Physics: Comparing Stone Drops from 100m Building

In summary, Newtonian mechanics states that the acceleration any object feels from the gravitational pull of the Earth is only dependent on the mass of the Earth, and not on the mass of the body being pulled - meaning everything gets pulled at the same rate.
  • #1
Hardik Batra
130
5
I have one doubt in physics...
If two stones(one stone is having 10 kg mass and other one is having 5 kg)are drop down from the 100 m building. After 5 second, how much distance they will cover ?
 
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  • #2


The mass of the stones does not affect the rate at which they fall. This was one of the idealogical breakthroughs of Newtonian mechanics. The acceleration any object feels from the gravitational pull of the Earth is only dependent on the mass of the Earth, and not on the mass of the body being pulled - meaning everything gets pulled at the same rate.

Because of this, the two stones would fall the exact same distance in 5 seconds. The distance is determined by the equation ##(Distance \ Fell) = \frac{1}{2} \cdot (Acceleration \ Due \ to \ Earth) \cdot (Time \ Elapsed)^2##.

We use ##g## to represent the acceleration due to Earth at the surface of the Earth so this equation simplifies to ##D = \frac{1}{2} \cdot g \cdot t^2##.
##g## is equal to about 10 (in the units we are using here), so the distance traveled is roughly ##\frac{1}{2} \cdot 10 \cdot 25 = 125 \ meters##.

The important thing to take away is that the acceleration a body feels in a gravitational feel is only dependent on the mass of the thing pulling the body, not on the mass of the thing being pulled.
 
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  • #3


Hardik Batra said:
I have one doubt in physics...
If two stones(one stone is having 10 kg mass and other one is having 5 kg)are drop down from the 100 m building. After 5 second, how much distance they will cover ?

If the air friction is ignored both of them will have the same acceleration. If the building is on the Earth the acceleration is approximately 9.81 m/(s^2).

If the initial velocities are zero the distance can be calculated by the equation:

x = (1/2).a.t^2

x = 0.5 x 9.81 x 5^2

x = 122.625 m

However as the height of the building is 100 m both of them will travel 100 m. At the end both of them will be on the ground.

If the air friction is not ignored, the shape of the stones and the density of the air are required to calculate the distance.
 
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  • #4


Your mean to say both will cover same distance..

But By practically 10 kg stone will cover more distance than 5 kg.

What to understand in this?
 
  • #5


Practically, there is a small difference due to air friction as Zalajbeg said. The 'slowing' force which air imparts onto a falling object does depend on the characteristics of the object itself - including it's mass (density would be a better term).

But, in a vacuum, there is no air resistance, and therefore two objects of different weights (even drastically different weights) will fall the exact same distance.

A lovely example of this is the following clip where a feather and a hammer are dropped in the airless environment of the moon and they fall at the exact same rate.
 
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  • #6


Hardik Batra said:
Your mean to say both will cover same distance..

But By practically 10 kg stone will cover more distance than 5 kg.

What to understand in this?

One stone may not have the same density as another stone. This is another factor if air resistance is to be taken into account - because the volumes of the stones or their cross sectional areas are what count.
The essence of getting to grips with Physics is to consider, whenever possible, the various effects one at a time. There are many examples where it becomes impossible to discuss some of the simplest phenomena when you add more and more extra variables into the model. Once each effect has been understood on its own then it's possible to combine them into a 'real' practical situation.
 
  • #7


Here is a fun and classic piece of experimental evidence;

 
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Related to Physics: Comparing Stone Drops from 100m Building

What is the purpose of comparing stone drops from a 100m building?

The purpose of comparing stone drops from a 100m building is to study the principles of gravity and acceleration, as well as the effects of air resistance on falling objects. This experiment can also give insight into the concept of terminal velocity.

What equipment is needed to conduct this experiment?

To conduct this experiment, you will need a 100m tall building, a stopwatch, a measuring tape, several different stones, and a method to drop the stones consistently and accurately from the top of the building.

How does air resistance affect the speed of falling objects?

Air resistance is a force that opposes the motion of an object through air. As objects fall, they experience an upward force from air resistance, which increases as their speed increases. This ultimately results in a maximum speed, known as terminal velocity, where the upward force of air resistance equals the downward force of gravity.

What is the relationship between the mass of an object and its rate of acceleration?

The mass of an object and its rate of acceleration are inversely proportional. This means that as the mass of an object increases, its acceleration decreases. This is evident in the formula F=ma, where F (force) is directly proportional to the acceleration (a) and inversely proportional to the mass (m).

How is the height of the building related to the final velocity of the falling stones?

The height of the building has a direct impact on the final velocity of the falling stones. As the height increases, the stones have more time to accelerate and therefore will reach a higher final velocity. This is due to the acceleration of gravity, which remains constant regardless of the height of the building.

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