# B Stopping acceleration and starting to move at constant speed

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1. Sep 15, 2016

### Zaephou

I have an example:

Let us say you are on a large object with a mass of 5x10^10kg accelerating upwards at a constant velocity of 5m/s^-2, and there is a ball 0.1kg on top of that object. This ball should be accelerating at the same pace.

The ball is then held up 5m from the surface of that object, and is let go. Would the ball stop accelerating and start moving at a constant velocity considering the downward forces are negligible.

Further questions:

-What force would this ball have when it is let go?

-Would the large object ever reach the ball again?

-If the ball does start moving at a constant velocity, when the large object reaches the ball, how large of a force will that object exert on the ball, and would this cause the ball to accelerate at what pace?

2. Sep 15, 2016

### andrewkirk

The situation can be understood in terms of Einstein's Equivalence Principle. The behavior of the ball, as observed by someone on the large mass, will be exactly the same as that of a ball on a planet that, at its surface, has a gravitational acceleration half that of what applies at the surface of the Earth - ie 'one half G'.

So when released, the ball will 'fall' towards the big mass (meaning it stops accelerating and the mass accelerates towards it). It will hit the mass after $\sqrt2$ seconds, at which point it will either stick to the mass or bounce, depending on the construction of the ball.

3. Sep 15, 2016

### jbriggs444

F=ma. No horizontal force = no horizontal acceleration.

4. Sep 15, 2016

### NihalRi

I agree. The ball would be at constant velocity and therefore there is no force acting on it. Since the object was accelerating to begin with, it would reach the ball and it would appear as if the ball was falling towards the object.

5. Sep 15, 2016

### Zaephou

Considering this, how much force would the object exert on the ball upon contact? (If the force is large, why does it only cause the ball to bounce on the surface?)

6. Sep 15, 2016

### andrewkirk

The force will vary over the period for which the ball is in contact with the mass. It will start at zero, increase to a maximum, then decline back to zero. The final zero is reached when the ball loses contact (if it bounces) or when it is fully stationary with respect to the mass (if no bounce). The pattern of force over time, and the maximum force experienced, depend on the construction of the ball and of the mass's surface. The calculation would be complex and need a great deal of extra information about the ball and surface.