What happens to an object that is free falling with a constant force acting upon it forever?

Question

What happens as it accelerates to near the speed of light? Can it ever exceed the speed of light?

Answer 1

Dispersion of masive particle:
E² = (mc²)²+p²c²
E = √[(mc²)²+p²c²]

Velocity of the partice:
v = ∂E/∂p = pc²/E

Dynamic equation::
dp/dt = F
p = Ft

v(t) = p(t)c²/E(t) = Ft c² / √[(mc²)²+(Ft)²c²]
v(t) = t / √[(m/F)²+(t/c)²]
v/c = 1 / √[1 + (mc/F)² 1/t²]

As it turns out, the distance travelled by the particle can be also be easily integrated:
X(t) = ∫ v dt = c/2 ∫ dt² 1 / √[t² + (mc/F)²] =
[√(t² + (mc/F)²) - (mc/F)] c


Introducing characteristic time To = (mc/F), which is time needed to acclerate to speed c in Newtonian case, speed and diplacement can be conveniently rewritten as
v/c = 1 / √[1 + To²/t²]
X(t) = [√(t² + To²) - To] c

Answer 2

A force is defined as the energy per unit distance that the force travels.
In a free fall amoving mass continually moves with increasing acceleration .The aceleration in a gravity field is calculated as an inverse function of the quare of the distance from the center of mass of the Gravitational mass.So as the approach distance of the moving object becomes smaller, the acceleration becomes bigger( a denser gravity field)
For a gravitational mass to produce an acceleration will would cause a particle mass to move at the speed of light,would have to be about 2 x 10^53 kg,which is close to the mass of the Universe.

Note in free fall the acceleration is never a constant.

Force dont act upon a mass to cause it to move . It is the Gravity Power which acts upon the mass to make it move.
As a result a force occurs and is described as Energy per unit distance that the produced force travels.

If a mass structure is given enough power to t cause it to move at the speed of light it would chalenge its structural energy and would break upart.
The speed of light inside atomic structure can be very closely approached by the Electron. However the electron would not exceed the speed of light.

Answer 3

It will continue to accelerate as long as there is a net force acting on it. But, and this is a big BUT, it will not accelerate to a velocity v = c.

This non intuitive result stems from the theory and observations that rest mass m0 inertia increases as the velocity increases; so that the effect is a mass m that behaves like m = m0/sqrt(1 - (v/c)^2). As you can see at v = c, m --> infinity, which is a really big mass that would require a really big net force to keep it accelerating.

In fact, f = ma = m0a/sqrt(1 - (v/c)^2) still holds; where f is that net force needed to accelerate the relativistic mass m. So, to keep that mass accelerating at some a, the force has to increase towards infinity as the mass goes toward infinity.

Thus, if the net force is "constant" as you propose, there will come a point where the force is no longer sufficient to accelerate the relativistic mass m any further. And at v = c, it would take an infinite amount of force, which is not possible. Even the whole universe has a finite amount of force.

Answer 4

Thats interesting... Given your conditions i would think that the object could exceed the speed of light. If it does exceed the speed of light, then it would become invisible and we wont be able to see it since light cant reach it fast enough to get reflected back.

Answer 5

best for you, dad. What happens relies upon on what assumptions are made. in case you anticipate the article falls in a vacuum, then it extremely is going to develop up close to Earth's floor at a fastened g = 32.2 ft/s^2 or 9.80 one m/s^2 reckoning on the contraptions used. All bodies develop up whilst acted on via a internet rigidity. in relation to a falling physique, the internet rigidity is the rigidity of gravity we call weight, W. So the linked fee of the falling merchandise in a vacuum maintains to get greater, develop up, till it impacts some thing and includes a screeching halt. As you will possibly think of, because of the fact the article is accelerating each and all the collectively as, its velocity at result gets greater with greater factors of launch. Theoretically, from 10 miles up, the end result velocity on your driveway in the front backyard can attain greater suitable than 1200 mph. yet it is in a vacuum. And Earth has air. as a result, the genuine result velocity with your driveway would be around one hundred twenty mph, that's called terminal velocity. This consequences because of the fact of air drag, a style of friction dragging on the falling physique to maintain it from accelerating to any extent further as quickly because it reaches around one hundred twenty mph subsequently. Drag is yet another rigidity; so on your gravity basically subject, it does not exist. The vacuum case applies there. I prevented equations purposely. in case you wanted them, please upload that for the duration of your question.

Answer 6

total force=ma
if u have a constant force,then there will be a change in the acceleration.

Answer 7

No, it reaches terminal velocity (as fast as it can go), then continues at that constant velocity

Answer 8

1) ITS SPEED WILL APPROACH THE SPEED OF LIGHT
2) ITS MASS WILL INCREASE
3) ITS LENGTH (IN THE DIRECTION OF MOTION) WILL DECREASE