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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 ) - PowerPoint PPT Presentation
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Momentum and MassIs Mass a Relative Quantity???
By Connie Wong
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
Mass
p = mov/ (√1- v2/c2)
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- 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
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)
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, 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
More Whiteboards:
2. 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
3. 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
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.
The End
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