3.6 Some other situations of falling objects from a feather to a hammer and in different gravitational fields, thought experiments described and explained!

The earliest theories on falling objects suggested that the heavier the object, the faster it falls.

We now know that all objects fall at the same speed if only the force of the local gravitational field is acting on the them.

Some 'actual' and 'thought' experiments.

You need to consider the W (weigh, depends on local gravitational field strength), U (upthrust) and F (friction, drag) forces described in the ball bearing - liquid filled tube experiment and the four objects illustrated above.

(a) The hammer and the feather experiment on the moon

When the first astronauts landed on the moon they carried a beautifully simple experiment.

One astronaut held up a feather and a hammer and let them both fall simultaneously.

Both objects (i) fell to the ground in the same time experiencing the same gravitational acceleration and (ii) they seemed to fall to the ground more slowly than if they had been dropped on Earth.

(Weight = mass x gravity, W = mg)

 

(i) Both objects experience the same gravitational acceleration of 1.62 m/s², BUT the Moon has no atmosphere so there is no air resistance. With no drag effect due to friction both objects, whatever their mass or shape (surface area) are free to fall with maximum acceleration due to the Moon's gravity.

(ii) Acceleration on Earth due to the gravitational field is 9.80 m/s². The Moon has a much smaller mass and gravity is much weaker and only produces an acceleration of 1.62 m/s². Therefore objects on the Moon will fall much more slowly than on Earth (ignoring air resistance).

On Earth: Hammer weight = 0.20 x 9.80 = 1.96 N 

and  feather weight = 0.002 x 9.80 = 0.0196 N

On the Moon:  Hammer weight = 0.20 x 1.62 = 0.32 N 

and  feather weight = 0.002 x 1.62 = 0.0032 N

(b) The hammer and the feather experiment on Earth

 If you drop the feather and hammer simultaneously on Earth, the feather takes much longer to fall to the ground because it has a relative greater surface area/mass ratio greatly increasing drag effect from air-feather friction.

If it wasn't for air resistance, no drag effect can happen and all objects would fall with the same acceleration.

You can do a laboratory experiment with two objects (one 'light' like a feather and one heavy like a lead weight) by allowing them to fall vertically in a large tube from which the air has been pumped out to create a vacuum.

It seems uncanny when they both hit the bottom of the tube at the same time.

 

(c) Dropping two spheres of equal surface area, but different mass

If you simultaneously dropped the dense pool ball and light hollow plastic ball with the same radius (giving same surface area) the pool ball will hit the ground before the lighter hollow plastic ball.

This is because the greater weight of the pool ball will overcome the drag effect of air resistance more than the less 'weighty' plastic ball and the pool ball will appear to accelerate at a greater rate.

The surface area is the same, and if both surfaces are smooth, the friction effect should be the same.

On the Moon you would not notice any difference, see (a) for the argument.

(d) The general behaviour of a falling object on a planet or a moon

 If you drop any object (safely!) from a tall building on Earth, it will always achieve a terminal velocity due to the friction effect of air resistance.

The terminal velocity s reached when the downward weight force equals the air resistance friction force.