What Happens To The Ball At The Top Of Its Path ?: Your partner argues the following about a ball that is tossed vertically upward: “At the top of its path the ball stops for a while so its...

What Happens To The Ball At The Top Of Its Path ?: Your partner argues the following about a ball that is tossed vertically upward: “At the top of its path the ball stops for a while so its velocity is zero. Also, the net force on it is zero so its acceleration is also zero.” Do you agree with your partner’s statement? What evidence do you have from your own observations and experiments to validate or invalidate the various assertions of your partner? 

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valentin68 | College Teacher | (Level 3) Associate Educator

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If we toss a ball upward, we can observe that on the ascending part of its trajectory the ball will slow down. Thus, the force on first half of the trajectory is directed downwards (it is the ball weight). On the second half on the trajectory (the descending part), the ball will speed up towards earth, so again the force is directed downwards (the same ball weight). Since weight is an intrinsic property of any mass that is located in a gravitational field, this force does not depend on the mass state of motion. It always exists regardless the ball moves or not. Therefore all the way of its trajectory there is a net force on the ball directed downwards.

Because of this fact, the corresponding acceleration on the ball is always non zero, and equal to `g` , the gravitational acceleration. Thus at the top of its path the ball the values of the net force and of the acceleration are non zero.

Now referring to the speed of the ball, it is true that the ball slows down until the top of the trajectory then it speeds up on its way down. Therefore there must be one single moment in time where the speed of the ball is zero (since speed it is a continuous function of time). But to say that the ball stops for a while is false. A while, means from both from a mathematical and physical point of view an interval of time (be it short) not a single moment. Because, as we demonstrated above, the acceleration is always non negative, the next moment immediate after the speed of the ball is zero, it will become again non zero.

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