why do two objects of different mass need the same time to hit the (horizontal) ground...?

Question

...when dropped off a tall building?

would air friction make the two objects make them land at different times??

Answer 1

Newton posited F = GmM/R^2; where m is the mass of an object, M is Earth mass, R is the distance between m and M at their centers of mass, and G is a constant of proportionality.

The force, F, is what we call weight. That's right, when you stand on your bathroom scale and decide you need to go on a diet, it's the force of gravity, your weight, that shows this.

Weight is W = F = GmM/R^2 = ma = mg; where a is acceleration and F = ma is the observation that force can be found by multiplying mass times its acceleration. Note g = a; where g is just a special acceleration due to the force of gravity...your weight for example.

So two objects dropped from a tall building have the following force of gravity on them F1 = Gm1M/R^2 and F2 = Gm2M/R^2. The weight of each is W1 = m1g1 = Gm1M/R^2 and W2 = m2g2 = Gm2M/R^2; where g1 and g2 are the respective accelerations as the objects drop to the cement below.

So the two objects will take the same time to hit the cement if their velocities are the same during the fall. That is, t = H/v where H is the building height and v is the respective average velocities. The average velocity for each one is v/2 = (u + at)/2; where u = 0 the initial velocity upon dropping; so v = at. So to show that t1 = t2, the respective drop times are equal, we need to show that a1 = a2, the respective accelerations are equal.

Back to Newt's law...W1 = m1g1 = Gm1M/R^2; so that g1 = GM/R^2. Similarly, W2 = m2g2 = Gm2M/R^2; so that g2 = GM/R^2 = g1. Thus, the accelerations due to gravity on mass 1 and on mass 2 are equal. That is, both objects will accelerate at g1 = g2 = constant = g = 9.81 m/sec^2 or 32.2 ft/sec^2 at Earth's surface R distance from the center of M.

The important physics lessons are these: an object falling due to gravitational force will fall at the same rate of acceleration no matter what its mass is. Also, this will be true without exception if and only if there are no other forces, like air drag forces, to modify this result. Thus, the masses may not fall in the same time (at the same rate) if air drag friction is a factor.

Answer 2

Isaac Newton's answer to this was as follows:

On the one hand, the heavier rock feels a stronger pull (downward) than the light rock; but on the other hand, the heavier rock _resists_ that pull more than the light rock does. The "resistance to pull", also called inertia, is due to the heavy rock's extra mass. The stronger pull exactly "cancels" the greater resistance to being pulled; so the heavy rock ends up falling at the same rate as the lighter rock.

Before Newton was born, Galileo had an even more elegant explanation:

Suppose you take two bricks, each weighing 1 pound, and drop them from a tall building. Certainly you would expect them to hit the ground at the same time (say, 3 seconds), right? So far, so good.

Now, suppose you hold those bricks together so they're touching each other, then you drop them again. It should still take 3 seconds, right? After all, it shouldn't make any difference whether the bricks are touching or they're 1 foot apart.

Okay, so now say you tie the two bricks together with a piece of string, and then drop them. Should it not still take 3 seconds? After all, what difference would the string make?

But now notice: Your "two bricks tied together" is really the same thing as ONE brick that weighs 2 pounds. That should mean that a 2 pound brick should fall in 3 seconds--the same as a 1-pound brick. In other words, the weight of the brick doesn't make any difference. All bricks fall at the same rate.

Regarding air friction: Yes, air friction does make a difference. Air friction produces an upward force that counteracts gravity. And it depends on the shape and speed of the falling object, so it acts on different objects in different ways. The result is that objects which are very large and/or very dense tend to fall faster than objects which are very small and/or have a low density.

Answer 3

Gravity accelerates objects towards the ground, and it acts with the same acceleration on all objects. So, if you drop two items, they both start with the same velocity, 0, and are accelerated at the same constant rate. So, ideally at each point on the way down the two objects will be next to each other, until they hit at the same time, regardless of whether they have the same mass as each other or not.

It's like if a big car and a little car start from a light and accelerate at the same rate, they'll always be side by side as long as the acceleration is maintained.

You are right, though, that friction can affect the rate of fall. This is influenced by the aerodynamics of the shapes of the objects. If two objects are different masses, but the same shape (a heavy ball and a lighter ball of the same size), then they will land at the same time. If, however, they are of different shapes, like a wing and a ball of the same weight, then they may well fall at different rates depending on things like friction and aerodynamic lift. The fastest rate at which an object can fall is known as its terminal velocity. The terminal velocity is what varies between different objects of the same mass but with different shapes - the force of gravity on the objects is still the same.

I guess for most of the things we drop, though, the slight differences in friction or aerodynamics aren't obvious in the amount of time it takes for them to hit the floor.

Answer 4

Think of it this way. When you drop an object it doesnt fall to earth, actually it has gravitational pull too, and the earth meets it with relation to the mass.
However the mass of the earth is so big that anything you could drop off a building would have negligable pull to the earth.
Thus both objects will accelerate at approximately 9.8 m/s^2 the gravitational constant. Of course, this is not counting other factors like air resistance and boyancy. But this would work in a vacuum.

Answer 5

Only in a vacuum would they hit the ground at the same time. EVEN if they are the same shape and size (wooden and metal ball) ,due to air friction.
I can hear people say but friction would be the same if they are the same shape and size. Yes, but 20N of friction would be more significant on the lighter object than on the heavier.

20kg has g-pull of 200N (assume g=10) -20 air friction=180 it will accelerate @ 9m.s2. 180N/20kg
4kg ball will have pull of 40N-20N air friction=20N it will accelerate @ 5m.s2. 20N/4kg.
I did simplify this to accommodate linlong
Very good question

Answer 6

The clue is "mass", not surface area. Since Gravity acting on a mass is constant and objects of the same density are attracted equally, then they will hit the ground at the same time.
If an object of the same density is given more surface area, then it will take longer as the air drag will lessen its terminal velocity.

Answer 7

You've got lot's of correct explanations here.

To see the effect of performing this in a vacuum, this experiment was performed on the moon by Scott on Apollo 15.

There's a couple of links below, the second of which is a Nasa video of the experiment.

Enjoy^_^

JBV^_^

Answer 8

if you had 1 item made of polystyrene shaped into a 1inch ball and then similar sized ball of Lead then the air friction would be the same as the surface area is the same.

Answer 9

the bigger the mass the bigger the pull of gravity(weight) downwards so they reach ground at same time but only if air resistance is same on both and this depends on size/shape

Answer 10

did you know that if you throw a cat off a 7 story building it will survive because it can reach its terminal velocity which slows it down enough for it not to be too badly injured.