Question

define terms momentum and impulse.state and explain the law of conservation of linear momentum​

Answer 1

Linear Momentum of System of Particles

We know that the linear momentum of the particle is

p = mv

Newton’s second law for a single particle is given by,

F = dPdt

where F is the force of the particle. For ‘ n ‘ no. of particles total linear  momentum is,

P = p1 + p2 +…..+pn

each of momentum is written as  m1 v1 + m2v2 + ………..+mnvn. We know that velocity of the centre of mass is V =  Σ  miviM,

mv =  Σ  mivi

So comparing these equations we get,

P = M V

Therefore we can say that the total linear momentum of a system of particles is equal to the product of the total mass of the system and the velocity of its center of mass. Differentiating the above equation we get,

dPdt = M dVdt = MA

dv/dt is acceleration of centre of mass, MA is the force external. So,

dPdt = Fext

This above equation is nothing but Newton’s second law to a system of particles. If the total external force acting on the system is zero,

Fext = 0 then, dPdt = 0

This means that P = constant. So whenever the total force acting on the system of a particle is equal to zero then the total linear momentum of the system is constant or conserved. This is nothing but the law of conservation of total linear momentum of a system of particles.

Conservation of Total Linear Momentum of a System of Particles

Let us take the example of radioactive decay. What is radioactive decay? It is a process where an unstable nucleus splits up in relatively stable nuclei releasing a huge amount of energy.

Suppose there is a parent nucleus which is unstable and it wants to become stable, in order to attain stability it will emit α particle and another daughter nucleus.

This daughter nucleus is much more stable than the parent nucleus. This what radioactive decay is. Now suppose the parent nucleus is at rest and also the mass of the α is ‘ m ‘ and the daughter nucleus is M.

So the mass of the parent nucleus will be m + M. Here everything that is happening is not due to the external force but all that happens is due to the internal force. So here Fext = 0, we can say that

dPdt = 0 ⇒ P = constant

Answer 2

ᴀɴsᴡᴇʀ࿐

ᴅᴇғɪɴɪᴛɪᴏɴ:-

ᴍᴏᴍᴇɴᴛᴜᴍ ɪs ᴛʜᴇ ᴛʜᴇ ᴀᴍᴏᴜɴᴛ ᴏғ ᴍᴏᴛɪᴏɴ ᴏғ ᴀ ᴍᴏᴠɪɴɢ ʙᴏᴅʏ, ᴍᴇᴀsᴜʀᴇᴅ ᴀs ᴀ ᴘʀᴏᴅᴜᴄᴛ ᴏғ ɪᴛs ᴍᴀss ᴀɴᴅ ᴠᴇʟᴏᴄɪᴛʏ.

=>ᴍᴏᴍᴇɴᴛᴜᴍ= ᴍᴀss × ᴠᴇʟᴏᴄɪᴛʏ

ᴅɪᴍᴇɴsɪᴏɴᴀʟ ғᴏʀᴍᴜʟᴀ ᴏғ ᴍᴏᴍᴇɴᴛᴜᴍ

=>ᴘ = [ᴍ]x [ʟᴛ^(-1)]

ᴄᴏɴsᴇʀᴠᴀᴛɪᴏɴ ᴏғ ᴍᴏᴍᴇɴᴛᴜᴍ:-

ʟᴀᴡ ᴏғ ᴄᴏɴsᴇʀᴠᴀᴛɪᴏɴ ᴏғ ᴍᴏᴍᴇɴᴛᴜᴍ ɪs ᴅᴇғɪɴᴇᴅ ᴀs ᴀ ᴘʀɪɴᴄɪᴘʟᴇ ɪɴ ᴘʜʏsɪᴄs ᴛʜᴀᴛ sᴛᴀᴛᴇs ᴛʜᴀᴛ ғᴇᴡ ᴘᴀʀᴛs ɪɴ ᴀɴ ɪsᴏʟᴀᴛᴇᴅ sʏsᴛᴇᴍ ʀᴇᴍᴀɪɴɪɴɢ sᴛᴇᴀᴅʏ ᴀɴᴅ ᴜɴᴄʜᴀɴɢɪɴɢ ᴏᴠᴇʀ ᴛɪᴍᴇ ᴇᴠᴇɴ ᴡʜᴇɴ ᴏᴛʜᴇʀs ᴀʀᴇ ᴍᴏᴠɪɴɢ.