The Effect of Terminal Velocity on the Time of Descent for a Thrown Object

The Effect of Terminal Velocity on the Time of Descent for a Thrown Object

🔹▪️🔹

If you throw the ball at a speed that is less than its terminal velocity then the ball should take almost exactly the same time to rise as it does to fall. (Ascending and descending time are equal)

On the other hand, if the ball is thrown faster than its terminal velocity speed, the ball will take a longer time to fall due to it reaching terminal velocity on the way.(ascending and descending time are unequal). In this case two forces are acting upon the thrown object.

This is the concept we are intended to discuss

🍁🍁🍁

Free fall body

1. Falling with Air Resistance

As an object falls through air, it usually encounters some degree of air resistance.

Air resistance is the result of collisions of the object's leading surface with air molecules.

The actual amount of air resistance encountered by the object is dependent upon a variety of factors.

To keep the topic simple:

it can be said that the two most common factors that have a direct effect upon

▪️The speed of the object and

▪️The cross-sectional area of the object.

Increased speeds result in an increased amount of air resistance.

Increased cross-sectional areas result in an increased amount of air resistance.

Examples:

Free falling of an elephant and a man

Look at the picture given below:

Does air resistance apply more on to an elephant or a man

Next:

Meaning of free fall motion

Free fall is a special type of motion in which the only force acting upon an object is gravity.

Objects that are said to be undergoing free fall, are not encountering a significant force of air resistance; they are falling under the sole influence of gravity.

Under such conditions, all objects will fall with the same rate of acceleration, regardless of their mass.

As an example:

Consider the free-falling motion of a 1000-kg baby elephant and a 1-kg overgrown mouse.

If Newton's second law were applied to their falling motion, and if a free-body diagram were constructed, then it would be seen that the 1000-kg baby elephant would experience a greater force of gravity.

This greater force of gravity would have a direct effect upon the elephant's acceleration; thus, based on force alone, it might be thought that the 1000-kg baby elephant would accelerate faster.

But acceleration depends upon two factors:

1. Force and

2. Mass.

The 1000-kg baby elephant obviously has more mass (or inertia).

This increased mass has an inverse effect upon the elephant's acceleration.

And thus, the direct effect of greater force on the 1000-kg elephant is offset by the inverse effect of the greater mass of the 1000-kg elephant; and so each object accelerates at the same rate - approximately 10 m/s²

The ratio of force to mass (Fnet/m) is the same for the elephant and the mouse under situations involving free fall.

Why does an object that encounters air resistance eventually reach a terminal velocity?

Shyam Sunder: I don’t know why terminal velocity of concept is including here…I know we can treat air as a fluid but we can solve this problem by finding netforce on a body easily…

Azeez: Here is the point:

In the diagrams below, free-body diagrams showing the forces acting upon an 85-kg skydiver (equipment included) are shown.

F

or each case, use the diagrams to determine the net force and acceleration of the skydiver at each instant in time.

The diagrams above illustrate a key principle.

As an object falls, it picks up speed. The increase in speed leads to an increase in the amount of air resistance.

Eventually, the force of air resistance becomes large enough to balances the force of gravity.

At this instant in time, the net force is 0 Newton; the object will stop accelerating.

The object is said to have reached a terminal velocity.

The change in velocity terminates as a result of the balance of forces.

The velocity at which this happens is called the terminal velocity.

In situations in which there is air resistance, more massive objects fall faster than less massive objects. But why?

Consider two objects of masses 100kg and 200kg falling freely in air resistance. Which one comes first. Of course the answer is 200kg.

B

ut when in the absence of air resistance what could be the situation? Which object reaches first? 200kg or 100 kg.

Buvana: Both reach same time. Due to absence of air resistance

Azeez: Correct. Why?

Buvana: No frictional force oppose the motion

Azeez: The reason is:

In the absence of air resistance, both objects would fall at the same rate, and therefore hit the ground at the same time.

This is because the acceleration due to gravity is the same for all objects regardless of their mass.

This is known as the principle of equivalence, which is a fundamental concept in physics.

Therefore, both the 100kg and 200kg objects would hit the ground at the same time if there is no air resistance.

Buvana: Means gravitational force same

Azeez: Now let's take one more situation ...

The situation is as shown in the figure given below.

W

hich one reaches the ground first?

Buvana: Once reach terminal velocity...speed remain same...before that 150 kg first. Means before critical velocity

Azeez: Our conceptual understanding comes to an end now.

A falling object will continue to accelerate to higher speeds until they encounter an amount of air resistance that is equal to their weight.

Since the 150-kg skydiver weighs more (experiences a greater force of gravity), it will accelerate to higher speeds before reaching a terminal velocity.

Thus, more massive objects fall faster than less massive objects because they are acted upon by a larger force of gravity; for this reason, they accelerate to higher speeds until the air resistance force equals the gravity force.

If both the objects reach to the terminal velocities, which means, at terminal velocities, force of gravity is equal to the upward force. So both the objects reach the ground at the same time.

Therefore the use of parachute is to reduce the speed of the objects or allowing the objects to reach terminal velocities so that force gravity equals upward force caused by the air resistance .