Formula For Maximum Kinetic Energy

Formula of Kinetic Free energy

Kinetic energy refers to a type of energy that an object or body possesses by virtue of its motion. It is possessed past every particle performing whatever kind of motion. Kinetic energy is a property of a moving body or object that does not depend on move but, but it besides depends upon the trunk'south mass. Mechanical energy can be divided into ii different types, the first 1 is Kinetic energy, and the second one is potential energy. Potential energy refers to a blazon of energy that an object or torso possessed by virtue of its position. For case, when an object is a free fall, the object possesses kinetic free energy. Kinetic energy can be due to rotation, translation, and vibration. We tin calculate KE using the mass and velocity of that trunk.

In this article, we will discuss the formula to calculate the kinetic energy with certain examples.

Method one:

Understanding Kinetic Energy

By knowing the Formula

The formula using for calculating the Kinetic energy is given below

KE = ½ mv²

Where

m = mass of an object or trunk.

v = velocity of an object or body.

Permit'southward sympathize what is the mass and what is the velocity of an object.

Mass: Mass of an object or trunk refers to how much affair is in the object. It is denoted past m. Unit of measurement of mass is the joule.

Velocity: The velocity of an object refers to the rate at which the object changes its position. Information technology is denoted past v. Unit of velocity is g/south.

Summate the mass of an object:

When nosotros solve a trouble where the mass is not given, and so first, y'all demand to summate the mass to proceed. This can be done past obtaining the mass in kg.

Find the velocity of an object:

You oft face the problem while solving any trouble, information technology does non give you the velocity of an object, but distance and time are given. Here, you need to calculate the velocity by applying the given formula.

Velocity = Distance/time = d/t

Example ane: If an object travels a distance of eight meters in two sec, find the velocity of an object?

Solution:

Given,

Distance = 8 meter

Fourth dimension = 2 sec

We know that,

V = distance/ fourth dimension = 8/2 = 4 m/sec

Example 2: If an object travels a distance of 10 meters in 5 sec, detect the velocity of an object?

Solution:

Given,

Distance = 10 meter

Fourth dimension = five sec

We know that,

V = distance/ time = ten/five = 2 k/sec

Method 2

Finding the Kinetic Energy

Write the equation:

The formula used to summate the Kinetic energy is given below.

KE = ½ mv²

Where

yard = mass of an object or body.

v = velocity of an object or trunk.

The value of KE should always be in joules J, which is the standard unit of measurement of KE.

Put the value of mass and velocity.

To calculate the KE, you demand to put the value of mass and velocity in the formula. If the value of mass and velocity are not given in the questions, you demand to calculate it.

Instance 1:

Notice the KE of an 80 kg men running with a velocity of viii m/southward.

Solution:

Given;

Mass = 80 kg

Velocity = 8 m/due south

We know that,

KE = ½ mv²

KE = ½ × 80 × 8ⁱⁱ

⁼½ × 80 × 64

= forty × 64

= 256 J

Example 2:

Find the KE of a 120 kg human being running with a velocity of 10 m/s.

Solution:

Given;

Mass = 120 kg

Velocity = 10 m/due south

We know that,

KE = ½ mv²

KE = ½ × 120 × 10²

= ½ × 120 × 100

= lx× 100

= 6000 J

Using KE summate velocity or Mass

The formula using for computing the Kinetic free energy is given below

KE = ½ mv^two

Where,

m = mass of an object or body

5 = velocity of an object or torso.

Put the Unknown Variables:

In some questions, you lot have the value of KE and mass. In that instance, you demand to summate the value of the velocity.

Allow's empathise this concept with the help of an example

Instance i: What is the velocity of a body with a mass of 50 kg, and the value of kinetic free energy is 2500 J?

Solution:

Given;

mass = 50 kg

Kinetic Energy = 2500 J

Nosotros know that

KE = ½ mv²

2500 = ½ × fifty × v²

fiveⁱⁱ = 2500/25

v^two= 100

v = x

Instance 2: What is the velocity of a body with a mass of 60 kg and the value of kinetic energy is 480 J?

Solution:

Given;

mass = sixty kg

Kinetic Energy = 480 J

We know that

KE = ½ mv²

480 = ½ × 60 × v²

v² = 480/thirty

5^two = 16

v = √sixteen = 4

Let's understand this concept with the help of an case

Suppose y'all take the value of KE and velocity. In that case, yous need to find the value of the mass.

Example i: Find the mass of an object with a kinetic free energy of 500 J and a velocity of x m/s?

Solution:

Given;

Kinetic free energy = 500 J

Velocity = 10 m/south

We know that

KE = ½ mv²

500 = ½ × k ×10 ⁱⁱ

500 = ½ × m ×100

500 = 50 × k

m = 10 kg

Example ii: Find the mass of an object with a kinetic free energy of 600 J and a velocity of twenty yard/s?

Solution:

Given;

Kinetic energy = 600 J

Velocity = 20 thou/due south

We know that

KE = ½ mv²

600 = ½ × m ×20 ^two

500 = ½ × m ×400

500 = 200 × m

m = two.5 kg

Questions based on kinetic energy

Question i: If a football game has a mass of 3 kg, travels with a speed of 12 m/s, calculate the kinetic energy possessed by it.

Solution:

Given;

Mass = 3 kg

Velocity = 12 1000/s

Nosotros know that,

Kinetic Energy = ½ mv²

KE = ½ ×three× (12)²

⁼½ ×3× 144

= 216 J

Question 2: If a basketball has a mass of iv kg, travels with a speed of sixteen 1000/southward, calculate the kinetic free energy possessed by it.

Solution:

Given;

Mass = 4 kg

Velocity = 16 m/southward

We know that,

Kinetic Free energy = ½ mv²

KE = ½ ×four× (sixteen)²

⁼½ ×iv× 256

= 512 J

Question 3: If a 12 kg object was traveling at a speed of 120 m/s. At present, this mass transfers all its energy to a mass of 24 k. What will be the velocity of the 24 kg mass subsequently being hit by it?

Solution:

We know that,

KE = ½ mv²

First, nosotros will calculate the KE of the heavier object

Given,

M = 12 kg and v = 120 m/s

We know that,

KE = ½ mv²

= ½ × 12 × (120)²

= ½ × 12 × 14400

= 86400 J

Now, this energy is transferred to some other ball

Given;

Mass = 24 Kg

Velocity =?

We take calculated the value of kinetic energy

KE = 86400

So,

We know that,

KE = ½ mv²

86400 = ½ (24) 5²

five²= 86400/12 = 7200

5 = lx m/south

Question 4: If an 8 kg object was traveling at a speed of 80 m/s. At present, this mass transfers all its energy to a mass of sixteen m. What will be the velocity of the 16 kg mass afterward being striking by information technology?

Solution:

We know that,

KE = ½ mv^two

First, nosotros will calculate the KE of the heavier object

Given,

Thou = 8 kg and 5 = lxxx m/southward

We know that,

KE = ½ mv²

= ½ × 8 × (80)²

= ½ × eight × 6400

= 25600 J

Now, this free energy is transferred to another brawl

Given;

Mass = 16 Kg

Velocity =?

We have calculated the value of kinetic free energy

KE = 25600

So,

We know that,

KE = ½ mv²

25600 = ½ (16) 5²

vⁱⁱ= 25600/16 = sixteen

five = 4 thousand/southward