Derive the equation betweem K.E. and momentum.
Answers
Explanation:
Relation between momentum and kinetic energy. Note that if a massive particle and a light particle have the same momentum, the light one will have a lot more kinetic energy. If a light particle and a heavy one have the same velocity, the heavy one has more kinetic energy.
Answer:
Explanation:
Kinetic Energy
The kinetic energy of an object is the energy associated with the object which is under motion. It is defined as “the energy required by a body to accelerate from rest to stated velocity.” It is a vector quantity.
Kinetic Energy formula
Mathematically expressed as-
K.E=12mv2
Where,
m is the mass of the object measured in kg.
v is the velocity of the object measured in m/s
Kinetic Energy unit
The SI Unit of Kinetic Energy is Joules.
Momentum
The momentum of an object is virtue of its mass. It os defined as the product of mass and velocity. It is a vector quantity.
Momentum formula
The momentum of a moving object can be mathematically expressed as –
p=mv
Where,
p is the momentum.
m is the mass of the object measure using kg.
v is the velocity of object measure using m/s.
Momentum unit
The SI Unit of Momentum is kg.m/s
Relation Between Momentum and Kinetic Energy
Kinetic energy and momentum of a moving body can be mathematically related as follow-
Consider the formula of kinetic energy-
K.E=12mv2
Multiply and divide R.H.S by m
⇒K.E=12mv2×mm =m2v22m =(mv)22m
We know that p=mv. Substituting for mv in the above equation we get-
K.E=p22m
The above equation gives the relation between Kinetic energy and momentum of the object which is under motion.
If the Momentum(p) is constant
K.E∝1m
If Kinetic Energy(K.E) is constant
p∝m−−√
If mass(m) is constant
p∝K.E−−−−√
Hope you have understood the relation between Kinetic energy and momentum of a moving object.