Free Fall Acceleration With Time: Detailed Analysis


This article discusses about free fall acceleration with time. We know that wehn a body falls freely, it undergoes a constant acceleration.

In this article we shall study the dependency of acceleration on time (if any). Later we shall study about free falling objects. Gravity is the attractive force responsible for objects to fall downwards freely. Let us start our discussion with the meaning of free fall.

What is a free fall?

Free fall is that state of an object in which it is reducing its altitude at a constant acceleration due to the influence of gravity.

The free falling acceleration is same. The value of acceleration does not change with time. We shall study about acceleration and time relation of a body under free fall in the later sections of this article. Now let us discuss about the acceleration first.

Acceleration of free falling object

Image: A fruit under free fall motion

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

When an object undergoes free fall, the acceleration of the body while falling remains constant and is equal to the value of g on Earth.

Value of g on Earth is 9.8 m/s2. This value can be calculated using simple formula. The formula is discussed in the section given below

g=GM/R2

Where,

G is the gravitation constant

M is the mass of planet

R is the radius of planet

What is the formula for acceleration with time?

When we need to find the time taken for the object to hit the ground after undergoing free fall, then we can use the equations of motion given by Newton. However we will discuss only the first equation that shows the relation between velocity, acceleration due to gravity g and the time taken t.

The equation of motion is discussed in the section given below-

V=gt (it is v=u+at but initial velocity is zero incase of free fall)

Where,

V is the velocity of the object while falling

g is the acceleration due to gravity

t is the time taken by the object to hit the ground

How to find free fall acceleration with time constant?

When we consider time as constant, that means we are reffering to that time instant at which the velocity is to be calculated.

For example, if the value of t is 5 sec then the we are actually calculating the value of velocity of object after 5 sec in free fall motion. Hence the formula v=at remains the same in this case. The free fall acceleration value is constant and it does not change.

Examples of free fall

The list below gives examples of free fall which we see in our daily lives-

  • Skydiving – When we go for skydiving, the only velocity we have is the horizontal velocity that is equal to that of the plane. When the instructor opens the door and we jump out of the door, we experience a strong pulling force in downward direction. This happens because of the fact that gravity acts inward. The acceleration during free fall will be equal to the value of g that is 9.8 m/s2.
  • Jumping off a cliff – Jumping off a cliff is a slight parabolic path we can ignore the parabolic quantities as they have very negligible effect on our motion. We follow a nearly free falling motion. Our acceleration becomes 9.8 m/s2. The higher the cliff, the more time we get to attain the terminal velocity and the greater will be the impact force.
  • Weapon dropping – When we drop weapons from the fighter jets, their initial vertical velocity is zero until dropped. As soon as they are ejected the weapons start descending. The weapons are on their own if there is no guidance system attached to it. The weapon will fall on the predicted area. The acceleration of the weapon becomes 9.8 m/s2.
  • Dropping an object – Dropping an object is similar to dropping a weapon from the aircraft. The object will follow a free fall motion after being dropped. its acceleration will become equal to 9.8 m/s2. They object should not be pushed otherwise it will not be considered a free fall. The term free fall itself says that the body will fall freely without any external force other than gravity acting on it.
  • Phone falling from pocket – When the phone is kept inside the pocket, the phone’s vertical velocity is zero. As soon as it slips out of pocket it starts descending, the velocity of the phone becomes non zero. The phone gets accelerated to a value of 9.8 m/s2. The phone will keep continuing its free fall until it experiences an impact on the surface.
  • Loose bolt -When we bolt is loosely attached to the nut, it has a tendency to fall anytime maybe even due to its own weight. When it is attached to the nut, the vertical velocity is zero. The bolt increases its velocity once it gets detached, the bolt experiences a free fall motion. The bolt descends with an acceleration of 9.8 m/s2.
  • Waterfall – Water experiences free fall motion when it flows down the cliff. The water flows in a slightly parabolic trajectory. However we neglect the parabolic effects as they are very insignificant. Water experiences an acceleration of t9.8 m/s2. This is equivalent to the value of g that is acceleration due to gravity. Gravity has same effect on everything including water and other material objects.
  • Falling in a hole – When we are walking and overlook a hole that might have been dug for drainage maintenance, we experience a free fall. The hole’s depth is responsible for how much pain we incur as the deeper the hole, more time we will get to attain the terminal velocity. The terminal velocity is so high that we will die if fallen with terminal velocity. The acceleration of body is equal to 9.8 m/s2 that is the value of acceleration due to gravity. Hence we can say that falling in to a hole is an example of free fall.
  • First stage of rockets– Rockets get rid of everything once it is no longer necessary for its further flight. This way the rocket can continue moving upward without having any dead weight to carry. Once the first stage of rocket is detached, the first stage experiences a free fall that is the rocket falls back on Earth with an acceleration of 9.8 m/s2.
  • Second stage of rockets – Second stage of rockets exist for many rockets but not all rockets. Usually the second stage is the satellite or a second engine that burns up to take the third stage that is the payload to orbit. This stage also falls freely in the same fashion as that of first stage. The second stage also falls with an acceleration of 9.8 m/s2.
  • Dry leaves falling from tree– When the leaves go dry, they are shed by the trees. When the leaves are detached from the branch, the leaves experience a free falling motion. They come down with an acceleration of 9.8 m/s2. If the winds are blowing at a very high speed the leaves will not be able to follow a free fall motion but in the absence of wind they do follow a free fall motion.
  • Fruits falling from tree – Similar to leaves, fruits also some times fall from the branch. When they are detached from the branch, the fruits fall with an acceleration of 9.8 m/s2. This way we can say that the motion of fruit is a free fall motion.

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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