What is acceleration of gravity on board a train moving at speed c/2?

Thick flat plate creates uniform gravitation field g=9.8m/s². The train moves at constant speed c/2 along straight track on the surface of the plate.





What is acceleration of gravity on board the train?








Could you, please, keep the solution within high school level, because otherwise I will be unable to understand it. Thank you.

What is acceleration of gravity on board a train moving at speed c/2?
I don't think other answerers are realizing that "c/2" means half the speed of light, and therefore you have to take relativity into account.





The acceleration of gravity on board the train would be about 13.1 m/s². Here's why:





Suppose you were on board the train and dropped a ball from a height of 4.9 meters. (it's a tall train). Let's see what that would look like from your point of view and from the point of view of somebody standing outside the train.





The outside observer would see the ball seem to follow a parabolic arc downward, and he would measure it as taking 1.0 second to hit the ground. This is consistent with his observation that the value of gravity is 9.8m/sec²





But, due to the train's great speed, the clocks of the people on the train are running slowly--only about 87% as fast as the outside observer's clock (this is a prediction of the theory of relativity). So, when the person INSIDE the train measures the time it takes for the ball to fall, HIS stopwatch reaches only 0.87 seconds.





So, the person inside the train concludes that it takes only 0.87 seconds for a ball to drop 4.9 meters. (In other words, it seems, to him, to fall a little FASTER than it does when you're measuring it from the outside).





The person in the train does a calculation and concludes that gravity is not 9.8m/sec², but rather 9.8m/sec²/(.87)², or about 13.1 m/sec². This is from the formula: g = (2h)/t².





Another way to interpret it, is to say that, according to the person inside the train, the mass of the plate (as it whizzes past) has increased by a factor of 1/(.87), thus increasing its gravitational pull. This (increased mass) is another prediction of the theory of relativity.





[EDIT]: BTW, I have to disagree with Philip J's assessment (below). He is basically saying that, If I throw a ball horizontally (in a uniform g-field), it will (relativistically) take longer to hit the ground than if I drop if from rest. (This is basically identical to the ball-in-train situation; where the initial horizontal speed of the ball (from the outsider's perspective) is c/2.)





But this seems to fly in the face of the equivalence principle, which says I can treat the situation as if I were in an accelerating spacecraft rather than in a "true" g-field. If I am in an accelerating spacecraft, and I throw a ball "sideways" (perpendicular to my acceleration vector), surely that ball will hit the floor at exactly the same instant as a second ball which I dropped from rest.
Reply:The interesting this is this - if you are inside of that train and close the blinds on the windows, everything is normal, whether you are moving relative to something else or not. If the train were moving at half the speed of light, inside of the train, nothing has changed. If you measure the speed of light from a flashlight inside of the train, it will still be C (roughly 186,000 + miles per second) - regardless if it is aimed in the direction the train is moving or in the opposite direction. Acceleration caused by gravity will appear the same. Nothing has changed in the *local* space-time aboard the train.





To an outside observer, of course, things will appear different. The train will appear very slightly shorter. Time progresses at a different rate. Whose time is correct? It is all relative %26lt;VBG%26gt;





Now, if you are aboard that train and open the windows (or, better yet, get on top of the thing if that were possible) and check the stars towards which you are moving and those you are moving away from, you'd find the speed of light from each is exactly C. The same. Regardless if you move towards or away from them. The color, however, would be shifted towards the blue spectrum in the case of the stars ahead of the train towards which you are moving and red-shifted in the case of the stars you are moving away from. Yet the speed the light arrives at you is still measured as the speed of light. In fact, this spectrum shifting can give us a fair idea as to how far away different galixies are from us. The more the red shift, the faster they are moving away and the further they are from us.





Hope this helps ;)








Best regards,


Jim
Reply:The acceleration from gravity would be 9.8m/s^2; the current velocity of the train would be irrelevant as long as it is constant.
Reply:Rick B is sort of on the right track; but he's got it backwards. Clocks on the train run slow from the viewpoint of an observer who is stationary relative to the plate. The acceleration of gravity is one of those clocks that seem to run slow. A stationary observer on the plate would see the ball drop at 9.8 m/s^2 times the square root of 3/4.





An observer on the train would see the ball drop at 9.8 m/s^2 because his clock is slowed by the same amount as the acceleration of gravity.
Reply:9.8 m/s^2, given in the problem. All bodies fall at the same rate under the influence of gravity.
Reply:dkk lil 88 is worng...thats velocity/speed hes talking about not acceleration..
Reply:The acceleration is still 9.8m/s^2.





Think of it this way. If a side view of the plate and the train were super imposed on an x-y graph, there would be two vectors: the gravitational acceleration vector pointing down on the train, and a velocity vector pointing in the direction the train is moving.





Now, looking at this mental picture, does the velocity of the train effect the gravitational field? Not really. And there are no other external forces on the train right? So the acceleration due to the field is independent of velocity of the train, hence the acceleration due to gravity is simply the same as the field.
Reply:acceleration is that if you run by a second then how faryou go


for instance, if you go 30 m by 6 s then your acceleration is 5 m/s.