Ball Thrown Up: Constant Speed Despite Height

[rajeshmarndi]

When a ball is thrown up straight overhead. It just follows the curved space with the speed it is being released and seems as if the ball gradually slows down to zero at the top most and return to earth.

If I'm right, according to Newtonian physics, the ball speed is zero at the top. And according to Einstein physics, the ball speed doesn't slows at all, it travel with the same speed it is being released.

So if an object is placed at the top most height the ball achieve. What impact the object would have with the ball at the top most, with zero speed or the speed it is being released.

 

[WannabeNewton]

And according to Einstein physics, the ball speed doesn't slows at all, it travel with the same speed it is being released.

No that isn't true. GR says the ball follows a geodesic of the space-time so that its 4-velocity is constant along its worldline; more precisely the 4-velocity of the ball is parallel transported along the geodesic worldline. But you're talking about the 3-velocity of the ball which is quite different from the 4-velocity. The 3-velocity can only be made sense of relative to some coordinate system or reference frame. If the reference frame is fixed to the Earth, such as in your example, then the 3-velocity of the ball will in fact behave in exactly the same way in both Newtonian gravity and GR, modulo higher order special relativistic effects.

 

[PeterDonis]

if an object is placed at the top most height the ball achieve. What impact the object would have with the ball at the top most, with zero speed or the speed it is being released.

Zero speed. As WannabeNewton pointed out, "speed" in the sense you are using the term (3-velocity) can only be defined relative to some coordinate system or reference frame. Since the object placed at the topmost height the ball achieves is at rest relative to the Earth, the obvious reference frame to use is one fixed relative to the Earth, and as WBN said, in this frame the ball's speed is zero when it passes the object.

However, we can also reach the same conclusion regarding the relative speed of the object and the ball when they meet by using a frame in which the ball is at rest. As long as the maximum height the ball reaches is not very large, so that the effects of tidal gravity can be neglected, we can construct a local inertial frame covering the entire experiment, in which the ball is always at rest. In this frame, both the ground and the object at the topmost height the ball achieves are accelerated and follow hyperbolic worldlines; and the hyperbolic worldline of the object is just tangent to the ball's worldline (i.e., to the time axis of the local inertial frame), indicating zero speed in this reference frame, at the instant when the ball reaches the object's height. So in this frame as well, we can derive the correct conclusion that the ball and the object have zero relative speed when they meet.

 

[George Jones]

I think the fact that the ball has zero 4-acceleration is confusing rajeshmarndi, and leading to the erroneous conclusion that, according to relativity, the speed of the ball doesn't change.[PLAIN]https://www.physicsforums.com/members/rajeshmarndi.179607/[/PLAIN]

 

[sardar]

I would like to clarify a few points about the scenario described. First, the statement that the ball follows the "curved space" is not entirely accurate. The ball is following a parabolic path, which is a result of the force of gravity acting on it. This is known as projectile motion and is a fundamental concept in classical mechanics.

Next, it is important to note that in both Newtonian and Einsteinian physics, the ball's speed at the top of its trajectory is zero. This is because at the highest point, the ball has reached its maximum potential energy and has no kinetic energy. This is a basic principle of conservation of energy.

In terms of the impact of an object at the topmost height achieved by the ball, it would depend on the speed and mass of the object. If the object is at rest or moving at a slower speed than the ball, the impact would likely be negligible. However, if the object is moving at a high speed or has a significant mass, the impact could be more significant and could potentially cause the ball to change its trajectory or even fall back to the ground.

It is also important to consider the effects of air resistance on the ball's motion. In reality, the ball would experience air resistance which would cause it to slow down gradually as it travels upwards and then speed up again as it falls back to the ground. This would result in a slightly different trajectory than the idealized scenario described.

In conclusion, the concept of a ball thrown up with constant speed despite height is a simplified model of projectile motion and does not fully capture the complexities of real-world scenarios. Both Newtonian and Einsteinian physics can be used to accurately describe the motion of the ball, but it is important to consider the limitations and assumptions of each theory.