Momentum and Mass Is Mass a Relative Quantity

Momentum and Mass Is Mass a Relative Quantity? ? ? By Connie Wong

Momentum Classical momentum: p = mo v For speeds much less than the speed of light Relativistic momentum: p = mov/ (√ 1 - v 2/c 2) For speeds closer to the speed of light

Mass p = mov/ (√ 1 - v 2/c 2) The equation of relativistic momentum suggests a relativistic interpretation of mass Mass is Relative!

Mass Increase Formula The mass of an object is measured to increase as its speed increases: m = mo/ (√ 1 - v 2/c 2) 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

Whiteboards: 1. Calculate the mass of an electron when it has a speed of a) 4. 00 E 7 m/s in the CRT of a TV set, and b) 0. 98 c in an accelerator used for cancer therapy. mo of an electron: 9. 11 E-31 kg m = mo/ (√ 1 - v 2/c 2)

1. Calculate the mass of an electron when it has a speed of a) 4. 00 E 7 m/s in the CRT of a TV set, and b) 0. 98 c in an accelerator used for cancer therapy. a) v = 4. 00 E 7 m/s, mo = 9. 11 E-31 kg, c = 3. 00 E 8 m/s b) m = mo / (√ 1 - v 2/c 2) 1. m = 9. 11 E-31 / (√ 1 - (4. 00 E 7)2/ (3. 00 E 8)2 2. m = 9. 19 E-31 kg 3. b) v = 0. 98 c, mo = 9. 11 E-31 kg, c = 3. 00 E 8 m/s 4. m = mo/ (√ 1 - (0. 98 c)2/ c 2) 5. m = 5. 0 mo = Five times its rest mass! 6. m = 4. 56 E-30 kg

More Whiteboards: 2. What is the mass of a proton traveling at v = 0. 75 c? Rest mass of proton= 1. 673 E-27 kg m = mo/ (√ 1 - v 2/c 2) m = 1. 673 E-27/ (√ 1 - (0. 75 c)2/c 2) m = 2. 53 E-27 kg

3. At what speed v will the mass of an object be 15 percent greater than its rest mass? m = mo/ (√ 1 - v 2/c 2) v=? 1. 15 mo = mo/ (√ 1 - v 2/c 2) 1. 15 mo* (√ 1 - v 2/c 2)= mo. . . mo cancels. . . √ 1 - v 2/c 2 = 1/1. 15. . . solve for v. . . v = 1. 48 E 8 m/s or 0. 494 c

The Ultimate Speed m = mo/ (√ 1 - v 2/c 2) 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.

The End