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

2. 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

3. Mass p = m o v/ (√1- v 2 /c 2 ) 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 = m o / (√1- v 2 /c 2 ) m o = 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. m o of an electron: 9.11 E-31kg m = m o / (√1- v 2 /c 2 )

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. a)v = 4.00E7m/s, m o = 9.11E-31kg, c = 3.00E8m/s m = m o / (√1- v 2 /c 2 ) m = 9.11E-31 / (√1- (4.00E7) 2 / (3.00E8) 2 m = 9.19E-31 kg b) v = 0.98c, m o = 9.11E-31kg, c = 3.00E8m/s m = m o / (√1- (0.98c) 2 / c 2 ) m = 5.0m o = Five times its rest mass! m = 4.56E-30kg

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

8. 3.At what speed v will the mass of an object be 15 percent greater than its rest mass? m = m o / (√1- v 2 /c 2 ) v = ? 1.15m o = m o / (√1- v 2 /c 2 ) 1.15m o * (√1- v 2 /c 2 )= m o...m o cancels... √1- v 2 /c 2 = 1/1.15...solve for v... v = 1.48E8m/s or 0.494c

9. The Ultimate Speed m = m o / (√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.

10. The End