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Momentum and Mass Is Mass a Relative Quantity???

Momentum and Mass Is Mass a Relative Quantity???. By Connie Wong. Momentum. Classical momentum: p = m o v  For speeds much less than the speed of light Relativistic momentum: p = m o v/ ( √1- v 2 /c 2 )  For speeds closer to the speed of light. Mass. p = m o v/ ( √1- v 2 /c 2 )

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Momentum and Mass Is Mass a Relative Quantity???

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  1. Momentum and MassIs Mass a Relative Quantity??? By Connie Wong

  2. Momentum Classical momentum: p = mov  For speeds much less than the speed of light Relativistic momentum: p = mov/ (√1- v2/c2)  For speeds closer to the speed of light

  3. Mass p = mov/ (√1- v2/c2) The equation of relativistic momentum suggests a relativistic interpretation of mass Mass is Relative!

  4. Mass Increase Formula The mass of an object is measured to increase as its speed increases: m = mo/ (√1- v2/c2) mo = the rest mass of the object, the mass it has as measured in a reference frame in which it is at rest m = the relativistic mass, the mass it will be measured to have in a reference frame in which it moves at speed v

  5. Whiteboards: 1. Calculate the mass of an electron when it has a speed of a) 4.00E7 m/s in the CRT of a TV set, and b) 0.98c in an accelerator used for cancer therapy. mo of an electron: 9.11 E-31kg m = mo/ (√1- v2/c2)

  6. 1. Calculate the mass of an electron when it has a speed of a) 4.00E7 m/s in the CRT of a TV set, and b) 0.98c in an accelerator used for cancer therapy. • v = 4.00E7m/s, mo = 9.11E-31kg, c = 3.00E8m/s • m = mo / (√1- v2/c2) • m = 9.11E-31 / (√1- (4.00E7)2/ (3.00E8)2 • m = 9.19E-31 kg • b) v = 0.98c, mo = 9.11E-31kg, c = 3.00E8m/s • m = mo/ (√1- (0.98c)2/ c2) • m = 5.0mo = Five times its rest mass! • m = 4.56E-30kg

  7. More Whiteboards: • What is the mass of a proton traveling at v = 0.75c? Rest mass of proton= 1.673E-27kg m = mo/ (√1- v2/c2) m = 1.673E-27/ (√1- (0.75c)2/c2) m = 2.53E-27kg

  8. At what speed v will the mass of an object be 15 percent greater than its rest mass? m = mo/ (√1- v2/c2) v = ? 1.15mo = mo/ (√1- v2/c2) 1.15mo* (√1- v2/c2)= mo ...mo cancels... √1- v2/c2 = 1/1.15 ...solve for v... v = 1.48E8m/s or 0.494c

  9. The Ultimate Speed m = mo/ (√1- v2/c2) As v increases, the mass of the object becomes larger and larger. If v = c, the denominator would equal zero and mass would be infinite. To accelerate an object up to v = c would require infinite energy, which is impossible. Thus: the speed of an object cannot equal or exceed the speed of light.

  10. The End

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