Free Fall Acceleration Of A Planet: Detailed Explanations


This article discusses about free fall acceleration of a planet. Free fall refers to an object decreasing its altitude due to the action of gravity. Gravity is the downward pulling force that is responsible for objects falling downwards and not upwards.

In this article we shall study about free fall acceleration of an object on a planet. For every planet, the gravity force is different due to which the acceleration of free falling objects also differ. We shall take the example of Earth and study about the acceleration of free falling object on Earth as similar procedures are applicable to other planets.

What is a free fall?

As discussed in the above section, free fall refers to the downward motion of an object subjected under the influence of gravity.

Anything that comes down on its own without the interference of external force other than gravity is referred to as free fall. The object accelerates at first then attains a constant velocity called as terminal velocity. We shall discuss about it in detail in further sections.

free fall acceleration of a planet
Image: Free fall of a fruit

Image credits: Zátonyi Sándor, (ifj.) FizpedFalling apple cropCC BY 3.0

How to find free fall acceleration of a planet?

To calculate the free fall acceleration of a planet we use the formula discussed in the section below-

g=GM/R2

Where,

G is the gravitational constant

R is the Radius of planet

M is the mass of planet

Free fall acceleration on Earth

The free fall acceleration on Earth is termed as g or acceleration due to gravity. The value of g is calculated using the formula discussed above.

After substituting the values of mass of Earth and Radius of Earth in the formula, we get the acceleration due to gravity on Earth as 9.8 m/s2.

Is acceleration ever 0 in free fall?

Yes. The object first accelerates upto some extent and then attains a constant velocity. This velocity is called as terminal velocity.

The maximum acceleration an object can attain is the free fall acceleration of the object on that particular planet. On Earth, the free falling object cannot exceed more than 9.8 m/s2. After achieving this value of acceleration, the objects will attain a constant velocity called as terminal velocity.

What is acceleration during free fall?

We have already discussed about acceleration attained by objects during free fall. The acceleration is the result of pulling force by gravity.

The gravity pulls an object towards the surface of the planet. This is because gravitational force is attractive in nature and masses attract other masses towards their centers. On Earth, the acceleration during free fall is g. The value of g is 9.8 m/s2.

Examples of free fall

Free fall is a very common thing which we might observe in our everyday lives. The section below states different examples of free fall.

  • Skydiving– When we go to skydiving, our vertical velocity is zero. Only the horizontal component of velocity is non zero. After we jump from the plane, our velocity starts increasing in negative y direction. We get attracted towards the ground due to gravity. We are experiencing free fall under the influence of gravity and our acceleration is equal to g that is 9.8 m/s2.
  • Jumping off a cliff – When we are standing at the edge of cliff and jump vertically down (diving creates a parabolic trajectory), we are experiencing free fall. We descend at an acceleration of 9.8 m/s2. The air resistance is considered negligible. The air resistance factor becomes significant while dealing with light objects like feather and cotton. The effect of gravity is same for all the objects, in vacuum conditions all the objects hit the ground at same time.
  • Arms dropping – We all must have seen the videos of weapon systems dropping from fighter planes or aircrafts. The lever is lifted and doors of the aircraft beneath the surface of fuselage are opened, due to this the weapon starts descending at an acceleration of 9.8 m/s2. Initially the vertical velocity of weapon is zero. The weapon increases its velocity when the doors are opened and it starts descending.
  • Dropping an object– Dropping of an object is similar to weapon dropping. The only condition needed for free fall to take place is that the initial velocity should be zero and no other external force other than gravity should act on the object. The object starts descending at the rate of 9.8 m/s2.
  • Phone falling from pocket – When a phone is inside the pocket the initial vertical velocity of the phone is zero. The phone gains vertical velocity only when it pops outside the pocket and starts falling down. When this happens the phone descends at the rate of 9.8 m/s2.
  • Loose bolt– When a bolt is set loose, it has tendency to fall on the ground. When it is attached to the nut the vertical velocity is zero, as soon as the bolt slips and starts falling down the bolt experiences free fall. The bolt will simply start descending with an acceleration of 9.8 m/s2.
  • Waterfall– In waterfalls, the water falls from the cliff in a free fall motion. The water comes down at the rate of 9.8 m/s2. The exact trajectory of water is parabolic but we can consider it under a free fall motion as the parabolic trajectory is negligible.
  • Falling in a hole– When we are walking and suddenly fall into a hole dug for maintenance purpose then we are experiencing a free fall. The acceleration of our body becomes equal to 9.8 m/s2. The greater is the depth of hole, the greater time we will have to attain maximum terminal velocity and greater will be the impact force.
  • First stage of rockets– When the rockets achieve a certain altitude, they release unwanted mass back to Earth. The first stage of rockets contain most of the propellant and engines. The first engine is detached from the rocket due to which it follows a free fall motion. The first stage rocket boosters fall down with the acceleration of 9.8 m/s2.
  • Second stage of rockets– Similar to first stage, the second stage also falls back to Earth. The reasons of them falling back to Earth are same. The second stage is also detached in a similar fashion as the first stage. The rate of acceleration with which the second stage falls is also equal to 9.8 m/s2.
  • Dry leaves falling from tree– When leaves become dry, they detach from the main branch and fall on the ground. When they are attached to the trunk or branch, their initial velocity is zero and are at rest. When they are detached, they fall down due to the force of gravity. They fall at the rate of 9.8 m/s2. The leaves may swing here and there due to air resistance when the wind velocity is very high but the effect of gravity is same on all objects including leaves.
  • Fruits falling from tree – Similar to leaves, the fruits also fall in similar fashion. Newton got the inspiration of studying about gravity from an apple which fell on his head. The rate of acceleration of the fruit falling from the tree is also equal to 9.8 m/s2. The fruit never goes in upward direction, rather it falls only in downward direction because the gravity acts in downward direction.

Also, please click to know about Free Fall Acceleration With Time.

Abhishek

Hi ....I am Abhishek Khambhata, have pursued B. Tech in Mechanical Engineering. Throughout four years of my engineering, I have designed and flown unmanned aerial vehicles. My forte is fluid mechanics and thermal engineering. My fourth-year project was based on the performance enhancement of unmanned aerial vehicles using solar technology. I would like to connect with like-minded people.

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