if the speed of light were only 45.0 m/s.
Numeric : A numeric value is expected and not an expression.
K = __________________________________________
Part (b) Find the ratio of the relativistic kinetic energy to the non-relativistic kinetic energy in this case.
Numeric : A numeric value is expected and not an expression.
K/Knr = __________________________________________
Problem 24: Alpha decay is nuclear decay in which a helium nucleus is emitted from an atom.
If the helium nucleus has a mass of 6.64 × 10-27 kg and is given 4.75 MeV of kinetic energy, what is its velocity, as a ratio to the speed of light? You must assume the alpha particle is moving relativistically.
Numeric : A numeric value is expected and not an expression.
v/c = __________________________________________
Problem 25: Beta decay is nuclear decay in which an electron is emitted from an atom.
If the electron is given 0.75 MeV of kinetic energy, what is its velocity, as a fraction of the speed of light? You will have to assume the electron is moving relativistically.
Numeric : A numeric value is expected and not an expression.
v/c = __________________________________________
Problem 26: The positron is the antiparticle of the electron, having exactly the same mass but opposite charge. When a positron and an electron meet, they annihilate, converting all of their mass into energy.
Part (a) Find the energy, in joules, released in this interaction assuming neither particle has any kinetic energy before the collision.
Numeric : A numeric value is expected and not an expression.
E = __________________________________________
Part (b) If this energy is given to a proton in the form of kinetic energy, what is its resulting velocity as a fraction of the speed of light? You should assume the proton will be moving relativistically.
Numeric : A numeric value is expected and not an expression.
vp/c = __________________________________________
Part (c) If this energy is given to another electron in the form of kinetic energy, what is its velocity as a fraction of the speed of light?
Numeric : A numeric value is expected and not an expression [Show Less]