Question

A 2.5 gram penny and a 1 gram paper clip are dropped from the Empire State Building.

Answer 1

Answer:

According to Newton's second law of motion, the force $F$  exerted on an object is directly proportional to its mass $m$  and acceleration $a$ :

$F=m.a$  (1)

In the case of this two objects with different masses the force will be the weight $W$ , the force with which the objects are atracted to the Earth center due gavity $g$ :

$W=m.g$  (2)

This means we wil have two weights in this particular situation, where the weight of the penny is greater than the weight of the paper clip.

Nevertheless, we have another situation here:

When objects are dropped from a certain height and fall to the ground with the acceleration due gravity $g$ (in this case we are on Earth, so the gravity value is $9.8\frac{m}{s^{2}}$) is called free fall.

According to the experiments, in vacuum (this means there is not air or any fluid), all objects in free fall experience the same acceleration, which is the acceleration of gravity.  This means these objects experience the acceleration of gravity regardless of their mass and therefore their weight.

For example, if we have two objects with different masses, the penny and the paper clip; where the first object is greater than the second; both will fall to the ground at the same time with the same gravity acceleration.

Now, in the real life we have air on Earth, and may have air resistance. In this case the greater object (the penny) will fall to the ground before the lesser object (the paper clip), because the paper clip was more affected by air resistance than the penny.

However, if the air resistance is too small that we can approximate it to zero in the calculations, in free fall the objects will accelerate downwards at $9.8\frac{m}{s^{2}}$ and hit the ground at approximately the same time.