Einstein developed the Theory of Relativity, to which momentum also applies.
A ball will not come to rest until something stops it.
Po = P1 + P2
Po^2 = P1^2 + P2^2
If one ball is at relative rest:
Po = P2
Po^2 = P2^2
When objects collide the change in force is equal and opposite, so is momentum.
p = mv
F = d/dt(p)
F1 = -F2
dp1/dt = -dp2/dt
d/dt (p1 + p2) = 0 the total momentum of both balls remains constant.
Momentum remains contant in Einstein's Theory of Relativity.
In outer space, the momentum of two colliding objects released while in motion is equal and opposite as on earth.
M delta(U) = delta(P)
However, according to the theory of relativity, a collision of two balls occurs and results in equal momentum where less velocity is accounted for with greater mass. This increase in mass is influenced by speed.
F = ma
Mass is an object's resistance to change in velocity.
According to the Theory of Relativity, the mass of a moving object depends on how fast it is moving. The mass m is equal to mo (rest mass) x gamma.
Mass, like time and distance, depends on one's point of view. An object at rest resists less than object in motion. Mass depends on speed, but no mass can reach the speed of light. Inside any accelerator electromagnetic fields exert force on a tiny ion. This force increases the ion's momentum mo(v), so the speed increases and so does the mass. As objects become more massive, it becomes more difficult to make them accelerate. The ion's momentum and energy continue to increase but the speed never reaches the speed of light.
Increasing the kinetic energy of a bod increases its mass.
x1
W = integral (F) dx
xo
Kinetic energy or force changes momentum.
K = integral dx/dt dp p = mv
= integral v dp dp = mo (1/(1-v^2/c^2)) dv
K = integral v mo (1/(1-v^2/c^2))^(3/2) dv
K = mo (c^2/(1-v^2/c^2)^(1/2)) - moc^2
K = (m - mo) c^2
Eo = moc^2 - rest mass energy
E = mc^2 - total energy of the body
A loss in energy accounts for a loss in mass.
No comments:
Post a Comment