The momentum of an object is something that keeps the object in motion. But is momentum responsible for the conservation of energy? We are going to discuss the same below.
If the velocity of a mass remains unvaried even after colliding with some obstacle in its wave or is transferred to another object then the momentum of the object is conserved and is directly proportional to the kinetic energy of the object with which it is moving.
How is momentum conservation of energy?
The momentum of the object is conserved on colliding with some other object too if the collision is elastic.
Well the kinetic energy of the object may differ as a part of the energy is converted into potential energy or sometimes heat energy too, but the total energy is conserved in the process.
The momentum of the object is related to the energy by the equation
P=√2mE
Where P is a momentum
m is a mass of the object
E is the energy of the object
The momentum of the object is directly related to the square root of the energy of the object.
What is the velocity of a man of mass 60 kg running with the energy of 270 joules?
Given: m= 60kg
E= 270 Joules
Using a formula
Hence, the velocity of a man is 3 m/s.
Is energy conserved when momentum is conserved?
The momentum is said to be conserved if the object continues to accelerate even after the collision of the object with any obstacle.
The energy is said to be conserved if the energy possessed by the object before the collision is equal to the total energy acquired and transmitted after the collision.
It is also true that the energy of the object may not be conserved if the energy of the object is lost after a collision. If the velocity of the object decreases after the collision then it is evident that the kinetic energy of the object has converted into the potential energy or lost due to friction in the form of heat.
Suppose an object having a mass ‘m’ is moving with velocity ‘v’ on the application of applied force on it. Hence, the kinetic energy with which the object is moving is
The momentum of the object is P=mv
Using this equation in the above equation, we get
Hence we see that the energy of the object is directly proportional to the momentum. This significantly implies that, if the momentum remains unvaried then so is the total energy.
What is the energy acquired by the person riding a bicycle of mass 7 kg cycling at a speed of 5m/s? Consider that the weight of a person is 55 kg.
Given: v=5m/s
The weight of a bicycle is m=7kg
The weight of a person is M= 55kg
The momentum of a bicycle is
P=mv
7* 5=35 kg.m/s
The momentum of a person is equal to the momentum of a bicycle as the person is moving along with the bicycle in the frame of reference.
Hence, the energy acquired by the body of a person is
The energy gained by the person’s body due to the momentum of a bicycle is 10.21 Joules.
Why momentum is conserved?
The momentum of the object remains unchanged until some external force is exerted on the object.
Upon collision too, the force equal in magnitude is exerted on both the colliding objects which act in the opposite directions thus conserving the momentum of the object.
The force imposed on the object imparts the energy to the object which keeps the object in momentum if the force corresponding to its mass is applied to the object. Any object in motion possesses momentum that keeps it going unless felt some external source of force on the object that will bring the object to the rest.
What is the momentum of the object of mass 80kg moving with velocity 40km per hour?
Given: m=80kg
v =40km/h =11.1m/s
Then the momentum of an object is
P=mv
=80*11.1=888 Kg.m/s
The momentum of the object is 888 kg.m/s.
How momentum is conserved?
The momentum of the object is conserved until some external force is imposed on the object that resists its motion.
The idea of conservation of momentum is based on Newton’s second law of motion according to which the object will continue to move in a fixed direction conserving its momentum until some external force is imposed on the object.
If the object of mass m1 moving with velocity u1 collides with another object of mass m2 moving with velocity u2 and after the collision, the mass m1 reduces its velocity to v1 and mass m2 gains the velocity v2 then if the momentum after the collision is conserved then the equation follows:-
The sum of the momentum of both the object before and after the collision remains the same according to the law of conservation of momentum.
Rearranging the above equation, we get
Hence, the final velocity of the second object is
If a mass of 2kg approaching with velocity 4m/s bombards with the object of 1.4 kg moving with velocity 4m/s too, then what is the velocity of the object having mass 1.4 kg after the collision if the velocity acquired by the object of mass 2 kg is 3m/s and momentum is conserved?
Given: m1 =2kg
m2 =1.4kg
u1 =4m/s
u2 =4m/s
v1 =3m/s
v2 =?
Using the formula
Hence the velocity of the object is 5.43 m/s.
Frequently Asked Questions
Is momentum conserved even after colliding with other objects?
The momentum is not always conserved after colliding with any object.
The total momentum of the colliding object remains unvaried as it may transfer or remains unchanged in an elastic collision. So is the kinetic energies of both the objects.
How energy and momentum of the object are conserved?
The energy possessed by the object is conserved provided it may transform into some other form of energy.
The object tends to remain in the state of motion until some external source of force is incident on the object to bring it to the rest until then the momentum of the object is conserved and the total energy of the object is also conserved.
Why does the energy not conserved in an inelastic collision?
In this type of collision, there is a loss of energy through the momentum is conserved.
A part of the energy of the object is lost after bombarding it with another object by converting it into some other form of energy and the momentum of the object also varies.
What is relativistic momentum?
The momentum of the object in different frames of reference is termed relativistic momentum.
The momentum is conserved in all the inertial frames of reference if the net external force imposed on that object is zero and hence the relativistic momentum is conserved.
Also Read:
- How to find center of mass and momentum
- How to find momentum in wave mechanics
- How to find momentum from wavelength
- Impulse vs momentum
- How to find total momentum in a system
- Momentum example
- How to find momentum from kinetic energy
- Conservation of momentum
- Gravity and angular momentum
- How to find momentum of a particle
Hi, I’m Akshita Mapari. I have done M.Sc. in Physics. I have worked on projects like Numerical modeling of winds and waves during cyclone, Physics of toys and mechanized thrill machines in amusement park based on Classical Mechanics. I have pursued a course on Arduino and have accomplished some mini projects on Arduino UNO. I always like to explore new zones in the field of science. I personally believe that learning is more enthusiastic when learnt with creativity. Apart from this, I like to read, travel, strumming on guitar, identifying rocks and strata, photography and playing chess.
