Category: Physics Notes PPT

The word energy is used a lot in our day-to-day life. You have often heard people saying that they have exhausted their energy. Though it is used very commonly, it has a significant meaning. Energy is said to be the person’s ability to do or perform certain work. Energy can be stored as well as measured in numerous forms. 

Are you aware of the fact that energy can not be destroyed? Often people say that they have exhausted their energy but this energy can never be destroyed, it can just be transferred from one form to another form of energy. In this transformation of energy, work is done there. There are differences in energy, just like some forms of energy are more useful to us than other forms of energy. The two most common kinds of energies are kinetic energy and Thermal energy. For the time being, you can understand kinetic energy from the energy possessed by an obvious body such as that of a moving bullet. While we talk about Thermal energy it uses energy in the form of heat. A piping hot cup of your regular tea has his Thermal energy stored in it.

In practice, there is a fact that whenever work is done one form of energy is converted to another formidable energy and thus transfer of energy includes loss of energy at some points also. Let’s take an example of a traditional bulb: only 3% if the bulb is efficient for converting electrical energy to the visible light, while if we talk about a human being he is able to convert only 25% of its energy into chemical energy. Here, in this article you will get the knowledgefaber the energy and the work done. For Any work done energy is required and for doing work also energy is lost. In this article you will receive knowledge about what do this work and energy means, when we can say the work to be done,example if work done,energy, work energy principle, difference between work and energy and at last some recently asked questions that will help you to enhance your knowledge regarding this topic work and energy

What do Work and Energy State for?

In physics, the concept of work and energy is thoroughly correlated and linked to force. It is because whenever force is applied to any object, there is some work done and also some change in the energy. Work is a physical activity that includes movement in the direction of applied force. 

When is Work Done?

Work is said to be done when we apply a force which causes a movement in an object through a distance. According to physics definition, work defines itself only when an object is lifted or moved. However, it is not about an object in a stationary position. 

The amount of work done is equal to the product of the acceleration due to gravity, the actual mass of the object, and the height with which it has travelled. Generally, the work done against gravity is represented by the following equation:

W = m*g*h

Here, m= mass of an object

g= acceleration due to gravity

W= work done

h= height through which the object is raised 

The above diagram shows the two work sorts, namely; positive and negative. When the direction of the force applied is the same in which the object is displaced, then the work done is positive. When the applied force displaces the object in the opposite direction then the work done is said to be negative. 

Example of Work Done

When an individual kicks a ball, they are exerting an external force. Due to this external force, say F, the ball moves to some distance. The distance, with which a ball moves from its rest position to another position, refers to displacement, say d. Hence, work is said to be done, and its equation is given by:

Work = Force * Displacement

 or

W= F * d

The equation of the work states that work done is the product of applied force and displacement. If you are applying a force on the body and the movement is done then only you can tell the work to be done, otherwise, if there is no movement for your applied force then you have not done any work. Let’s take a simple example if you apply force on a wooden lock and the block moved then the work is said to be done by you but if you apply the same amount of force or even a bit of extra force for moving a wall the wall will not show any movement and thus the work is not said to be done in this case.

What is Energy?

Energy refers to the ability of an individual to do work. It can be either absorbed or destroyed and can transform from one object to another. The two general forms of energy are potential energy and kinetic energy. The most common way to measure energy is to measure the amount of work done or the ability of an individual to do work. Kinetic energy is the energy that is possessed by a body when in motion while potential energy is the energy possessed by the edify when it is in a rest state or still state.

The kinetic energy is given by the formula: K.E. = 1/2 * m * v2

P.E. = m * g * h

Different types of Energy are

The unit of the energy is given by Joule (J). It is the same as that of work.

Like work, energy also has magnitude but no direction. Thus,  energy is said to be a scalar quantity.

What is the Work-Energy Principle?

According to the principle of work and energy, the change in the kinetic energy of a body is directly proportional to or equivalent to the total work done on the body. The work-energy principle can be represented as:

Work was done = Final Kinetic Energy- Initial Kinetic Energy 

or

W = K_f – K_i

The work-energy principle is derivable from the physics law, that is, the conservation law of energy. 

The diagram shows a man applying force to move the box in the upward direction. In this case, the man’s kinetic energy is equivalent to the amount of work done in moving the box. 

What is the Difference Between Work and Energy?

• Whenever an applied force changes the object’s distance, it is said to be work done on an object. However, the ability to create or produce some work refers to energy.

• There is no further work; however, there are different types of energy, like sound energy, mechanical energy, and many more.
  

Work is said to be accomplished only if there is some displacement of the object. In case there is no displacement, but the force is applied, then the work done is zero. However, energy does not depend on whether some displacement is or not. For example, a man pushing a wall is applying force to move to a certain distance. The wall does not move, and hence the work done comes out to be zero. However, the energy of the man is released while pushing a wall.

The understanding of concepts in Physics is a basic block without which you are nowhere.

Often when one understands that the theories thoroughly, we see that they can easily discover the relation between the quantities by which they can construct the formulas that generally derive it and learning for them will be simple.

The questions which are in the subject physics are something which challenges your skills and physics knowledge as well. These are grounded on three things:

1. To examine what is provided and what is asked in the numerical.

2. Next is the making use of the correct formula.

3. Filling in the values and computing properly.

To crack all these kinds of challenges which are in the form of questions one needs to have a proper understanding of the subject of Physics formulae as well as its concepts.

Here,  provided all physics formulas in a simple format in our effort to create a repository where a scholar can get hold of any sought after formulas.

Important Physics Formulas

• Planck constant h = 6.63 × 10⁻³⁴ J.s = 4.136 × 10^-15 eV.s

• Gravitation constant G = 6.67×10⁻¹¹ m³ kg⁻¹ s⁻²

• Boltzmann constant k = 1.38 × 10⁻²³ J/K

• Molar gas constant R = 8.314 J/(mol K)

• Avogadro’s number NA = 6.023 × 10²³ mol⁻¹

• Charge of electron e = 1.602 × 10⁻¹⁹ C

• Permittivity of vacuum 0 = 8.85 × 10⁻¹² F/m

• Coulomb constant 1/4πε₀ = 8.9875517923(14) × 10⁹ N m²/C²

• Faraday constant F = 96485 C/mol

• Mass of electron m_e = 9.1 × 10⁻³¹ kg

• Mass of proton m_p = 1.6726 × 10⁻²⁷ kg

• Mass of neutron m_n = 1.6749 × 10⁻²⁷ kg

• Stefan-Boltzmann constant σ = 5.67 × 10⁻⁸ W/(m² K⁴)

• Rydberg constant R_∞ = 1.097 × 10⁷ m⁻¹

• Bohr magneton µ_B = 9.27 × 10⁻²⁴ J/T 

• Bohr radius a₀ = 0.529 × 10⁻¹⁰ m 

• Standard atmosphere atm = 1.01325 × 10⁵ Pa 

• Wien displacement constant b = 2.9 × 10⁻³ m K .

• Wave = ∆x ∆t wave = average velocity ∆x = displacement ∆t = elapsed time.

• V_avg = (vi + vf*)²

V_avg = The average velocity 

vi = initial velocity 

vf = final velocity that is another definition of the average velocity which works where letter a is constant.

A = acceleration 

∆v = change in velocity 

∆t = elapsed time.

∆x = the displacement 

vi = the initial velocity 

∆t = the elapsed time 

a = the acceleration 

Use this formula when you don’t have vf. 

∆x = displacement 

vf = is the final velocity 

∆t = elapsed time 

a = acceleration 

Use this formula when you don’t have vi.

F = force 

m = mass 

Then a = acceleration Newton’s Second Law. 

F is the net force on the mass m. 

W = weight 

m = mass 

g = acceleration which is due to gravity.

Then we see that the weight of an object with mass m. This is said to be really just Newton’s Second Law. 

µ = coefficient of friction 

N = normal force 

Here µ can be either the kinetic coefficient of friction µk or the static coefficient of friction. 

W = work t

F = force 

d = distance 

θ = angle between F and the direction of motion 

KE = kinetic energy

m = mass

v = velocity

PE = potential energy 

m = mass 

g = acceleration due to gravity 

h = height

W = work done 

KE = kinetic energy. 

The “work-energy” which we have learnt is the theorem that is the work done by the net force on an object equals the change in kinetic energy of the object. 

We can write it as E = KE + PE 

E = total energy

KE = kinetic energy

PE = potential energy

W = work

∆t = elapsed time

Power is the amount of work which is done per unit time that is power is the rate at which work is done.

Mechanical energy refers to the total of kinetic energy and potential energy possessed by an object that is used to do a particular work. In other words, it describes the energy of an object because of its motion or position, or both.

If K E and P E refers to the kinetic and potential energies of a body, its mechanical energy is given by,

M.E = K.E + P.E

For an object thrown upwards, its total mechanical energy is given by:

E = ½ mv² + mgh

Where,m is the mass of an object, v , the velocity of that object, g, the acceleration due to gravity and h tells at what height the object is from the ground.

Example: The kinetic energy of a body flying at a certain height from the ground is 4500 J and its potential energy is 8000 J. Find the total mechanical energy associated with it. 

Solution:

KE = 4500 J, PE = 8000 J, ME=?

ME = KE + PE = 4500 + 8000 = 12500 J

Example: An object of mass 2 kg has been projected vertically upwards with a kinetic energy of 100 J. Find the maximum height it can reach (take g = 10 m/s² and PE of the object at the point of projection is zero).

Solution: In motion under gravity, total mechanical energy is conserved.

Total Mechanical energy at the point of projection = total mechanical energy at the maximum height.

At the point of projection: KE₁ = 100 J, PE₁ = 0 

At the maximum height: KE₂ = 0, PE₂ = mgh

Now, KE₁ + PE₁ = KE₂ + PE₂

Therefore, 100 + 0 = 0 + mgh

⇒h=100mg=1002×10=5m

The object will reach upto a maximum height of 5 m.

Question: A ball thrown up with certain kinetic energy can reach a maximum height of 8 m. An identical ball thrown up with four times kinetic energy can reach a maximum height of:

Options:

(a) 8 m

(b) 32 m

(c) 64 m

(d) 128 m

Answer: (d)

Kinetic Energy and Potential Energy

The energy that a body possesses when it is in motion is defined as kinetic energy, Irrespective of the direction of the motion (horizontal or vertical).

The types of kinetic energy can be classified into vibrational kinetic energy, rotational kinetic energy, and translational kinetic energy based on its movement.

e.g: Any object falling from a height.

 

Potential Energy

The stored energy that the body has when it is not in motion is defined as potential energy. 

The types of potential energy can be classified into gravitational potential energy and elastic potential energy.

e.g: A ball resting in its position.

The four kinds of kinetic energy include:

• Electrical Energy:  The energy produced by electricity is known as electrical energy.

• Radiant Energy: The energy produced by the light waves is called radiant energy.

• Sound Energy: The energy produced by the sound waves is known as sound energy.

• Thermal Energy: The energy produced by the heat is called thermal energy.

Conversion of Energy

The energy can never be created or destroyed, rather converted and transferred.

Any kind of energy that is transferred if it causes an object or thing to move is an example of the conversion of energy.

Below are some of the examples of how various kinds of energy are converted into mechanical energy:

On the other hand, mechanical energy can also be converted into various other kinds of energy.

Below are some examples of how mechanical energy is converted into various kinds of energy.

• Turning a switch on converts the mechanical energy into electrical energy and later on to radiant energy.

• The human body digesting food converts mechanical energy into chemical energy.

Mechanical Energy and its Origin

Mechanical energy is found everywhere in the world and around us. Any object or a thing that moves or doesn’t move consists of some of the other forms of mechanical energy in it. The mechanical energy comes from the position as well as the speed of the moving object. The two energies, that is, kinetic and potential energies are still there and are combined. 

For example, the car moving at the speed of 40km/h still has some potential energy left that needs to be released on the gas pedal.

Fact: Imagine the amount of mechanical energy the mountains store in them, The landslides are examples of how much energy they can release.

The Law of Conservation of Mechanical Energy

According to the law of conservation of mechanical energy, in a given closed system, the amount of mechanical energy remains the same. There is no change in the total energy, and it can only convert from potential energy to kinetic energy and vice versa. The outside external forces cannot dissipate the mechanical energy. The total amount of mechanical energy can neither be destroyed nor created.

Ibn al-Haitham was a physicist who had described the theory of vision. Scientists used to call him the father of optics.

Mirror Equation Derivation is very common among the students. Many questions are asked from this section of various boards as well as entrance tests. Mirror Formula Proof is very easy. It can be explained as the relation between the distance of an object, the distance of an image, and the focal length of the mirror.

Facts on Spherical Mirror

Some facts are there that you must know about the spherical mirror:

The object distance(u) is the length between the object and the pole of the mirror.

Image distance(v) is the length between the image and the pole of the mirror. 

Focal Length(f) is the distance between the principal focus and the pole of the mirror.

[frac{1}{f}] = [frac{1}{V}] + [frac{1}{U}]  

Where, 

f = focal length of the mirror

V = the distance of the image

U = the distance of the object

Proof of Mirror Formula

The formula which gives the relation between object distance (u), image distance (v) and focal length is defined as Mirror Formula.

[frac{1}{V}] + [frac{1}{U}] = [frac{1}{f}]  

In Triangle XYZ  and Triangle X’Y’Z



Triangle XYZ ~Triangle X’Y’Z (XX similarity)              => XY /X’Y’ =XZ/X’Z —-(I) dfpe

Similarly, In PQRS  ~ X’Y’F
  

SR /X’Y’ = RQ/X’F
[frac{XY}{X’Y}] = [frac{RQ}{X’F}]   

[frac{XY}{X’Y}] = [frac{RQ}{X’F}]        (XY=SR)  —-(II)

From(i) &(ii)
[frac{XZ}{X’Z}] = [frac{RQ}{X’F}]     

[frac{XZ}{X’Z}] = [frac{RQ}{X’F}]     

=> [frac{X’Z}{XZ}] = [frac{X’F}{RQ}]       

=> [frac{(ZR-X’R)}{(XR-ZR)}] = [frac{(X’R-RF)}{RF}]


Now, RF = -f ;  ZR = 2RF = -2f ; XR = -u ; and X’R = -v

Put these value in above relation:

[frac{(-2f)-(-v)}{(-u)-(-2f)}] = [frac{(-v)-(-F)}{-f}]


=> uv = fv +uf

=>  [frac{1}{f}] = [frac{1}{U}] + [frac{1}{v}]  

Derive Mirror Formula for Convex

From the below diagram, you can get to know the Derivation of Mirror Formula for Convex Mirror.

The above picture shows the following value:

 -u = PB

+V = PB’

+b = PF

+R = PC

In triangle ABC and A’B’C

[frac{AB}{A’B}] = [frac{CB}{CB’}] → 1

In triangle ABP and A/B/P

[frac{AB}{A’B}] = [frac{PB}{PB’}] → 2

From 1 and 2, we get

[frac{CB}{CB’}] = [frac{PB}{PB’}] …. 3

We also know CB = PB + PC and CB’ = PC – PB’

Putting the above values in eq (3)

[frac{PB+PC}{PC-PB’}] = [frac{PB}{PB’}] = [frac{-u+R}{R-v}] = [frac{-u}{v}]

⇒ -uv + vR = -uR + uv

⇒ uR + vR = 2uv

After dividing, uvR The final form of the equation is

[frac{1}{V}] + [frac{1}{U}] = [frac{1}{f}]  

Derive Mirror Formula for Concave Mirror

The Derivation of Mirror Formula for Concave Mirror is shown hereunder:

From the above image, we get

[frac{B’A’}{PM}] = [frac{B’F}{FP}] or [frac{B’A’}{BA}] = [frac{B’F}{FP}] (∵ PM = AB)….1

 [frac{B’A’}{BA}] = [frac{B’P}{BP}] ( ∵A P B angle = A’ P B’ angle)….. 2  

Equating 1 and 2, we will get,

[frac{B’F}{FP}] = [frac{B’P-FP}{FP}] = [frac{B’P}{BP}]

Also, B’P = -v, FP = -f, BP = -u

[frac{-v+f}{-f}] = [frac{-v}{-u}]

or, [frac{v-f}{f}] =[frac{v}{u}]

or, [frac{1}{u}] + [frac{1}{v}] = [frac{1}{f}]  

Derivation of Mirror Formula for Convex Lens

In the above image, you can notice two similar triangles i.e. △ABO and △A’B’O.

We can write 

[frac{A’B’}{AB}] = [frac{OB’}{OB}]   (1)

Also, △A’B’F and △OCF are similar.

We can write a relation as

[frac{A’B’}{OC}] = [frac{FB’}{OF}]

However, OC = OB

Then, [frac{A’B’}{AB}] = [frac{FB’}{OF}]   (2)

Equating both the equation 1 and 2, we get

[frac{OB’}{OB}] = [frac{FB’}{OF}] = [frac{OB’-OF}{OF}]  

If we conduct some sign convention, we will find

• OB=-u,  

• OB’=v 

• and OF=f

[frac{v}{-u}] = [frac{v-f}{f}]   

vf = -uv + uf or uv = uf – vf 

Dividing uvf into both sides, we get

[frac{uv}{uvf}] = [frac{uf}{uvf}] – [frac{vf}{uvf}]

⇒ [frac{1}{f}] = [frac{1}{v}] – [frac{1}{u}] (This is the convex lens formula)

Sign Conventions for Mirror Equation

Mirror Equation follows certain sign conventions given below:

• In the rectangular coordinate system, the principal axis of the mirror is taken along the x-axis, and its pole is taken as the origin.

• All the distances parallel to the principal axis of the mirror are measured from the pole of the mirror.

• The object is taken on the left side of the mirror. Hence, light is incident on the mirror from the left-hand side.

• The distances measured in the direction of the incident light are taken as positive.

• The distances measured in the direction opposite to the direction of incident light are taken as negative.

• The heights measured upwards and perpendicular to the principal axis of the mirror are taken as positive.

• The heights measured downwards and perpendicular to the principal axis of the mirror are taken as negative. 
  

Solved Examples

Derive the relation u₁+v₁=R₂ for a concave mirror

Solution:

The relationship between object distance (u), the image distance (v) and the focal length (f) of the mirror is known as the mirror formula.

Suppose, an object AB is placed at a distance u from the pole of the concave mirror of a small aperture, just beyond the center of curvature. Hence, its real, inverted and diminished image AB is formed at a distance v in front of the mirror.

According to the Cartesian sign convention,

Object distance (PB)=−u

Image distance (PB)=−v

Focal length (PF)=−f

Radius of curvature (PC)=−R

It is clear from the geometry of the figure, right-angled △ ABP and △ABP are similar.

∴ABA′B′=PBP′B′=u−v

​∴ABA′B′=uv ……..(i)

Similarly, △ ABC and △ A′B′C’ are similar.

∴ABA′B′​=CBC′B′ …….(ii)

From figure,

CB′PC′PB′=−R−(−v)=−R+v

and CB=PB−PC=−u−(−R)=−u+R

From (ii),

 ABA′B′​=−u+R−R+V …… (iii)

Comparing (i) and (iii),

uv=−u+R−R+v

∴−uv+Rv=−Ru+vu 

or, R(u+v)=2uv

∴v₁+u₁=R₂

(Dividing both sides by Ruv)

Hence, Proved.

Conclusion

This article will help you to know about the mirror formula and its relevant usages. With the use of optics, we can calculate and analyze the behaviour of light and image formation. Thus, this chapter is very helpful.

When you talk about the potential energy formula, Physics will come up with several definitions. That is because there are different forms of potential energy. In general terms, Potential energy is the energy stored in the body of an object. Some of the different kinds of potential energy include electric potential energy, gravitational potential energy, spring potential energy, elastic potential energy, etc. The potential energy formula depends on the type of potential energy.  Potential energy is an important factor in determining the state of rest or motion of the body.

 

What are the Potential Energy Types?

There are different kinds of potential energy. Some of them include:

Gravitational potential energy can be defined as the body’s energy by virtue of the gravitational force acting on them.

 

Electric potential energy is defined as the energy stored in the body by virtue of its electrons’ arrangements.

 

Elastic potential energy is known as the energy stored in the body by virtue of its elastic properties.

 

Spring potential energy is a modified form of elastic potential energy that takes place in the spring.

 

What is the Potential Energy Formula?

As stated earlier, the potential energy formula depends on the type of Potential energy. The gravitational potential energy formula is

 

PE= mgh

 

Where PE is Potential energy

 

m is the mass of the body

 

h is the height at which the body is placed above the ground

 

g is the acceleration due to gravity. 

 

The elastic potential energy formula or spring potential energy formula is

 

U= ½ k∆x²

 

Where U is the elastic potential energy

 

K is the spring constant

 

∆x is the change in position.

 

The electric potential energy formula is

 

UE= kq₁q₂/r

 

Where UE is the electric potential energy

 

k stands for Coulomb’s constant

 

whereas q₁ and q₂ stands for charges of the two separate points present in the circuit

 

r stands for distance of the separation. 

 

In general, the SI unit of Potential energy is Joule, and the dimensional formula is M¹L²T^-2.

 

Potential Energy Examples

There are several examples of potential energy. When a ball is thrown upward, mechanical energy is converted to kinetic energy by virtue of its motion. As it reaches the highest point, the kinetic energy is converted to potential energy. However, the potential energy is converted to kinetic energy as the ball comes down.

 

Potential Energy Formula Derivation

According to the potential energy function for a conservative force, the force acting on an object can be described as,

 

F = dUdx dU = −Fdx ∫x₂x₁U = −∫x₂x₁Fdx

 

According to the definition of potential energy, the force acting on the object is F= mg

 

H is the height from the point of reference

 

Substituting these formulas,

 

U = −[mg(h₁−h₂)] 

 

or, U = [mg(h₂−h₁)] 

 

Where,

 

U – Potential energy

 

M- the mass of the object

 

G – acceleration due to gravity 

 

h₁ – the height of the point of reference

 

h₂ – the height at which the object is positioned.

 

Applications of Potential Energy

An object’s potential energy is derived from its position when it is stationary rather than from its motion, i.e., movement and potential energy do not have velocity, unlike kinetic energy. Following are some of the applications of potential energy:

• When an elastic band is stretched to tie something, it gains potential energy, and when it is released, it gains kinetic energy, which has velocity. Here, potential energy is converted to kinetic energy without any loss of energy.

• When the river water is dammed and used to generate hydroelectricity, it attains potential energy and is converted to kinetic energy when the river water flows freely.

• When an archer drags back an arrow, the arrow has potential energy converted to kinetic energy to move forward towards the target when released. 

• If you hold a ball vertically upwards from the ground, it is subjected to potential energy caused by the gravitational force. 

• In chemistry, chemical potential energy stored in the molecules is the reason for chemical reaction and bonding. 

• We see a pendulum in a clock. When it is held at an end, it has potential energy which is converted to kinetic energy when it is released. 

• Elastic potential energy is present in spring when it is compressed or released freely, but when the spring is in movement, it is subjected to kinetic energy.

• Even the food we eat has some form of chemical potential energy that reaches our stomach. Our body enzymes convert it to kinetic energy and use it to perform different tasks. 

• When snow falls on mountains or a surface, it has potential energy. When this energy exceeds the holding capacity of the surface, it is released as an avalanche and gets converted to kinetic energy when it falls.

• A bullet loaded in a gun also works on the same principle similar to the bow and arrow. It has potential energy when it is at rest and gets converted to kinetic energy when it is shot by anyone.

 

Conclusion

Potential energy is known as the energy possessed by the body by virtue of its position. There are different forms of potential energy. Different potential energy formulas represent all the
se forms.

A free-falling object formula describes the self-governing phenomena of the body having some mass. A free-fall concept that talks about the body freely falling under gravity. 

 

Assume that a body with velocity v is descending freely from a mountain of height (h) for time (t) seconds. Now, because of gravity (g), the body falls in the following manner:

 

 

From this example, we can describe the free-fall motion formula. As it covers a certain distance, we can describe the free fall distance formula. An object possessing a free-fall object formula bears velocity, which we can calculate by using the free-fall velocity formula.

 

Since the object falling from a mountain has a maximum height, so does the object. The eight can be calculated by using the maximum height formula free fall. As there is a rate of change of velocity in an object while free-falling, so we can determine the free-fall acceleration formula as well.

 

So, on this page, we will cover all the equations for a falling body along with the free fall physics formula, and then derive the free fall formula as well.

 

Free Fall Physics Formula

We know that any object that is moving and being acted upon only by the force of gravity is said to be “in a state of free fall.” Such an object experiences a downward acceleration of 9.8 ms^-2. 

 

We must note that whether the object is falling or rising towards its peak if it is under the sole influence of gravity, its acceleration value will always remain 9.8 ms^-2. 

 

So, the free-fall acceleration formula says that ‘a’ always equals ‘g’ under free fall. 

 

Free Falling Bodies Formula

The free-fall motion formula covers the following equations for a falling body:

The maximum height formula free fall is:

                  h    =   1/2 gt²

The free velocity formula is:

                    v²  =  2gh, and

                      v   =  gt

Now, let us derive free fall formula:

 

Free Falling Object Formula

Below are the following kinematic equations for deriving the free-fall motion formula:

First equation: if   =  v_i  +  at  ………..(1)

The second equation: d  =  v_i + v_f/2 . t…..(2)

The third equation: v_f²   =  v_i²  +  2* a* d…..(3)

The fourth equation: d  =  v_it +  1/2 at²…..(4)

Here, we replaced ‘s’ with ‘d’, and ‘d’ is the displacement

v_i  and v_f are the initial and the final velocities of a falling object

a = acceleration, and

t = time in seconds

 

Free Fall Velocity Formula

We must note that the initial velocity of the object will become zero, so the first equation becomes:

v_f   =   at

Also, according to the free-fall object formula, ‘a = g,’ so the equation (1) becomes:

v_f   =   gt

This free-falling bodies formula is the free-fall velocity formula.                        

Also, from equation (3), we have:

v_f²   =  v_i² +  2* a* d

Or,

v_f²   =  2gh…….(5)

This is again the free-fall velocity formula.

 

Free Fall Distance Formula

From equation (4), we see that displacement is the height traveled by the falling object. So substituting ‘with ‘h,’  and ‘a’ with ‘a,’ we have:

                                   h  =  v_it +  1/2 at²                        

Putting v_i   = 0:

                                h  =  1/2 gt²   

This is the required  free fall equation with height ‘h.’    

                         

Maximum Height Formula Free Fall

From equation (5), we have:

                        v_f²   =  2gh

The maximum height formula free fall is:

                            h   =   v_f²/2g

 

Concepts to Free Falling Objects Problem Solving

There are a few concepts of free-fall motion that hold paramount importance when using the equations to analyze free-fall motion. These concepts are as follows:

• A freely falling object experiences an acceleration of 9.8 ms^-2.  (Here, the negative sign indicates a downward acceleration or deceleration).Whether clearly stated or not, the value of the acceleration in the kinematic equations remains 9.8 ms^-2 for any freely falling object.

• If an object is mistakenly dropped (as opposed to being thrown) from an elevated height, its initial velocity remains 0 m/s.

• If an object is projected upwards in an exactly vertical direction, it slows down as it rises upward. The point at which it reaches the peak of its trajectory is the point where the velocity is 0 m/s. This value can be used as one of the important motion parameters in the kinematic equations; for instance, the final velocity (v_f) after traveling to the peak reaches a value of 0 m/s.

• If an object is projected upwards in an exactly vertical direction, its velocity at which it is projected equals in magnitude but in a sign opposite to the velocity after it returns to the same height. 

In the nutshell, a ball projected with an upward velocity of + 50 m/s will have a downward velocity of – 50 m/s when it returns to the same height.

Now, let’s apply these concepts in solving problems on a free fall formula:

 

Free Fall Formula Calculator

For understanding the free fall formula; let’s have a look at the below examples to apply the
equation for the freely falling body:

 

Example 1: What will be the height of the body if it has a mass of 3 kg and after 8 seconds it reaches the ground?

Solution:

Given data: 

Height h =?

Time t = 8s

You are acquainted with the concept that free fall is independent of mass. So, using the free-fall formula here:

h  =  1/2 gt² 

Putting g  = 9.8 ms^-2 and t = 8s:

h = 1/2 *  9.8* (8)²

On solving, we get:

h = 313.6 m

Answer: Therefore, the maximum height that a body covers to reach the ground is 313.6 m.

 

Example 2:  The cotton ball falls after 4 s and the iron ball falls after 7 s. Determine which object falls with a higher velocity?

Solution:

Since the velocity in free fall is independent of mass, so apply the following formula:       

v (Velocity of cotton ball) = gt = 9.8 m/s² × 4 s = 39.2 m/s

v (Velocity of iron ball) = gt = 9.8 m/s² × 7 s = 68.6 m/s

We see that the iron ball falls with a higher velocity than the cotton ball.

 

Study Habits Students should adopt for Better Scores

Inculcating good habits in daily routine helps an individual to make their days more productive in many ways. Science is a scoring subject and one can secure a good percentage with required hard work. Many students find science a tough subject but it can surely help you to gain more marks as it is based on logistics and reason. Read on to know a few study habits students can adopt to gain more than 95% in science:

• Maintain different notebooks for your formulas, equations, and theories as it will help students to find what they are looking for easily from the vast sea of the syllabus. This will also help in making the revision process quick and easy. 

• While preparing for the science exam make sure to solve all the numericals by yourself first. Surely students can take help from their teachers or books if they are stuck with some question but the first efforts should be made to do it all by yourself and try again and again. Learning and understanding concepts are important but it is also important that students are aware of when these are to be implemented and how. 

• Students should analyze while studying the topics they are finding difficult to understand and focus on them. If students are aware of their weak points only then they can focus more on them and make it their strength. 

• Regularity is an important habit students must inculcate to secure good marks. A student regular with his/ her syllabus will help them to understand their grasp on concepts. Regularity not only includes attending classes, lectures, and tuitions but also self-study sessions. 

• Students should first concentrate on the course books that are provided by the NCERT. Many students have the habit of jumping to reference books before finishing the NCERT. It is an observation that most of the questions asked in board exams are asked from NCERT books. Reference books can be used as a source of extra material or for in-depth study of a particular concept. However, NCERT is a student’s bible during the exam season.

• Students should maintain a notebook for notes. Notes work as a summary of each concept during the revision period. It speeds up the process of revision and is a convenient way to learn from. Students can also include insights from their teachers or their insights for particular topics. 

 

Conclusion

We call the free fall bodies formula the kinematic equations free fall because they are derived from kinematic equations.

 

Also, free fall is independent of the mass and it only depends on the height the object fell from.