Kinetic Energy and Momentum

Kinetic energy is the type of energy that an item or particle has as a result of its movement. When work is done on an object by exerting a net force, the object accelerates and gains kinetic energy as a result. Kinetic energy is a property of a moving item or particle that is determined by its mass as well as its motion. Translation (movement along a path from one location to another), rotation around an axis, vibration, or any combination of motions are possible.

In athletics, the term “momentum” is frequently used. A team with momentum is on the march, and stopping them will take some work. A team with a lot of momentum is on the march and will be difficult to stop. Momentum is a physics term that refers to the amount of motion possessed by an item. The momentum belongs to a sports team that is on the rise. When an object is in motion (moving), it is said to have momentum.

Kinetic energy

The kinetic energy of an object is the energy associated with it when it is moving. “The energy required by a body to accelerate from rest to a stated velocity,” according to the definition. It’s a quantity with a vector.

We must apply force to accelerate an item. We must work in order to exert force. Energy is transferred when work is done on an object, and the object moves at a new constant speed. The energy transferred is known as kinetic energy, and it is determined by the mass and speed reached.

Formula for Kinetic Energy

As a mathematical expression:

K.E= 12mv2

Where,

m is the object’s mass in kg.

v is the object’s velocity in m/s.

Kinetic Energy Unit

Joules are the SI unit of kinetic energy.

Momentum

The virtue of an object’s mass is its momentum. The product of mass and velocity is what it’s called. It’s a quantity with a vector.

The quantity of motion of the body is defined as momentum. Because all objects have mass, if they are moving, they have momentum — their mass is moving. The factors mass and velocity influence momentum. We can change momentum by changing its mass or velocity; a momentum unit is created by multiplying a mass unit by a velocity unit.

• Because all objects have a certain amount of mass, they have momentum as they move or are in motion.
• As a vector quantity, momentum has both magnitude and direction.
• A particle’s momentum is the amount of time it takes for a constant force to bring it to a stop.
• Any item that is at rest has no momentum.
• If the mass of an item remains constant, its momentum is proportional to its velocity.
• The momentum of an object is equal to the mass times the velocity of the object in terms of an equation.

Formula of Momentum

A moving object’s momentum can be described mathematically as –

p=mv

Where,

The momentum is represented by the letter p.

The object’s mass, measured in kg, is m.

v denotes the object’s velocity in m/s.

Unit of Momentum

1. m/s is the SI unit of momentum.

Relation between Kinetic Energy and Momentum Formula

The following is a mathematical relationship between kinetic energy and momentum of a moving body:

Consider the kinetic energy formula:

K.E=12mv2

Divide and multiply m’s R.H.S

⟹K.E=12mv2mm

=m2v22m

=mv22m

We are aware of this.

p=mv

When we replace mv in the above equation, we get-

K.E=p22m

The given equation expresses the relationship between kinetic energy and momentum of a moving object.

• If Momentum(p) is constant, K.E∝1m
• If K.E (Kinetic Energy) is constant, p∝m
• If mass(m) is constant, p∝K.E

Example of Kinetic Energy

• Because a truck’s mass is substantially greater than a car’s, a truck travelling down the road has more kinetic energy than a car travelling at the same speed.
• Because water has a specific velocity and mass, a river moving at a certain speed contains kinetic energy.
• An asteroid colliding with Earth has a lot of kinetic energy.
• Due to its enormous mass and fast velocity, the aero plane’s kinetic energy is higher during flight.

Example of Momentum

• A train travelling at 120 kilometres per hour
• A baseball is being thrown through the air.
• A large truck is moving.
• a bullet fired by a firearm
• When you toss a ball at someone and it lands firmly on his head. It’s a measure of how difficult it would be to stop the object.

Conclusion

The kinetic energy of an object is the energy it has due to its motion in physics. It is the amount of work required to accelerate a body of a given mass from rest to a certain velocity. The body retains its kinetic energy after gaining it during acceleration unless its speed changes. When the body decelerates from its current speed to a condition of rest, it does the same amount of work. A kinetic energy is any term in the Lagrangian of a system that has a derivative with respect to time.

The term “momentum” refers to “mass in motion.” Because all objects have mass, if they are moving, they have momentum – their mass is moving. The amount of momentum that an object possesses is determined by two factors: the amount of material moving and the speed at which it is travelling. The factors mass and velocity influence momentum. The momentum of an object is equal to the mass times the velocity of the object in terms of an equation.