Which travels faster when dropped from the same height?

Question

1st marble which weigh 0.020 kg. or the 2nd marble which weighs 0.005kg?

Answer 1

The formulas used for calculating velocities of a falling object do not include the mass of the object, only distance, time and gravity.  However, air resistance has a dramatic effect.  This was demonstrated by David Scott on the Apollo 15 mission who dropped a hammer and a feather on the surface of the Moon and they both fell at the same rate.  So, in our atmosphere, if one marble was significantly smaller or more aerodynamic than the other, it would drop faster.  As marbles tend to be all the same shape and made out of the same materials, it seems logical to assume that marble 2 is smaller than marble 1 since it is only one quarter its weight.  So the answer is marble 2.

However, unless the marbles are dropped from an appreciable height, like a few hundred feet or more, the difference may be so small as to not be measurable except with extremely accurate equipment.

Answer 2

in a vacuum, both travel the same speed, however, the heavier marble has a higher terminal velocity in non-ideal (i.e. non vacuum) situation

The equation for acceleration (a) is a=F/m where F is force and m is mass. Gravity acts on more massive objects with a greater force. The increase in force is directly proportional to the mass; Force of gravity=gravitational constant*mass. However, in the acceleration equation, mass is canceled out; acceleration due to gravity is a constant.

However, when not in a vacuum, the acceleration of the marble is best represented as a=(Force of gravity+Force of air resistance)/m. Air resistance is a force that acts in the opposite direction of gravity in this case, so the two are subtractive. However, this affect becomes increasingly negligible as the Force of gravity increases.

consider a planet where force of gravity=mass*10, and air resistance on a marble=1 (of course, air resistance would actually change with velocity, but for the sake of simplicity...)

the acceleration of a 1000kg marble would be (10000-1)/1000 which roughly equals 10

the acceleration of a .1kg marble would be (1-1)/1 is zero.

Therefor the heavier marble accelerates more.

Of course, this assumes that both the marbles have the same surface area; the difference in mass is because of different densities. If, in fact, the lighter marble was small, the question would be impossible to answer.

Answer 3

the same, providing both are dropped the same way and neither is larger than the other (air resistance).

Before Galileo, people thought the heavier marble would fall faster because it would have a greater pull toward the earth. Galileo showed that an object would decelerate as it falls, this acceleration cause the mass to increase and therefore decrease the speed just the right amount that it cancels out the difference in acceleration

Answer 4

They should travel about the same speed.

Gravity is a constant. So if you were to drop two objects with different masses, they should hit the ground at the same time, provided you don't count in wind resistance, which is impossible to measure with such a short drop.

Answer 5

In air or in a vacuum?  

In air, if the marbles are the same size, the mass-to-air resistance of the 0.005 kg marble is smaller than that of the 0.02 kg marble, and it will travel slower.     If the marbles are different sizes, then all bets are off, you'd need to include each marble's air resistance into the fall time.  

In a vacuum, they'll both hit the ground at the same time.