Question 1

How much energy would be required to accelerate a 77-kg professor from rest to 90% the speed of light? (c = 3.0 × 10⁸ m/s) A) 1.6 × 10¹⁹ J B) 2.1 × 10¹⁹ J C) 9.0 × 10¹⁹ J D) 2.8 × 10¹⁹ J E) 3.5 × 10¹⁹ J

Accepted Answer

The equation for calculating the energy required to accelerate an object to a certain velocity is:

E = (γ - 1)mc^2

where 
E = energy required 
γ = Lorentz factor = 1/sqrt(1 - v^2/c^2) 
m = mass of object 
c = speed of light 
v = final velocity

Substituting the given values, we get:

γ = 1/sqrt(1 - (0.9c)^2/c^2) = 2.96

E = (2.96 - 1) x 77 kg x (3.0 x 10^8 m/s)^2 = 9.0 x 10^19 J

Therefore, the energy required to accelerate the professor to 90% the speed of light is 9.0 x 10^19 J, which is option C.

Question 2

A person with an initial mass of 70 kg climbs a stairway and thereby rises 6.0 m in elevation. By how much does his mass increase by virtue of his increased potential energy? (c = 3.0 × 10⁸ m/s)

Accepted Answer

The answer of A person with an initial mass of...

Question 3

An electron has a speed of 0.783c. Through what potential difference would the electron need to be accelerated from rest in order to reach this speed? The rest mass energy of an electron is 0.511 MeV.
A) 310 kV
B) 260 kV
C) 360 kV
D) 400 kV

Accepted Answer

The correct answer is A because the electron needs to be accelerated through a potential difference of 310 kV in order to reach a speed of 0.783c.

Question 4

One of the first atomic bombs released energy equivalent to that of 20,000 tons of TNT explosive. How much mass was converted to energy by this explosion, given that 1000 tons of TNT produce 4.3 × 10¹² J of energy. Incidentally, modern H-bombs have energy yields 1000 times as much! (c = 3.0 × 10⁸ m/s)

Accepted Answer

The answer of One of the first atomic bombs released...

Question 5

If the kinetic energy of a particle is 3.00 times its rest energy, the speed of the particle is closest to which of the following values?
A) 0.950c
B) 0.968c
C) 0.976c
D) 0.984c
E) 0.990c

Accepted Answer

According to the equation E^2 = (pc)^2 + (mc^2)^2, where E is the total energy, p is the momentum, m is the rest mass, and c is the speed of light, we have E = mc^2 + K, where K is the kinetic energy. Given K = 3mc^2, we have E = 4mc^2. Equating this to the relativistic energy-momentum equation E^2 = (mc^2)^2 + (pc)^2, we get (pc)^2 = 3(mc^2)^2. Therefore, p = (√3)mc. The velocity of the particle is given by v = p / (√(p^2 + m^2c^2)). Substituting p and m, we get v = (√3)c / 2, which is closest to 0.968c. Therefore, the best choice is B.

Question 6

If, instead of the correct formula for kinetic energy, we carelessly use the classical expression for kinetic energy for a particle moving at half the speed of light, by what magnitude percent will our calculation be in error? (c = 3.0 × 10⁸ m/s) A) 24% B) 19% C) 27% D) 7% E) 1%

Accepted Answer

The answer of If, instead of the correct formula for...

Question 7

If a typical city consumes electrical energy at a rate of $2.0 \mathrm { GW }$ how many kilograms of matter would have to be converted entirely into electrical energy in order to keep this city running for $14 \text { weeks? }$ $\left( c = 3.0 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } \right)$
A) 0.19 kg
B) 0.21 kg
C) 0.27 kg
D) 0.32 kg

Accepted Answer

The energy required is $2.0 \, \text{GW} \times 14 \times 7 \times 24 \times 3600 \, \text{s}$. Using $E=mc^2$, solve for $m$ to find the mass.

Question 8

In a nuclear plant, 10¹⁷ J of energy is available from mass conversion. How much mass of fuel was lost to produce this energy? (c = 3.0 × 10⁸ m/s) A) 0.1 kg B) 1 kg C) 10 kg D) 100 kg

Accepted Answer

The answer of In a nuclear plant, 10¹⁷ J of...

Question 9

During a reaction, 170 µJ of energy is released. What change of mass would accompany this release? (c = 3.0 × 10⁸ m/s) A) 5.1 × 10^-4 kg B) 1.5 × 10^-13 kg C) 4.8 × 10^-18 kg D) 1.9 × 10^-21 kg

Accepted Answer

The answer of During a reaction, 170 µJ of energy...

Question 10

How much energy would be released if 2.0 kg of material was lost during a reaction? (c = 3.0 × 10⁸ m/s) A) 1.8 × 10¹⁷ J B) 1.5 × 10¹⁶ J C) 6.0 × 10⁸ J D) 4.7 × 10^-8 J

Accepted Answer

The energy released can be calculated using the equation E=mc^2, where m is the mass lost (2.0 kg) and c is the speed of light (3.0 × 10^8 m/s). Plugging in the values, E = 2.0 kg × (3.0 × 10^8 m/s)^2 = 1.8 × 10^17 J.

Question 11

During a reaction, a reactant loses 4.8 × 10^-28 kg of mass. How many joules of energy are released? (c = 3.0 × 10⁸ m/s) A) 4.3 × 10^-11 J B) 1.4 × 10^-19 J C) 1.6 × 10^-36 J D) 5.3 × 10^-45 J

Accepted Answer

The energy released can be calculated using Einstein's equation, E=mc^2, where m is the mass lost (4.8 × 10^-28 kg) and c is the speed of light (3.0 × 10^8 m/s). Plugging in the values, E = (4.8 × 10^-28 kg)(3.0 × 10^8 m/s)^2 = 4.32 × 10^-11 J, which rounds to 4.3 × 10^-11 J.

Question 12

An electron-volt is the energy gained by an electron if it is accelerated through a potential difference of one volt. What is the equivalent to an electron-volt in kilograms? (c = 3.00 × 10⁸ m/s, e = 1.60 × 10^-19C)

Accepted Answer

The answer of An electron-volt is the energy gained by...

Question 13

Consider a student whose mass is 70 kg. If all his mass were converted to electrical energy, for how many years could he keep a 100-W light bulb burning? (c = 3.0 × 10⁸ m/s)

Accepted Answer

The answer of Consider a student whose mass is 70...

Question 14

A space barge pushes on a spaceship with a rest mass of 15,000 kg and accelerates it from a speed of 0.600c to a speed of 0.700c. How much work does the barge have to do to accomplish this? (c = 3.00 × 10⁸ m/s) A) 1.35 × 10²⁰ J B) 2.03 × 10²⁰ J C) 2.70 × 10²⁰ J D) 5.42 × 10²⁰ J E) 8.78 × 10¹⁹ J

Accepted Answer

The work done on the spaceship can be calculated using the relativistic work-energy theorem, which states that the work done is equal to the change in relativistic kinetic energy. The relativistic kinetic energy (K) is given by $K = (\gamma - 1)mc^2$, where $\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$ is the Lorentz factor, $m$ is the rest mass, and $c$ is the speed of light. For the initial speed $v_i = 0.600c$, the initial Lorentz factor $\gamma_i$ is calculated using $v_i$, and for the final speed $v_f = 0.700c$, the final Lorentz factor $\gamma_f$ is calculated using $v_f$. The change in kinetic energy ($\Delta K$) is then $\Delta K = (\gamma_f - \gamma_i)mc^2$.Plugging in the given values and calculating gives a result in the range of $2.03 \times 10^{20}$ Joules, which corresponds to choice B.

Question 15

If the mass of a 1.0-kg book could be entirely converted into electrical energy, how many kW ∙ h of energy would that generate? (c = 3.0 × 10⁸ m/s)

Accepted Answer

The answer of If the mass of a 1.0-kg book...

Question 16

In a certain chemical reaction, 8.1 × 10^-19 J of energy is released per molecule formed. What is the difference in mass per molecule between the sum of the masses of the molecules of the reagents before the reaction and the mass of the molecules produced by the reaction? (c = 3.0 × 10⁸ m/s) A) 8.1 × 10^-28 kg B) 2.7 × 10^-27 kg C) 3.2 × 10^-27 kg D) 5.4 × 10^-32 kg E) 9.0 × 10^-36 kg

Accepted Answer

The answer of In a certain chemical reaction, 8.1 ×...

Question 17

An alpha particle has a mass of 6.64 × 10^-27 kg and a charge of 3.20 × 10^-19 C, and it is traveling at 0.9650c. (c = 3.00 × 10⁸ m/s), 1 eV = 1.60 × 10^-19 J) (a) What is its rest energy (in GeV)? (b) What is its total energy (in GeV)? (c) What is its kinetic energy (in GeV)?

Accepted Answer

The answer of An alpha particle has a mass of...

Question 18

How many MeV of energy is released during a reaction in which 1.67 × 10^-25 kg of material is converted to energy? (c = 3.0 × 10⁸ m/s, 1 eV = 1.67 × 10^-19 J) A) 5.0 × 10^-14 MeV B) 4.1 × 10^-7 MeV C) 3.1 × 10^-4 MeV D) 9.4 × 10⁴ MeV

Accepted Answer

The equation E=mc^2 relates energy (E) to mass (m) and the speed of light (c). We are given the mass (1.67 × 10^-25 kg) that is converted to energy, so we can use this equation to calculate the energy released:

E = (1.67 × 10^-25 kg) * (3.0 × 10^8 m/s)^2
E = 1.503 × 10^-8 J

To convert J to MeV, we divide by the conversion factor 1.67 × 10^-19 J/MeV:

E = (1.503 × 10^-8 J) / (1.67 × 10^-19 J/MeV)
E = 89.88 MeV

Therefore, the answer is D, 9.4 × 10^14 MeV.

Question 19

How much mass is lost during a reaction in which 1.7 × 10⁸ MeV of energy is released? (c = 3.0 × 10⁸ m/s, 1 eV = 1.6 × 10^-19 J) A) 1.8 × 10^-8 kg B) 5.7 × 10^-9 kg C) 1.9 × 10^-17 kg D) 3.0 × 10^-22 kg

Accepted Answer

The answer of How much mass is lost during a...

Question 20

How many joules of energy are required to accelerate a 1.0-kg rock from rest to a speed of 0.866c? (c = 3.0 × 10⁸ m/s) A) 1.8 × 10¹⁷ J B) 9.0 × 10¹⁶ J C) 3.0 × 10³ J D) 3.3 × 10¹⁶ J

Accepted Answer

The answer of How many joules of energy are required...

Quiz 27: Relativity

How much energy would be required to accelerate a 77-kg professor from rest to 90% the speed of light? (c = 3.0 × 108 m/s)

A person with an initial mass of 70 kg climbs a stairway and thereby rises 6.0 m in elevation. By how much does his mass increase by virtue of his increased potential energy? (c = 3.0 × 108 m/s)

An electron has a speed of 0.783c. Through what potential difference would the electron need to be accelerated from rest in order to reach this speed? The rest mass energy of an electron is 0.511 MeV.

If the kinetic energy of a particle is 3.00 times its rest energy, the speed of the particle is closest to which of the following values?

If, instead of the correct formula for kinetic energy, we carelessly use the classical expression for kinetic energy for a particle moving at half the speed of light, by what magnitude percent will our calculation be in error? (c = 3.0 × 108 m/s)

In a nuclear plant, 1017 J of energy is available from mass conversion. How much mass of fuel was lost to produce this energy? (c = 3.0 × 108 m/s)

During a reaction, 170 µJ of energy is released. What change of mass would accompany this release? (c = 3.0 × 108 m/s)

How much energy would be released if 2.0 kg of material was lost during a reaction? (c = 3.0 × 108 m/s)

During a reaction, a reactant loses 4.8 × 10-28 kg of mass. How many joules of energy are released? (c = 3.0 × 108 m/s)

An electron-volt is the energy gained by an electron if it is accelerated through a potential difference of one volt. What is the equivalent to an electron-volt in kilograms? (c = 3.00 × 108 m/s, e = 1.60 × 10-19C)

Consider a student whose mass is 70 kg. If all his mass were converted to electrical energy, for how many years could he keep a 100-W light bulb burning? (c = 3.0 × 108 m/s)

A space barge pushes on a spaceship with a rest mass of 15,000 kg and accelerates it from a speed of 0.600c to a speed of 0.700c. How much work does the barge have to do to accomplish this? (c = 3.00 × 108 m/s)

If the mass of a 1.0-kg book could be entirely converted into electrical energy, how many kW ∙ h of energy would that generate? (c = 3.0 × 108 m/s)

In a certain chemical reaction, 8.1 × 10-19 J of energy is released per molecule formed. What is the difference in mass per molecule between the sum of the masses of the molecules of the reagents before the reaction and the mass of the molecules produced by the reaction? (c = 3.0 × 108 m/s)

An alpha particle has a mass of 6.64 × 10-27 kg and a charge of 3.20 × 10-19 C, and it is traveling at 0.9650c. (c = 3.00 × 108 m/s), 1 eV = 1.60 × 10-19 J) (a) What is its rest energy (in GeV)? (b) What is its total energy (in GeV)? (c) What is its kinetic energy (in GeV)?

How many MeV of energy is released during a reaction in which 1.67 × 10-25 kg of material is converted to energy? (c = 3.0 × 108 m/s, 1 eV = 1.67 × 10-19 J)

How much mass is lost during a reaction in which 1.7 × 108 MeV of energy is released? (c = 3.0 × 108 m/s, 1 eV = 1.6 × 10-19 J)

How many joules of energy are required to accelerate a 1.0-kg rock from rest to a speed of 0.866c? (c = 3.0 × 108 m/s)

How much energy would be required to accelerate a 77-kg professor from rest to 90% the speed of light? (c = 3.0 × 10⁸ m/s)

A person with an initial mass of 70 kg climbs a stairway and thereby rises 6.0 m in elevation. By how much does his mass increase by virtue of his increased potential energy? (c = 3.0 × 10⁸ m/s)

If, instead of the correct formula for kinetic energy, we carelessly use the classical expression for kinetic energy for a particle moving at half the speed of light, by what magnitude percent will our calculation be in error? (c = 3.0 × 10⁸ m/s)

In a nuclear plant, 10¹⁷ J of energy is available from mass conversion. How much mass of fuel was lost to produce this energy? (c = 3.0 × 10⁸ m/s)

During a reaction, 170 µJ of energy is released. What change of mass would accompany this release? (c = 3.0 × 10⁸ m/s)

How much energy would be released if 2.0 kg of material was lost during a reaction? (c = 3.0 × 10⁸ m/s)

During a reaction, a reactant loses 4.8 × 10^-28 kg of mass. How many joules of energy are released? (c = 3.0 × 10⁸ m/s)

An electron-volt is the energy gained by an electron if it is accelerated through a potential difference of one volt. What is the equivalent to an electron-volt in kilograms? (c = 3.00 × 10⁸ m/s, e = 1.60 × 10^-19C)

Consider a student whose mass is 70 kg. If all his mass were converted to electrical energy, for how many years could he keep a 100-W light bulb burning? (c = 3.0 × 10⁸ m/s)

A space barge pushes on a spaceship with a rest mass of 15,000 kg and accelerates it from a speed of 0.600c to a speed of 0.700c. How much work does the barge have to do to accomplish this? (c = 3.00 × 10⁸ m/s)

If the mass of a 1.0-kg book could be entirely converted into electrical energy, how many kW ∙ h of energy would that generate? (c = 3.0 × 10⁸ m/s)

In a certain chemical reaction, 8.1 × 10^-19 J of energy is released per molecule formed. What is the difference in mass per molecule between the sum of the masses of the molecules of the reagents before the reaction and the mass of the molecules produced by the reaction? (c = 3.0 × 10⁸ m/s)

An alpha particle has a mass of 6.64 × 10^-27 kg and a charge of 3.20 × 10^-19 C, and it is traveling at 0.9650c. (c = 3.00 × 10⁸ m/s), 1 eV = 1.60 × 10^-19 J) (a) What is its rest energy (in GeV)? (b) What is its total energy (in GeV)? (c) What is its kinetic energy (in GeV)?

How many MeV of energy is released during a reaction in which 1.67 × 10^-25 kg of material is converted to energy? (c = 3.0 × 10⁸ m/s, 1 eV = 1.67 × 10^-19 J)

How much mass is lost during a reaction in which 1.7 × 10⁸ MeV of energy is released? (c = 3.0 × 10⁸ m/s, 1 eV = 1.6 × 10^-19 J)

How many joules of energy are required to accelerate a 1.0-kg rock from rest to a speed of 0.866c? (c = 3.0 × 10⁸ m/s)