Deck 26: Relativity

Question 1

According to special relativity, what is the speed of light measured in a spaceship traveling at $0.40 \mathrm{c}$ ?

A) $0.86 \mathrm{c}$
B) $0.60 \mathrm{c}$
C) $1.0 \mathrm{c}$
D) $1.4 \mathrm{c}$
E) None of these choices are correct.

Answer 1

$1.0 \mathrm{c}$

Question 2

What is the Lorentz factor $\gamma$ for a speed of $0.800 \mathrm{c}$ ?

A) 0.360
B) 0.600
C) 1.67
D) 0.800
E) 1.25

Answer 2

1.67

Question 3

At what speed would a clock be moving if time dilation caused it to run slow by $50 \%$ ?

A) $0.866 \mathrm{c}$
B) $0.500 \mathrm{c}$
C) $0.414 \mathrm{c}$
D) $0.250 \mathrm{c}$
E) $0.750 \mathrm{c}$

Answer 3

$0.866 \mathrm{c}$

Question 4

Radioactive particles moving at $0.80 \mathrm{c}$ are measured to have a half-life of $4.3 \times 10^{-8} \mathrm{~s}$ . What is their half-life when at rest?

A) $1.7 \times 10^{-7} \mathrm{~s}$
B) $7.2 \times 10^{-8} \mathrm{~s}$
C) $3.4 \times 10^{-8} \mathrm{~s}$
D) $2.6 \times 10-8 \mathrm{~s}$
E) $1.6 \times 10^{-8} \mathrm{~s}$

Question 5

The mean lifetime of muons is $2.2 \mu \mathrm{s}$ . How fast are they moving if their measured mean lifetime is $1.1 \mu \mathrm{s}$ ?

A) $0.56 \mathrm{c}$
B) $0.50 \mathrm{c}$
C) $0.94 \mathrm{c}$
D) $0.87 \mathrm{c}$
E) This cannot happen.

Question 6

What speed is required for a length to contract to $80 \%$ of its proper length?

A) $0.20 \mathrm{c}$
B) $0.40 \mathrm{c}$
C) $0.50 \mathrm{c}$
D) $0.60 \mathrm{c}$
E) $0.80 \mathrm{c}$

Question 7

If a spaceship of proper length $40 \mathrm{~m}$ is measured to have a length $30 \mathrm{~m}$ , how fast is it moving?

A) $0.75 \mathrm{c}$
B) $0.66 \mathrm{c}$
C) $0.43 \mathrm{c}$
D) $0.81 \mathrm{c}$
E) $0.50 \mathrm{c}$

Question 8

Two cars are traveling down the highway in the same direction. Car A is traveling at $30.0 \mathrm{~m} / \mathrm{s}$ and car B is passing car A at a relative speed of $3.0 \mathrm{~m} / \mathrm{s}$ . Using Galilean relativity to calculate the speed of car B relative to the highway results in an answer that is incorrect by how much?

A) $3.3 \times 10^{-5} \mathrm{~m} / \mathrm{s}$
B) $3.3 \times 10-11 \mathrm{~m} / \mathrm{s}$
C) $3.3 \times 10-14 \mathrm{~m} / \mathrm{s}$
D) $3.3 \times 10^{-2} \mathrm{~m} / \mathrm{s}$
E) $3.3 \times 10^{-8} \mathrm{~m} / \mathrm{s}$

Question 9

What is the magnitude of the momentum of a proton moving at $0.95 \mathrm{c}$ ? $\left(\mathrm{m}_{\mathrm{p}}=1.67 \times 10-27 \mathrm{~kg}\right)$

A) $4.4 \times 10-18 \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}$
B) $1.5 \times 10-18 \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}$
C) $9.5 \times 10-18 \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}$
D) $4.8 \times 10-18 \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}$
E) $5.0 \times 10-18 \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}$

Question 10

If a proton has a kinetic energy of $1.000 \mathrm{GeV}$ , what is its momentum? $\left(m_{p}=938.3 \mathrm{MeV} / \mathrm{c}^{2}\right)$

A) $938.0 \mathrm{GeV} / \mathrm{c}$
B) $1.938 \mathrm{GeV} / \mathrm{c}$
C) $1.000 \mathrm{GeV} / \mathrm{c}$
D) $1.696 \mathrm{GeV} / \mathrm{c}$
E) $2.872 \mathrm{GeV} / \mathrm{c}$

Question 11

At what speed is the relativistic momentum five times the value calculated classically?

A) $0.80 \mathrm{c}$
B) $0.99 \mathrm{c}$
C) $0.98 \mathrm{c}$
D) $0.96 \mathrm{c}$
E) $0.20 \mathrm{c}$

Question 12

How much mass must be converted to energy to release one million kilowatt-hours?

A) $4.0 \mathrm{~g}$
B) $3.6 \times 10^{-12} \mathrm{~g}$
C) $3.6 \times 10^{-6} \mathrm{~g}$
D) $40 \mu \mathrm{g}$
E) $40 \mathrm{pg}$

Question 13

Tritium ( $3 \mathrm{H}$ ) decays to $3 \mathrm{He}$ releasing $18.6 \mathrm{keV}$ of energy. How much mass is converted into energy during this process?

A) $2.07 \times 10^{-13} \mathrm{~kg}$
B) $2.07 \times 10^{-10} \mathrm{~kg}$
C) $3.31 \times 10^{-32} \mathrm{~kg}$
D) $3.31 \times 10^{-29} \mathrm{~kg}$
E) $2.07 \times 1010^{-16} \mathrm{~kg}$

Question 14

How much energy is released in a nuclear reactor if the total mass of the fuel decreases by $1.0 \mathrm{~g}$ ?

A) $9.0 \times 1013 \mathrm{~J}$
B) $3.0 \times 1011 \mathrm{~J}$
C) $3.0 \times 1014 \mathrm{~J}$
D) $9.0 \times 1014 \mathrm{~J}$

Question 15

How fast is a particle moving if its kinetic energy is equal to its rest energy?

A) 0.00
B) $0.75 \mathrm{c}$
C) $0.50 \mathrm{c}$
D) $0.57 \mathrm{c}$
E) $0.87 \mathrm{c}$

Question 16

In a radioactive decay, $2.37 \times 10^{-3} \mathrm{u}$ are converted into kinetic energy. How much kinetic energy is this? ( $1 \mathrm{u}$ $=1.66 \times 10^{-27} \mathrm{~kg})$

A) $3.93 \times10^{30} \mathrm{~J}$
B) $2.13 \times 10^{14} \mathrm{~J}$
C) $3.54 \times 10^{-13} \mathrm{~J}$
D) $9.31 \times 10^{8} \mathrm{~J}$
E) $1.60 \times 10^{-13} \mathrm{~J}$

Question 17

An electron has a rest energy of $0.511 \mathrm{MeV}$ . At what speed would its kinetic energy equal $1.022 \mathrm{MeV}$ ?

A) $0.866 \mathrm{c}$
B) $0.500 \mathrm{c}$
C) $0.943 \mathrm{c}$
D) $0.971 \mathrm{c}$
E) $0.888 \mathrm{c}$

Question 18

If a proton has a kinetic energy of $1.000 \mathrm{GeV}$ , what is its speed? $\left(m_{p}=938 \mathrm{MeV} / \mathrm{c}^{2}\right)$

A) $0.343 \mathrm{c}$
B) 0.766 c
C) $0.586 \mathrm{c}$
D) $0.875 \mathrm{c}$
E) $0.935 \mathrm{c}$

Question 19

If the momentum of an electron is $1.53 \mathrm{MeV} / \mathrm{c}$ , what is its kinetic energy? The rest energy of an electron is $511 \mathrm{keV}$ .

A) $1.10 \mathrm{MeV}$
B) $1.44 \mathrm{MeV}$
C) $1.02 \mathrm{MeV}$
D) $1.53 \mathrm{MeV}$
E) $2.59 \mathrm{MeV}$

Question 20

An electron is accelerated from rest through a potential difference of $1.0 \mathrm{MV}$ . If the rest energy of the electron is $0.511 \mathrm{MeV}$ , how fast is the electron moving?

A) $0.30 \mathrm{c}$
B) $0.67 \mathrm{c}$
C) $0.57 \mathrm{c}$
D) $0.90 \mathrm{c}$
E) $0.94 \mathrm{c}$

Question 21

Calculate the speed of a beam of neutrons with kinetic energies of $1.0 \mathrm{MeV}$ . The mass of a neutron is 940 $\mathrm{MeV} / \mathrm{c}^{2}$ .

A) $9.8 \times 106 \mathrm{~m} / \mathrm{s}$
B) $1.4 \times 10^{7} \mathrm{~m} / \mathrm{s}$
C) $640 \mathrm{~km} / \mathrm{s}$
D) $799 \mathrm{~m} / \mathrm{s}$

Question 22

expression used for momentum, $p=m v$ ,

A) is correct, provided we properly understand v.
B) always gives too high a value for $p$ .
C) is a good high-velocity approximation.
D) is a good low-velocity approximation.