Question

Mathematical
Formulation
of 2nd Law
Rate of Change of
Momentum is
nothing but the
'Applied Force"
Explain​

Answer 1

ᴛʜᴇ sᴇᴄᴏɴᴅ ʟᴀᴡ ɪs ᴛʜᴇ ᴏɴᴇ ᴛʜᴀᴛ ᴛᴇʟʟs ʏᴏᴜ ʜᴏᴡ ᴛᴏ ᴄᴀʟᴄᴜʟᴀᴛᴇ ᴛʜᴇ ᴠᴀʟᴜᴇ ᴏғ ᴀ ғᴏʀᴄᴇ. ғᴏʀᴄᴇ (ᴍᴇᴀsᴜʀᴇᴅ ɪɴ ɴᴇᴡᴛᴏɴs) ɪs ᴏɴᴇ ᴏғ ᴛʜᴇ ғᴜɴᴅᴀᴍᴇɴᴛᴀʟ ᴘʜʏsɪᴄᴀʟ ᴘʀᴏᴘᴇʀᴛɪᴇs ᴏғ ᴀ sʏsᴛᴇᴍ ᴀɴᴅ ᴄᴏᴍᴇs ɪɴ ᴍᴀɴʏ ғᴏʀᴍs. ʏᴏᴜ ᴍɪɢʜᴛ ғᴇᴇʟ ɪᴛ ᴀs ᴀ ᴘᴜsʜ ᴏʀ ᴘᴜʟʟ (ᴀ ᴍᴇᴄʜᴀɴɪᴄᴀʟ ғᴏʀᴄᴇ), ᴡʜɪʟᴇ ɪᴛ ɪs ᴛʜᴇ ᴠᴀʟᴜᴇ ᴏғ ʏᴏᴜʀ ᴡᴇɪɢʜᴛ (ᴛʜᴇ ɢʀᴀᴠɪᴛᴀᴛɪᴏɴᴀʟ ғᴏʀᴄᴇ ᴏғ ᴛʜᴇ ᴇᴀʀᴛʜ ᴘᴜʟʟɪɴɢ ᴏɴ ʏᴏᴜ) ᴀɴᴅ ᴄᴀɴ ʙᴇ sᴇᴇɴ ɪɴ ᴛʜᴇ ʀᴇᴘᴜʟsɪᴏɴ ᴏʀ ᴀᴛᴛʀᴀᴄᴛɪᴏɴ ᴏғ ᴍᴀɢɴᴇᴛs ᴏʀ ᴇʟᴇᴄᴛʀɪᴄ ᴄʜᴀʀɢᴇs (ᴇʟᴇᴄᴛʀᴏᴍᴀɢɴᴇᴛɪᴄ ғᴏʀᴄᴇ). ᴀ ғᴏʀᴄᴇ ᴍɪɢʜᴛ ʙᴇ ᴛʜᴇ ʀᴇsᴜʟᴛ ᴏғ ᴀɴʏ ɴᴜᴍʙᴇʀ ᴏғ ғᴜɴᴅᴀᴍᴇɴᴛᴀʟ ᴘʜʏsɪᴄᴀʟ ɪɴᴛᴇʀᴀᴄᴛɪᴏɴs ʙᴇᴛᴡᴇᴇɴ ʙɪᴛs ᴏғ ᴍᴀᴛᴛᴇʀ ʙᴜᴛ ɴᴇᴡᴛᴏɴ's sᴇᴄᴏɴᴅ ʟᴀᴡ ᴀʟʟᴏᴡs ʏᴏᴜ ᴛᴏ ᴡᴏʀᴋ ᴏᴜᴛ ʜᴏᴡ ᴀ ғᴏʀᴄᴇ, ᴡʜᴇɴ ɪᴛ ɪs ᴘʀᴇsᴇɴᴛ, ᴡɪʟʟ ᴀғғᴇᴄᴛ ᴛʜᴇ ᴍᴏᴛɪᴏɴ ᴏғ ᴀɴ ᴏʙᴊᴇᴄᴛ.

ɪɴ ᴛʜᴇ ғᴏʀᴍ ᴘɪᴄᴛᴜʀᴇᴅ, ᴀʙᴏᴠᴇ, ɪᴛ sᴀʏs ᴛʜᴀᴛ ғᴏʀᴄᴇ (ғ) ɪs ᴇϙᴜᴀʟ ᴛᴏ ᴛʜᴇ ʀᴀᴛᴇ ᴏғ ᴄʜᴀɴɢᴇ ᴏғ ᴍᴏᴍᴇɴᴛᴜᴍ (ᴘ) ᴡɪᴛʜ ʀᴇsᴘᴇᴄᴛ ᴛᴏ ᴛɪᴍᴇ (ᴛ). ᴛʜᴇ sᴍᴀʟʟ "ᴅ"s ᴀʀᴇ ᴅɪғғᴇʀᴇɴᴛɪᴀʟ ɴᴏᴛᴀᴛɪᴏɴ, ᴀɴᴏᴛʜᴇʀ ɴᴇᴡᴛᴏɴɪᴀɴ ɪɴᴠᴇɴᴛɪᴏɴ ᴛʜᴀᴛ ᴀᴘᴘᴇᴀʀs ɪɴ ᴄᴏᴜɴᴛʟᴇss ᴘʜʏsɪᴄᴀʟ ᴇϙᴜᴀᴛɪᴏɴs ᴀɴᴅ ᴛʜᴀᴛ ᴀʟʟᴏᴡs ʏᴏᴜ ᴛᴏ ᴍᴀᴛʜᴇᴍᴀᴛɪᴄᴀʟʟʏ ᴘʀᴇᴅɪᴄᴛ ʜᴏᴡ sᴏᴍᴇᴛʜɪɴɢ ᴡɪʟʟ ᴄʜᴀɴɢᴇ ᴀs ᴀɴᴏᴛʜᴇʀ ʀᴇʟᴀᴛᴇᴅ ᴘᴀʀᴀᴍᴇᴛᴇʀ ɪs ɪɴᴄʀᴇᴍᴇɴᴛᴀʟʟʏ ᴀʟᴛᴇʀᴇᴅ – ɪɴ ᴛʜɪs ᴄᴀsᴇ, ᴛɪᴍᴇ.

ᴍᴏᴍᴇɴᴛᴜᴍ ɪs ᴛʜᴇ ᴍᴀss (ᴋɪʟᴏɢʀᴀᴍs) ᴏғ ᴀɴ ᴏʙᴊᴇᴄᴛ ᴍᴜʟᴛɪᴘʟɪᴇᴅ ʙʏ ɪᴛs ᴠᴇʟᴏᴄɪᴛʏ (ᴍᴇᴛʀᴇs ᴘᴇʀ sᴇᴄᴏɴᴅ). ɪɴ ᴍᴏsᴛ sɪᴛᴜᴀᴛɪᴏɴs, ᴛʜᴇ ᴍᴀss ᴏғ sᴏᴍᴇᴛʜɪɴɢ ᴅᴏᴇs ɴᴏᴛ ᴄʜᴀɴɢᴇ ᴀs ɪᴛ ᴍᴏᴠᴇs sᴏ ᴛʜᴇ ᴇϙᴜᴀᴛɪᴏɴ ᴄᴀɴ ʙᴇ sɪᴍᴘʟɪғɪᴇᴅ ᴛᴏ ᴍᴀss (ᴍ) ᴍᴜʟᴛɪᴘʟɪᴇᴅ ʙʏ ᴛʜᴇ ʀᴀᴛᴇ ᴏғ ᴄʜᴀɴɢᴇ ᴏғ ᴠᴇʟᴏᴄɪᴛʏ, ᴡʜɪᴄʜ ᴡᴇ ᴋɴᴏᴡ ᴀs ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ (ᴀ). ᴛʜᴀᴛ ɢɪᴠᴇs ᴜs ᴛʜᴇ ᴍᴏʀᴇ ғᴀᴍɪʟɪᴀʀ sᴄʜᴏᴏʟ ᴛᴇxᴛʙᴏᴏᴋ ᴠᴇʀsɪᴏɴ ᴏғ ᴛʜᴇ sᴇᴄᴏɴᴅ ʟᴀᴡ: ғ=ᴍᴀ.

Answer 2

Question:-

Mathematical Formulationof 2nd Law Rate of Change of Momentum is nothing but the 'Applied Force"Explain

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Mathematical Formulation of Second Law of Motion

It is uniformly accelerated to velocity, v in time, t by the application of a constant force, F throughout the time, t. The initial and final momentum of the object will be, p1 = mu and p2 = mv respectively. ... Thus, the rate of change of momentum of the ball will be large.

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