What happens when you drop a plastic ball and a metal ball from the same height at the same time

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A 1-pound ball and a 100-pound ball are dropped from a height of 10 feet at the same time. In the absence of air resistance, __________. A 1-pound ball and a 100-pound ball are dropped from a height of 10 feet at the same time. In the absence of air resistance, __________. the 100-pound ball hits the ground first the 1-pound ball hits the ground first the two balls end in a tie There's not enough information to determine which ball hits the ground first

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This question was in my exam today :

A metallic and glass sphere of same size were dropped at same height. Which sphere would hit the ground first and why?

I have thought about several things and cannot come to conclusion. An emf will be developed as electrons will move due to earth's magnetic field. So we have a charged sphere? What now? Magnetic force will be perpendicular to velocity hence no work done by it.

If only someone could just point me in the right direction.

Here is a better example. In this case I have a crumpled up piece of paper and some type of foam board. The paper has a mass of 5 grams and the board is 240 grams. Just as a hint, that's a big difference in mass. But which one hit the ground first? Yup, the piece of paper. Awesome, right? And then when I turn the foam board so that the thin side faces down, BOOM. They both hit the ground at the same time.

So, what hits the ground first? Everything. Above you can see it all. Both heavier and lighter things can fall faster. Clearly, you can't just say "heavier is faster".

Acceleration of Falling Objects

Let's look at the case of a falling bowling ball and basket ball. This is a force diagram showing the two objects.

The bowling ball has a greater mass so it also has a greater gravitational force. You can calculate this gravitational force as the product of the mass (m) and the gravitational field (g). There is something else that depends on the mass, the acceleration. If there is only one force on an object then the following would be true (in one dimension):

Since both the acceleration AND the only force depend on mass, I can write:

Heavier things have a greater gravitational force AND heavier things have a lower acceleration. It turns out that these two effects exactly cancel to make falling objects have the same acceleration regardless of mass.

Air Resistance

Clearly, I didn't fully address all the issues above. If all objects have the same falling acceleration, then why did the crumpled up paper hit the ground before the foam board? The problem is that I left off a force - the air resistance force.

Here's another experiment. Put your hand out the window of a moving car. What do you feel? You can feel the air pushing against your hand. If the car drives faster, the air resistance force gets larger. If you make your hand into a fist instead of an open hand, the force decreases.

This air resistance force is really just the sum of the tiny impacts with your hand and the air. It depends on the air speed as well as the size of the object.

Then what happens as you drop both a foam board and a crumpled piece of paper? At first, they have the same acceleration since they both have a zero velocity which makes zero air resistance force. However, after some short time the forces might look like this:

The foam board has a larger gravitational force but it also has a very large air resistance force. The net (total) force on the foam board will give it a smaller acceleration than paper.

But what about the basketball and the bowling ball? Shouldn't they have different accelerations? Technically, yes. Let me redraw the force diagrams for these two objects and include air resistance.

For these objects, the gravitational force is huge in comparison to the air resistance force. Essentially, it doesn't do much to change the falling acceleration of these objects. But when does it matter? This is a tough question. First, anything at a very low speed will have a mostly negligible air resistance and at high speed will have significant air resistance. Here are some cases where you would NOT ignore air resistance:

A falling piece of paper or a feather.
A falling human at high speeds (a sky diver).
A professionally thrown baseball (100 mph).
A ping pong ball.
Tiny rocks or gravy.

I know that doesn't fully answer the question about air resistance, but it gives you an idea of where to start. But it turns out that there are many situations where a heavier object does indeed hit the ground before a lighter object (because of air resistance). I guess this is why Aristotle and many others think this is always true.

Oh, Veritasium has a some great videos about falling objects. Here are my favorite three videos with questions to consider.

Option 4 : All will reach at the same time

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10 Questions 10 Marks 10 Mins

CONCEPT:

Acceleration due to gravity (g):

The acceleration achieved by any object due to the gravitational force of attraction by the earth is called acceleration due to gravity of earth.
It always acts in a downward direction.
It is same for all the particles or objects.

The equation of motion is given by:

$S = ut + \;\frac{1}{2}a{t^2}$

Where S =the distance travelled, a is acceleration, u is initial velocity and t is the time taken.

EXPLANATION:

As all three particles are in the vacuum so there is no air resistance or air friction experienced by the objects.
All are dropped simultaneously so all will have the same initial velocity (u).
Since for all three objects, the acceleration due to gravity is the same so the acceleration of each particle will be the same.

a1 = a2 = a3 = g = acceleration due gravity

$S = u{t_1} + \;\frac{1}{2}g{t_1}^2\;$= distance travelled by steel ball

$S = u{t_2} + \;\frac{1}{2}g{t_2}^2\;$ = distance travelled by feather

$S = u{t_3} + \;\frac{1}{2}g{t_3}^2$ = distance travelled by plastic ball

So t1= t2 =t3

As all three are dropped from the same height so the distance for all is the same. Hence time taken by each object will be same. So option 4 is correct.