Gravitational mass and inertial mass of an object
Gravitational mass and inertial mass of an object in high speed motion
Chen jin you
Room 904, room 447, block A, No. middle Binjiang Road, Nanping, Fujian, Postal code 353000 Tel: 131********
Abstract
In this paper, the objects in the immense gravity of the black hole under the action of high motion of inertial mass and gravitational mass were studied by digital simulation calculation, it is concluded that the object of the inertial mass and the gravitational mass, in the objects moving at a high speed, it will be possible to become inconsistent conclusions.
Keywords: gravitational mass;inertial mass;high speed PACS:04.90.+e;04.70.-s
1 introduction
In modern physics, people do many experiments, to demonstrate the high accuracy, the inertial mass of a body is always directly proportional to its gravitational mass, in the selection of appropriate units of, make the inertial mass and the gravitational mass completely equal in value, so we often think the two kinds of quality of a object are not distinguished. Established in Einstein's general theory of relativity that inertial mass and gravitational mass are equal. When the velocity of the object approaches the speed of light, what happens? Here we in this research.
2 The digital simulation under the two cases
Suppose there is a black hole, its gravitational mass is M and in the position of the distance R o of black hole, have a object A ,its gravitational mass is m o , the
gravitational mass M of the black hole is 100 billion times the sun gravitational mass, known the sun's gravitational mass mt=301.99*10kg, the gravitational constant G =116.67*10 meters 3/(seconds 2.kg),R o =111.5*10meters, so
G*M=11406.67*10*1.99*10-=301.334*10 Here are two cases to discuss.
1、Hypothesis object A in high-speed motion, both inertial mass mg and its gravitational mass my of the objects A increase with the increase of a moving speed of the object, inertial mass mg always equal its gravitational mass my, the gravity of the black hole is :
F=
o 2
**()G M my
R s -
Here s represents the moving distance of the object A at the t time.
Under the action of the gravitational force of the black hole, the object A begins to move toward the black hole, assuming that the acceleration is a:
a=
F mg
So: F=a*mg
o 2
**()G M my
R s -=a*mg
Because my=mg So:
o 2
*()G M
R s -=a
Set the two order derivative of s to s' ', then: a=s' ' So:
S'' =
o 2
*()
G M
R s - S'' =130
12
1.334*10(1.5*10)
s - (1) According to (1) type, we can get the following matlab digital simulation model:
STOP
Stop Simulation
Scope Product
1s
Integrator1
1s
Integrator -1
Gain Divide
1.329e+011Display2
1
Display1
-1.313e+010
Display
double Data Type Conversion -C-Constant2
-C-Constant
<= 0Compare
To Zero
Add
x'
x
Model in the model file hd1.mdl The simulation results obtained are as follows:
Simulation graphics generated by the model file hd1.mdl
In the picture above, above objects A and black hole distance curve, below the velocity curve of the moving object A. From the above graph can see, when the object A is with the black hole at the time of the collision, the emergence of the velocity of the object A sharp increase, final speed reached 1.329*10^11 meters/ sec, 443 times the speed of light.
2、Hypothesis object A in high-speed motion, inertial mass mg of the object A increases with the increase of a moving speed of the object A, and it's gravitational mass my has remained unchanged, being the initial mass m o of the object A, namely inertial mass mg and the gravitational mass my is not equal, the gravity of the black hole is:
F=
o 2**()G M my R s -=2
**()
o G M m R s -。
Under the action of the gravitational force of the black hole, the object A begins to move toward the black hole, assuming that the acceleration is a:
a=
F mg
So: F=a*mg
2
**()
o G M m R s -。
=a*mg According to Einstein's general theory of relativity, there are
mg=
2
v 1()c
m -。
So:
o 2**()G M m R s -。=2
*v
1()c a m -。
2
*()
o G M
R s -=2
v 1()c
a -
Here, V represents the speed of movement of the object A, C represents the speed of light.
Set the one order derivative of s to s',the two order derivative of s to s' ', then:
v=s '
a=s' ' So:
S'' =
2*()o G M R s -*
2
'1()s c
-
S'' =
30
112
1.334*10
(1.5*10)s
-
*2'
1()
c
s
- (2)
According to (2) type, we can get the following matlab digital simulation model: Subtract
STOP
Stop Simulation
Scope
Product2
Product1
Product
1
s
Integrator1
1
s
Integrator
-1
Gain
sqrt(u)
Fcn Divide1
Divide
Display2
Display1
Display
double
Data Type Conversion
1
Constant3
-C-
Constant2
-C-
Constant1
-C-
Constant
<= 0
Compare
To Zero
Add
x'x
Model in the model file hd_1.mdl
The simulation results obtained are as follows:
Graphics generated by the model file hd_1.mdl
In the picture above, above distance curve of the objects A and black hole, below the velocity curve of a moving object A. From the above graph can see, when object A start moving toward the black hole, the velocity of the object A appear rapidly rising, when object A movement for 10 seconds or so, they reach speeds close to the speed of light, then the velocity of the object A remained at close to the speed of light, when object A movement 350 seconds after, its velocity began to decline, when object A motion the 420 seconds after, its velocity began to appear dramatic changes, but the velocity of the object A are not always travel faster than the speed of light.
From the above discussion, we can see that when the object in high-speed motion, if we consider the inertial mass mg and its gravitational mass my all increases with moving velocity of the object increasing , the inertial mass mg and its gravitational mass my always is equal, in great gravitational force of the black hole, the movement speed of the objects will be faster than light; if we think it's inertial mass mg of the object A increases with the velocity increasing, but it's gravitational mass my has always remained the same as the initial mass m o of the objects A ,inertial mass mg and its gravitational mass my is not equal, under the huge effction of the black hole’s great gravitational force. The motion speed of the objects will not exceed the speed of light.
3 conclusion
From this we can see that the inertial mass mg and its gravitational mass my of the object A , in high-speed motion, will be possible to become inconsistent. That's when the object in high-speed motion, its inertial mass mg will increases with the increase of the velocity of the object, but its gravitational mass my is always remain unchanged.