Energy and Mass

Question 1

Show how the mass m of a particle changes from its rest mass m0 as its speed v increases from zero

Answer 1

There must be visible white space between the curve and the v = c line; also, the curve must reach 7mo at least. curve is asymptotic at v = c ( and does not cross or touch v =c or curve back )

Question 2

By considering the relationship between the energy of a particle and its mass, explain why the theory of special relativity does not allow a matter particle to travel as fast as light.

Answer 2

Energy = mc2 so as vc energy of particle increases as mass increases. Massinfinity as vc so energy infinity which is physically impossible. Force=ma so force increases as mass increases, Massinfinity as vc so forceinfinity which is impossible

Question 3

The speed of an object cannot be greater than or equal to the speed of light yet its kinetic energy can be increased without limit. Explain the apparent contradiction that the speed of an object is limited whereas its kinetic energy is not limited.

Answer 3

As speedc massinfinity. Gain of EK causes large gain of mass when speed is close to c. Gain of EK causes small gain of speed when speed is close to c. EK = 0.5mv2 valid at speeds &laquo_space;c

Question 4

Explain why a matter particle can not travel as fast as a photon in free space even though its kinetic energy can be increased without limit. –

Answer 4

as vc m infinity v=c would require infinite kinetic energy =c^2(m-m0) which is physically impossible

Question 5

By considering the law of conservation of momentum in different inertial frames of reference, Einstein shows that relativistic mass =

Answer 5

m = ym0

m = relativistic mass
m0 = rest mass = mass of body in own inertial reference frame = mass of body when at rest

Question 6

Relativistic mass equation shows that when speed increases… however…

Answer 6

mass increases

However this is only noticeable when v is close to c, when v &laquo_space;c then m = m0

Question 7

What does it mean if the mass increases

Answer 7

• doesn’t mean the amount of matter increases

- means the force needed to cause the object to accelerate further becomes larger

Question 8

Why v never reach c

Answer 8

As v–>c , m–>infinity so no amount of additional force can accelerate the mass further - the work required for v to equal c is infinite and therefore no object that has a mass can ever reach c

No material object can ever reach the speed of light as its mass would become infinite and therefore can never travel faster than light and so c is the ultimate cosmic speed limit.

Question 9

Energy =

Answer 9

mc^2 = m0yc^2 therefore energy and mass are equivalent and interchangeable

Question 10

As energy is supplied to an object…
As energy is removed from an object
However

Answer 10

its mass increases
its mass decreases

However the change is usually too small to measure

Question 11

What are the applications of Einstein’s E=mc^2

Answer 11

Large amounts of energy can be gained from a small mass at high speeds therefore has applications in nuclear fission, power and weapons

Question 12

Graph of m/m0 y axis and v/c x axis

Answer 12

Cuts 1 on y axis

Horizontal until about x = 0.9 y = 2 then increases rapidly with limit at x=1

Question 13

Graph of m y axis v x axis

Answer 13

Cuts y axis at m0

Horizontal until about x = 0.9c y = 2m0 then increases rapidly with limit at x = c

Question 14

Rest energy E0 =

Answer 14

m0c^2

E = ym0c^2
When v=0 y =1
E0 = m0c^2

Question 15

For a moving mass at speed v, the difference between its total energy and its rest energy represents its

Answer 15

energy due to its speed i.e. its kinetic energy

Question 16

Kinetic energy, Ek =

Answer 16

Total energy - rest energy
E - E0
mc^2 - m0c^2
m0yc^2 - m0c^2
m0c^2(y-1)

Question 17

As speed increases…

Answer 17

kinetic energy increases but only noticeable near c therefore if speed increases then kinetic energy increases and so mass increases

therefore mass increases with speed and kinetic energy

Question 18

Ek graph classical and relative and explain

Answer 18

Usual shape graph for Ek (y) v (x) for relativity while for classical increases much slower and beyond c

As v–>c , Einstein’s theory predicts kinetic energy increases much more rapidly than classical kinetic energy as predicted by Newton’s classical mechanics approach of 0.5mv^2
For this reason do not use 0.5mv^2 at relativistic speeds

Question 19

Mass of 1kg =…J

1u =…MeV

Answer 19

9x10^5

932

Question 20

DO NOT USE 0.5MV^2 AT RELATIVISTIC SPEEDS

Answer 20

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