Energy and Mass Flashcards
Show how the mass m of a particle changes from its rest mass m0 as its speed v increases from zero
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 )
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.
Energy = mc2 so as vc energy of particle increases as mass increases. Massinfinity as vc so energy infinity which is physically impossible. Force=ma so force increases as mass increases, Massinfinity as vc so forceinfinity which is impossible
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.
As speedc massinfinity. 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 «_space;c
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. –
as vc m infinity v=c would require infinite kinetic energy =c^2(m-m0) which is physically impossible
By considering the law of conservation of momentum in different inertial frames of reference, Einstein shows that relativistic mass =
m = ym0
m = relativistic mass m0 = rest mass = mass of body in own inertial reference frame = mass of body when at rest
Relativistic mass equation shows that when speed increases… however…
mass increases
However this is only noticeable when v is close to c, when v «_space;c then m = m0
What does it mean if the mass increases
- doesn’t mean the amount of matter increases
- means the force needed to cause the object to accelerate further becomes larger
Why v never reach c
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.
Energy =
mc^2 = m0yc^2 therefore energy and mass are equivalent and interchangeable
As energy is supplied to an object…
As energy is removed from an object
However
its mass increases
its mass decreases
However the change is usually too small to measure
What are the applications of Einstein’s E=mc^2
Large amounts of energy can be gained from a small mass at high speeds therefore has applications in nuclear fission, power and weapons
Graph of m/m0 y axis and v/c x axis
Cuts 1 on y axis
Horizontal until about x = 0.9 y = 2 then increases rapidly with limit at x=1
Graph of m y axis v x axis
Cuts y axis at m0
Horizontal until about x = 0.9c y = 2m0 then increases rapidly with limit at x = c
Rest energy E0 =
m0c^2
E = ym0c^2
When v=0 y =1
E0 = m0c^2
For a moving mass at speed v, the difference between its total energy and its rest energy represents its
energy due to its speed i.e. its kinetic energy