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# Weight and Gravitational Acceleration – Free Fall Experiment

May 15, 2023

### Introduction:

Now suppose an object of mass m is kept on the surface of the Earth, then according to the universal law of gravitation, the Force of gravity acting on the body FF can be given as follows:

Mass of the Earth = mE

The radius of the Earth = rE

Group of the object = m

According to the universal law of gravitation, the gravitational

Force on the mass m due to the gravitational pull of the Earth = FG

The gravitational Force on the object =

We know from Newton’s second law = Force = mass x acceleration

We can write

Gravitational Force = mass x gravitational acceleration

We denote gravitational acceleration = g

FG = mg

## Explanation:

The image below is taken from a multi-flash photograph showing the movement pattern when an object falls on the surface of the Earth.

• There are seven images of the ball taken at equal intervals of time. The ball falls further in each successive time interval. This shows that its speed is increasing.
• This ball falling under gravity is executing uniformly accelerated motion.

Example – An apple falling under gravity

Acceleration due to gravity does not depend upon mass

Now tell me, if you release a hammer and a feather on the surface of the Earth from the same height, then what observation would you expect?

The Force of gravity is affected by the masses of the two interacting objects and the distance between their centers.

Aristotle thought that heavier items fall more quickly than lighter ones. He expected that a ten times larger mass than another group would fall ten times faster.

Galileo reasoned that because a large mass has more inertia than a small mass, a more significant force is needed to change its motion than that of the smaller mass.

Inertial of hammer >>> Inertial of feather

Force to move a hammer >> Force to move a feather

The masses should move similarly under the influence of gravity since the gravitational Force on a large mass is larger than the gravitational Force on a small mass.

Galileo carried out the experiment and discovered that every object dropped at nearly the same rate.

## Free fall Experiment

The figure shows the release of an apple and a feather from rest inside a vacuum container. The horizontal alignment of the several photos showed that the two items dropped at the same velocity. Therefore, the interval between the first and second photographs equals the interval between the fifth and sixth images.

But if we look at the image, the displacement did not stay the same during each period. As a result, the velocity was variable. Nevertheless, the feather and the fruit were moving quickly.

The distance between the second and third photographs should be compared to the distance between the first and second images. As you can see, the displacement of the feather increased uniformly during each time interval as the displacement of the apple.

We know that each object’s velocity rises by the same amount in each time interval since the time intervals are equal. Put another way, the apple and the feather descend at the same constant acceleration.

All objects dropped near a planet’s surface fall with the same constant acceleration if air resistance is ignored. This motion is known as acceleration due to gravity, and the acceleration due to gravity is indicated by the symbols ag (usually) or g (on the surface of the Earth), and g has a magnitude of around 9.81 m/sec2.

### Conclusion

The acceleration due to gravity is independent of the object’s mass falling toward the Earth’s center. Therefore, if air resistance and friction are negligible (or in a vacuum), both object falls at the same rate.

We are so accustomed to the effect of air resistance and friction that we think that the light object (feather) falls slower than the heavy (hammer) one. However, if light and heavy objects are dropped from the same height simultaneously, they will reach the ground simultaneously.

The Earth applies gravitational Force on all objects, and objects also apply the same gravitational pull on the Earth; then why do we not see the Earth moving towards the mango or the Moon?

#### Weight of a Body:

The Earth attracts everybody towards its center with a certain force that depends on the mass of the body and the gravitational acceleration at that place. So weight is determined by the Force with which it is attracted toward the center of the Earth.

Weight of a body on Earth = Gravitational Force exerted by the Earth on the body

W = mass of the body x gravitational acceleration

W = mg

Weight is measured using a spring balance.

Variation in g due to the shape of the Earth:

Earth is elliptical in shape. It is flattened at the poles and bulged out at the equator. The equatorial radius is about 21 km longer than the polar radius.

Mass of the Earth = M

Since Re > Rp therefore gequator < gpole and approximately ge + 0.018 m/s2 = gp

Therefore, the weight of a body increases as it is taken from the equator to the pole.

It has been experienced that when astronauts land on the surface of the Moon, they feel less weight.

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