fizikzauglom

GRADE 11 PRACTICE

Physics Problems: Special relativity, Grade 11

Relativistic mass, time and length.

11 problems across 2 sub-topics
Practise in the interactive mode

Here the conditions and analysis of the solution can be read without an account. In the simulator, you need to collect the same analyzes yourself: “Given,” formulas, order of steps and answer.

Problem statements

The answer options are there to check against, and the walkthrough opens under each problem.

11 problems
Position in this set: 1 from 11

Problem #54

Fundamentals of Special Relativity

How far will light travel in a vacuum in an hour?

Answer options

  1. 5{,}4 \cdot 10^{11}\,\text{м}
  2. 2{,}16 \cdot 10^{12}\,\text{м}
  3. 1{,}08 \cdot 10^{13}\,\text{м}
  4. 1{,}08 \cdot 10^{12}\,\text{м}
Show the walkthroughHide the walkthrough
Given
t
1\,\text{ч}3600\,\text{с}
c
3\cdot 10^{8}\,\text{м/с}
Find

S

  1. S = ctS = 3\cdot 10^{8}\cdot 3600S = 1{,}08\cdot 10^{12}\,\text{м} = 1{,}08\cdot 10^{9}\,\text{км}

    The speed of light is the maximum speed at which interaction can be transmitted.

AnswerS = 1{,}08\cdot 10^{12}\,\text{м}

Position in this set: 2 from 11

Problem #57

Fundamentals of Special Relativity

At what speed of a moving clock does 2 times more time pass between its two signals in the laboratory frame of reference than according to this clock? Inertial reference systems.

Answer options

  1. 5{,}2 \cdot 10^{8}\,\text{м/с}
  2. 2{,}6 \cdot 10^{9}\,\text{м/с}
  3. 2{,}6 \cdot 10^{8}\,\text{м/с}
  4. 1{,}3 \cdot 10^{8}\,\text{м/с}
Show the walkthroughHide the walkthrough
Given
\tau
2\tau_0
c
3\cdot 10^{8}\,\text{м/с}
Find

v

  1. \tau = \dfrac{\tau_0}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}\ \Rightarrow\ 2\tau_0 = \dfrac{\tau_0}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}\sqrt{1 - \dfrac{v^{2}}{c^{2}}} = \dfrac{1}{2}
  2. 1 - \dfrac{v^{2}}{c^{2}} = \dfrac{1}{4}\ \Rightarrow\ v^{2} = 0{,}75c^{2}v = \sqrt{0{,}75}\,c = 0{,}866\cdot 3\cdot 10^{8}v = 2{,}6\cdot 10^{8}\,\tfrac{\text{м}}{\text{с}}

Answerv = 2{,}6\cdot 10^{8}\,\tfrac{\text{м}}{\text{с}}

Position in this set: 3 from 11

Problem #58

Fundamentals of Special Relativity

Burnt out 100\,\text{г} gunpowder with specific heat of combustion 10^{7}\,\text{Дж/кг}. All released energy is transferred to the bullet. Find the increase in E/c² for the bullet, where E is its total energy. This is the energy equivalent of the energy transferred; The rest mass of the bullet does not change during acceleration.

Answer options

  1. 5{,}5 \cdot 10^{-12}\,\text{кг}
  2. 2{,}2 \cdot 10^{-11}\,\text{кг}
  3. 1{,}1 \cdot 10^{-10}\,\text{кг}
  4. 1{,}1 \cdot 10^{-11}\,\text{кг}
Show the walkthroughHide the walkthrough
Given
m
100\,\text{г}0{,}1\,\text{кг}
q
10^{7}\,\tfrac{\text{Дж}}{\text{кг}}
c
3\cdot 10^{8}\,\text{м/с}
Find

\Delta m

  1. \Delta E = Q = mq\Delta E = 0{,}1\cdot 10^{7}\Delta E = 10^{6}\,\text{Дж}
  2. \Delta m = \dfrac{\Delta E}{c^{2}} = \dfrac{mq}{c^{2}}\Delta m = \dfrac{0{,}1\cdot 10^{7}}{\left(3\cdot 10^{8}\right)^{2}}\Delta m = 1{,}1\cdot 10^{-11}\,\text{кг}

    This is the increase in E/c², traditionally called the increase in relativistic mass. An increase in kinetic energy does not change the rest mass of the bullet.

Answer\Delta m = 1{,}1\cdot 10^{-11}\,\text{кг}

Position in this set: 4 from 11

Problem #59

Fundamentals of Special Relativity

The first satellite had a mass 80\,\text{кг} and flew at speed 8\,\text{км/с}. By how much did its relativistic mass increase?

Answer options

  1. 2{,}84 \cdot 10^{-8}\,\text{кг}
  2. 1{,}42 \cdot 10^{-8}\,\text{кг}
  3. 5{,}68 \cdot 10^{-8}\,\text{кг}
  4. 2{,}84 \cdot 10^{-7}\,\text{кг}
Show the walkthroughHide the walkthrough
Given
m
80\,\text{кг}
v
8\,\tfrac{\text{км}}{\text{с}}8000\,\text{м/с}
c
3\cdot 10^{8}\,\text{м/с}
Find

\Delta m

  1. \Delta E = E_{\text{к}} = \dfrac{mv^{2}}{2}\Delta E = \dfrac{80\cdot 8000^{2}}{2}\Delta E = 2{,}56\cdot 10^{9}\,\text{Дж}
  2. \Delta m = \dfrac{\Delta E}{c^{2}} = \dfrac{mv^{2}}{2c^{2}}\Delta m = \dfrac{80\cdot 8000^{2}}{2\cdot\left(3\cdot 10^{8}\right)^{2}}\Delta m = 2{,}84\cdot 10^{-8}\,\text{кг} = 2{,}84\cdot 10^{-2}\,\text{мг}

Answer\Delta m = 2{,}84\cdot 10^{-8}\,\text{кг}

Position in this set: 5 from 11

Problem #60

Fundamentals of Special Relativity

Find the magnitude of the accelerating voltage, after passing which the total energy of the initially resting electron will become 4 times greater than its rest energy.

Answer options

  1. 1{,}53 \cdot 10^{7}\,\text{В}
  2. 1{,}53 \cdot 10^{6}\,\text{В}
  3. 7{,}65 \cdot 10^{5}\,\text{В}
  4. 3{,}06 \cdot 10^{6}\,\text{В}
Show the walkthroughHide the walkthrough
Given
m
4m_0
m_0
9{,}1\cdot 10^{-31}\,\text{кг}
\left|q\right|
e = 1{,}6\cdot 10^{-19}\,\text{Кл}
c
3\cdot 10^{8}\,\text{м/с}
Find

U

  1. \Delta m = m - m_0 = 3m_0\Delta m = 3\cdot 9{,}1\cdot 10^{-31}\Delta m = 2{,}73\cdot 10^{-30}\,\text{кг}
  2. \Delta E = \Delta m\,c^{2}\Delta E = 2{,}73\cdot 10^{-30}\cdot 9\cdot 10^{16}\Delta E = 2{,}457\cdot 10^{-13}\,\text{Дж}
  3. \Delta E = A = \left|q\right|U\ \Rightarrow\ U = \dfrac{\Delta E}{\left|q\right|}U = \dfrac{2{,}457\cdot 10^{-13}}{1{,}6\cdot 10^{-19}}U = 1{,}54\cdot 10^{6}\,\text{В}

AnswerU = 1{,}54\cdot 10^{6}\,\text{В}

Position in this set: 6 from 11

Problem #134

Relativistic effects

Object mass 0{,}001 kg. Find the rest energy at c = 300000000 m/s.

Answer options

  1. 90000000000000\,\text{Дж}
  2. 180000000000000\,\text{Дж}
  3. 45000000000000\,\text{Дж}
  4. 270000000000000\,\text{Дж}
Show the walkthroughHide the walkthrough
Given
m
0{,}001\,\text{кг}
c
300000000\,\text{м/с}
Find

E_0

  1. E_0=mc^2E_0=0{,}001 \cdot {300000000}^{2}E_0=90000000000000\,\text{Дж}

    Rest energy is inherent in the body even without movement.

Answer90000000000000\,\text{Дж}

Position in this set: 7 from 11

Problem #135

Relativistic effects

Object mass 0{,}002 kg. Find the rest energy at c = 300000000 m/s.

Answer options

  1. 360000000000000\,\text{Дж}
  2. 180000000000000\,\text{Дж}
  3. 90000000000000\,\text{Дж}
  4. 540000000000000\,\text{Дж}
Show the walkthroughHide the walkthrough
Given
m
0{,}002\,\text{кг}
c
300000000\,\text{м/с}
Find

E_0

  1. E_0=mc^2E_0=0{,}002 \cdot {300000000}^{2}E_0=180000000000000\,\text{Дж}

    Rest energy is inherent in the body even without movement.

Answer180000000000000\,\text{Дж}

Position in this set: 8 from 11

Problem #136

Relativistic effects

Own process time 4 s. System speed is 0{,}6 from the speed of light. Find the duration in the laboratory system.

Answer options

  1. 10\,\text{с}
  2. 5\,\text{с}
  3. 2{,}5\,\text{с}
  4. 15\,\text{с}
Show the walkthroughHide the walkthrough
Given
t
4\,\text{с}
b
0{,}6\,\text{доля c}
Find

T

  1. k=\sqrt{1-\beta^2}k=\sqrt{1 - {0{,}6}^{2}}k=0{,}8\,\text{безразм.}

    β = v/c is less than one.

  2. T=\frac{t}{\sqrt{1-\beta^2}}T=\frac{4}{0{,}8}T=5\,\text{с}

    Laboratory duration is longer than your own time.

Answer5\,\text{с}

Position in this set: 9 from 11

Problem #137

Relativistic effects

Own process time 6 s. System speed is 0{,}8 from the speed of light. Find the duration in the laboratory system.

Answer options

  1. 20\,\text{с}
  2. 5\,\text{с}
  3. 10\,\text{с}
  4. 30\,\text{с}
Show the walkthroughHide the walkthrough
Given
t
6\,\text{с}
b
0{,}8\,\text{доля c}
Find

T

  1. k=\sqrt{1-\beta^2}k=\sqrt{1 - {0{,}8}^{2}}k=0{,}6\,\text{безразм.}

    β = v/c is less than one.

  2. T=\frac{t}{\sqrt{1-\beta^2}}T=\frac{6}{0{,}6}T=10\,\text{с}

    Laboratory duration is longer than your own time.

Answer10\,\text{с}

Position in this set: 10 from 11

Problem #138

Relativistic effects

Particle rest energy 3 MeV, the speed is 0{,}8 from the speed of light. Find the kinetic energy.

Answer options

  1. 4\,\text{МэВ}
  2. 1\,\text{МэВ}
  3. 2\,\text{МэВ}
  4. 6\,\text{МэВ}
Show the walkthroughHide the walkthrough
Given
E
3\,\text{МэВ}
b
0{,}8\,\text{доля c}
Find

K

  1. k=\sqrt{1-\beta^2}k=\sqrt{1 - {0{,}8}^{2}}k=0{,}6\,\text{безразм.}

    Find the factor in the denominator.

  2. W=\frac{E_0}{k}W=\frac{3}{0{,}6}W=5\,\text{МэВ}

    This is the total energy of a moving particle.

  3. K=W-E_0K=5 - 3K=2\,\text{МэВ}

    Subtract the rest energy.

Answer2\,\text{МэВ}

Position in this set: 11 from 11

Problem #139

Relativistic effects

Particle rest energy 6 MeV, the speed is 0{,}6 from the speed of light. Find the kinetic energy.

Answer options

  1. 3\,\text{МэВ}
  2. 0{,}75\,\text{МэВ}
  3. 4{,}5\,\text{МэВ}
  4. 1{,}5\,\text{МэВ}
Show the walkthroughHide the walkthrough
Given
E
6\,\text{МэВ}
b
0{,}6\,\text{доля c}
Find

K

  1. k=\sqrt{1-\beta^2}k=\sqrt{1 - {0{,}6}^{2}}k=0{,}8\,\text{безразм.}

    Find the factor in the denominator.

  2. W=\frac{E_0}{k}W=\frac{6}{0{,}8}W=7{,}5\,\text{МэВ}

    This is the total energy of a moving particle.

  3. K=W-E_0K=7{,}5 - 6K=1{,}5\,\text{МэВ}

    Subtract the rest energy.

Answer1{,}5\,\text{МэВ}

The theory behind these problems

Work through the topic if a problem will not give in.

Relativistic effectsChanges in mass, clock rates and length at high speeds.