# Why Do Objects of Different Mass Fall at the Same Time? Get Answers Here!

• ConcealedDreamer
In summary: F=2m/r^2=4m/r^2=2g.In summary, the two objects will drop at the same time because the force of gravity is the same for both objects.
ConcealedDreamer
If I drop 2 of the same object but different mass like a pocket book and a encylopedia, they drop at the same time. Why is that? Anyone can get a detailed explanation? Thanks!

If and only if you're doing the experiment in vacuum.Assuming that,Newton's law of gravitation attraction will give the same acceleration for two bodies with different mass falling in the Earth's gravitational field.That's all to it.

Daniel.

ConcealedDreamer said:
If I drop 2 of the same object but different mass like a pocket book and a encylopedia, they drop at the same time. Why is that? Anyone can get a detailed explanation?

It's because the force that's pulling down on your objects is the gravitational force:

$$F=\frac{GM_em}{r^2}$$

That's Newton's Law of Gravity, where G is the gravitational constant, Me is the mass of the earth, m is the mass of your pocketbook (or encyclopedia), and r is its distance from the center of the earth. What else do we know about forces? Well, Newton's Second Law of Motion says:

$$a=\frac{F}{m}$$

That is, an object's acceleration is equal to the force acting on it divided by its mass. I just said that the force acting on it was gravity, so that gives us

$$a=\frac{GM_em}{r^2m}=\frac{GM_e}{r^2}$$

This tells us that the acceleration an object experiences from gravity is equal to the gravitational constant times the mass of the Earth divided by its distance from the center squared. If your objects are accelerating at the same rate, it means this number is the same for both of them, and if you take a look, you'll see why that is. The gravitational constant is universal, so it won't vary from object to object. The mass of the Earth certainly doesn't depend on the object being used.

Now, you might say that the two objects have a slightly different distance from the center (and it's certainly possible that they do), but remember that we're very far from the Earth's center. That is, the average distance to the Earth's center from the surface is around 6,380,000 meters, while the two books you're holding up probably won't have a difference in distance from the center that's more than a few centimeters. Thus, r=Re, the radius of the earth, and their accelerations will be the same, for all intents and purposes. It's because this number is roughly constant on the Earth's surface that we talk about another constant, g:

$$g=\frac{GM_e}{R_e^2} \simeq 9.8 \thinspace\thinspace m/s^2$$

This is the acceleration you'd expect your books to have.

So, you may ask, why doesn't a feather hit the ground at the same time? The answer to this question is a bit more complicated and it has to do with "air resistance". It turns out that all falling objects experience a slight upward force from the air molecules that they're falling through, but you don't notice it unless you object has a high surface area and low mass (as with a feather). It's for this reason that your books wouldn't hit the ground at exactly the same time, but the difference would be hard to measure without decent equipment.

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that's _not_ all there is to it, dexter.

One must postulate the equivalence principle, i.e. the gravitational mass of a body is identical to inertial mass of the same body.

axl said:
One must postulate the equivalence principle, i.e. the gravitational mass of a body is identical to inertial mass of the same body.

No need to postulate anything. Measurements indicate that to the uncertainty that this person can observe, they are equivalent. Whether or not they're exactly equivalent doesn't matter for his/her purposes.

IF you want evidence that the feather falling at a different speed is not due to its mass... put the feather on top of one of your books then drop the book, this is so beautiful when you do this.

axl said:
One must postulate the equivalence principle, i.e. the gravitational mass of a body is identical to inertial mass of the same body.

YOU ARE RIGHT. I remember,sorry for the imprecision. It's the first thing taught in a classical mechanics course when introducing Newton's gravity theory...

Daniel.

let's assume that the pocket book is half the mass of the encyclopedia.

are you familiar with the formula F=ma (force acting on an object is equal to the mass of the object times the acceleration caused by the force)?

here, we are interested in acceleration, so with a little division, we come to a new formula: a=F/m.

the only force (F) acting here is gravity. an object of double mass should have double gravitational pull. if you double "m", you have to double "F".

so let's say F is the force (weight) acting on the pocket book and m is the mass of the pocket book. If the encyclopedia has twice the mass, then the encyclopedia's mass is 2m. it's weight is therefore 2F.

so, the acceleration of the handbook can be represented now as
a=F/m

and the acceleration of the encyclopedia would be
a[encyclopedia]=(2F)/(2M). The 2's cancel out. That's where the magic happens.
a[encyclopedia]=F/m, just like the pocket book.

mass and weight are different. weight is how heavy something is. mass is an object's unwillingness to change. if you double the mass, you double the weight. these factors cancel each other out for downward acceleration in a vacuum.

## 1. Why do objects of different mass fall at the same time?

This is because of the force of gravity. All objects experience the same acceleration due to gravity regardless of their mass. This is known as the principle of equivalence.

## 2. Does the shape of an object affect its falling time?

No, the shape of an object does not affect its falling time as long as there is no air resistance. In a vacuum, all objects will fall at the same rate regardless of their shape or size.

## 3. How was it proven that objects of different mass fall at the same time?

Galileo Galilei was the first to experimentally demonstrate that objects of different mass fall at the same time. He dropped two objects of different masses from the Leaning Tower of Pisa and observed that they reached the ground at the same time.

## 4. Are there any factors that can affect how objects fall at the same time?

Yes, air resistance and the presence of other forces such as wind can affect how objects fall at the same time. In a vacuum, where there is no air resistance, all objects will fall at the same rate regardless of their mass.

## 5. Why is it important to understand why objects of different mass fall at the same time?

Understanding this concept is important in the fields of physics and engineering. It allows us to accurately predict the motion of objects and design structures that can withstand gravitational forces. It also helps us understand the behavior of objects in space and on other planets with different gravitational strengths.

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