Prove the formula of force
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ᴘʀᴏᴠᴇ ғ = ᴍᴀ
ᴘʀᴏᴠᴇ ᴛʜᴀᴛ ғᴏʀᴄᴇ= ᴍᴀss* ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴᴀʟ.sᴛᴀᴛᴇ ᴛʜᴇ ᴄᴏɴᴅɪᴛɪᴏɴ ᴡʜᴇɴ ɪᴛ ʜᴏʟᴅs.
ᴅᴇʀɪᴠᴀᴛɪᴏɴ ᴏғ ɴᴇᴡᴛᴏɴ’s sᴇᴄᴏɴᴅ ʟᴀᴡ ᴏғ ᴍᴏᴛɪᴏɴ
ɴᴇᴡᴛᴏɴ’s sᴇᴄᴏɴᴅ ʟᴀᴡ ᴏғ ᴍᴏᴛɪᴏɴ sᴛᴀᴛᴇs ᴛʜᴀᴛ ᴛʜᴇ ʀᴀᴛᴇ ᴏғ ᴄʜᴀɴɢᴇ ᴏғ ᴍᴏᴍᴇɴᴛᴜᴍ ᴏғ ᴀɴ ᴏʙᴊᴇᴄᴛ ɪs ᴘʀᴏᴘᴏʀᴛɪᴏɴᴀʟ ᴛᴏ ᴛʜᴇ ᴀᴘᴘʟɪᴇᴅ ᴜɴʙᴀʟᴀɴᴄᴇᴅ ғᴏʀᴄᴇ ɪɴ ᴛʜᴇ ᴅɪʀᴇᴄᴛɪᴏɴ ᴏғ ғᴏʀᴄᴇ.
sᴜᴘᴘᴏsᴇ ᴀɴ ᴏʙᴊᴇᴄᴛ ᴏғ ᴍᴀss, ᴍ ɪs ᴍᴏᴠɪɴɢ ᴀʟᴏɴɢ ᴀ sᴛʀᴀɪɢʜᴛ ʟɪɴᴇ ᴡɪᴛʜ ᴀɴ ɪɴɪᴛɪᴀʟ ᴠᴇʟᴏᴄɪᴛʏ, ᴜ. ɪᴛ ɪs ᴜɴɪғᴏʀᴍʟʏ ᴀᴄᴄᴇʟᴇʀᴀᴛᴇᴅ ᴛᴏ ᴠᴇʟᴏᴄɪᴛʏ, ᴠ ɪɴ ᴛɪᴍᴇ, ᴛ ʙʏ ᴛʜᴇ ᴀᴘᴘʟɪᴄᴀᴛɪᴏɴ ᴏғ ᴀ ᴄᴏɴsᴛᴀɴᴛ ғᴏʀᴄᴇ, ғ ᴛʜʀᴏᴜɢʜᴏᴜᴛ ᴛʜᴇ ᴛɪᴍᴇ ᴛ. ᴛʜᴇ ɪɴɪᴛɪᴀʟ ᴀɴᴅ ғɪɴᴀʟ ᴍᴏᴍᴇɴᴛᴜᴍ ᴏғ ᴛʜᴇ ᴏʙᴊᴇᴄᴛ ᴡɪʟʟ ʙᴇ, ᴘ1⃣⃣ = ᴍᴜ ᴀɴᴅ ᴘ2⃣⃣ = ᴍᴠ ʀᴇsᴘᴇᴄᴛɪᴠᴇʟʏ.
ᴛʜᴇ ᴄʜᴀɴɢᴇ ɪɴ ᴍᴏᴍᴇɴᴛᴜᴍ = ᴘ2⃣⃣ – ᴘ1⃣⃣
ᴛʜᴇ ᴄʜᴀɴɢᴇ ɪɴ ᴍᴏᴍᴇɴᴛᴜᴍ = ᴍᴠ – ᴍᴜ
ᴛʜᴇ ᴄʜᴀɴɢᴇ ɪɴ ᴍᴏᴍᴇɴᴛᴜᴍ = ᴍ × (ᴠ – ᴜ).
ᴛʜᴇ ʀᴀᴛᴇ ᴏғ ᴄʜᴀɴɢᴇ ᴏғ ᴍᴏᴍᴇɴᴛᴜᴍ = ᴍ × (ᴠ – ᴜ)/ᴛ(ᴠ - ᴜ)ᴛ
ᴏʀ, ᴛʜᴇ ᴀᴘᴘʟɪᴇᴅ ғᴏʀᴄᴇ, ғ ∝ ᴍ × (ᴠ – ᴜ)/ᴛ (ᴠ - ᴜ)ᴛ
ғ = ᴋᴍ × (ᴠ – ᴜ)/ᴛ
ғ = ᴋᴍᴀ ---------------------------- (ɪ)
ʜᴇʀᴇ, ᴀ ɪs ᴛʜᴇ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ [ɪ.ᴇ., ᴀ= (ᴠ – ᴜ)/ᴛ], ᴡʜɪᴄʜ ɪs ᴛʜᴇ ʀᴀᴛᴇ ᴏғ ᴄʜᴀɴɢᴇ ᴏғ ᴠᴇʟᴏᴄɪᴛʏ. ᴛʜᴇ ϙᴜᴀɴᴛɪᴛʏ, ᴋ ɪs ᴀ ᴄᴏɴsᴛᴀɴᴛ ᴏғ ᴘʀᴏᴘᴏʀᴛɪᴏɴᴀʟɪᴛʏ.
ᴛʜᴇ sɪ ᴜɴɪᴛs ᴏғ ᴍᴀss ᴀɴᴅ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ ᴀʀᴇ ᴋɢ ᴀɴᴅ ᴍ s-2⃣⃣ ʀᴇsᴘᴇᴄᴛɪᴠᴇʟʏ. ᴛʜᴇ ᴜɴɪᴛ ᴏғ ғᴏʀᴄᴇ ɪs sᴏ ᴄʜᴏsᴇɴ ᴛʜᴀᴛ ᴛʜᴇ ᴠᴀʟᴜᴇ ᴏғ ᴛʜᴇ ᴄᴏɴsᴛᴀɴᴛ, ᴋ ʙᴇᴄᴏᴍᴇs ᴏɴᴇ. ғᴏʀ ᴛʜɪs, ᴏɴᴇ ᴜɴɪᴛ ᴏғ ғᴏʀᴄᴇ ɪs ᴅᴇғɪɴᴇᴅ ᴀs ᴛʜᴇ ᴀᴍᴏᴜɴᴛ ᴛʜᴀᴛ ᴘʀᴏᴅᴜᴄᴇs ᴀɴ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ ᴏғ 1⃣⃣ ᴍ s-2⃣⃣ ɪɴ ᴀɴ ᴏʙᴊᴇᴄᴛ ᴏғ 1⃣⃣ ᴋɢ ᴍᴀss. ᴛʜᴀᴛ ɪs,
1⃣⃣ ᴜɴɪᴛ ᴏғ ғᴏʀᴄᴇ = ᴋ × (1⃣⃣ ᴋɢ) × (1⃣⃣ ᴍ s-2⃣⃣).
ᴛʜᴜs, ᴛʜᴇ ᴠᴀʟᴜᴇ ᴏғ ᴋ ʙᴇᴄᴏᴍᴇs 1⃣⃣.
ғʀᴏᴍ ᴇϙ. (ɪ)
ғ = ᴍᴀ
ᴛʜᴇ ᴜɴɪᴛ ᴏғ ғᴏʀᴄᴇ ɪs ᴋɢ ᴍ s-2⃣⃣ ᴏʀ ɴᴇᴡᴛᴏɴ, ʀᴇᴘʀᴇsᴇɴᴛᴇᴅ ᴀs ɴ.
ʜᴏᴘᴇ ɪᴛ ʜᴇʟᴘs ʏᴏᴜ
ᴘʀᴏᴠᴇ ᴛʜᴀᴛ ғᴏʀᴄᴇ= ᴍᴀss* ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴᴀʟ.sᴛᴀᴛᴇ ᴛʜᴇ ᴄᴏɴᴅɪᴛɪᴏɴ ᴡʜᴇɴ ɪᴛ ʜᴏʟᴅs.
ᴅᴇʀɪᴠᴀᴛɪᴏɴ ᴏғ ɴᴇᴡᴛᴏɴ’s sᴇᴄᴏɴᴅ ʟᴀᴡ ᴏғ ᴍᴏᴛɪᴏɴ
ɴᴇᴡᴛᴏɴ’s sᴇᴄᴏɴᴅ ʟᴀᴡ ᴏғ ᴍᴏᴛɪᴏɴ sᴛᴀᴛᴇs ᴛʜᴀᴛ ᴛʜᴇ ʀᴀᴛᴇ ᴏғ ᴄʜᴀɴɢᴇ ᴏғ ᴍᴏᴍᴇɴᴛᴜᴍ ᴏғ ᴀɴ ᴏʙᴊᴇᴄᴛ ɪs ᴘʀᴏᴘᴏʀᴛɪᴏɴᴀʟ ᴛᴏ ᴛʜᴇ ᴀᴘᴘʟɪᴇᴅ ᴜɴʙᴀʟᴀɴᴄᴇᴅ ғᴏʀᴄᴇ ɪɴ ᴛʜᴇ ᴅɪʀᴇᴄᴛɪᴏɴ ᴏғ ғᴏʀᴄᴇ.
sᴜᴘᴘᴏsᴇ ᴀɴ ᴏʙᴊᴇᴄᴛ ᴏғ ᴍᴀss, ᴍ ɪs ᴍᴏᴠɪɴɢ ᴀʟᴏɴɢ ᴀ sᴛʀᴀɪɢʜᴛ ʟɪɴᴇ ᴡɪᴛʜ ᴀɴ ɪɴɪᴛɪᴀʟ ᴠᴇʟᴏᴄɪᴛʏ, ᴜ. ɪᴛ ɪs ᴜɴɪғᴏʀᴍʟʏ ᴀᴄᴄᴇʟᴇʀᴀᴛᴇᴅ ᴛᴏ ᴠᴇʟᴏᴄɪᴛʏ, ᴠ ɪɴ ᴛɪᴍᴇ, ᴛ ʙʏ ᴛʜᴇ ᴀᴘᴘʟɪᴄᴀᴛɪᴏɴ ᴏғ ᴀ ᴄᴏɴsᴛᴀɴᴛ ғᴏʀᴄᴇ, ғ ᴛʜʀᴏᴜɢʜᴏᴜᴛ ᴛʜᴇ ᴛɪᴍᴇ ᴛ. ᴛʜᴇ ɪɴɪᴛɪᴀʟ ᴀɴᴅ ғɪɴᴀʟ ᴍᴏᴍᴇɴᴛᴜᴍ ᴏғ ᴛʜᴇ ᴏʙᴊᴇᴄᴛ ᴡɪʟʟ ʙᴇ, ᴘ1⃣⃣ = ᴍᴜ ᴀɴᴅ ᴘ2⃣⃣ = ᴍᴠ ʀᴇsᴘᴇᴄᴛɪᴠᴇʟʏ.
ᴛʜᴇ ᴄʜᴀɴɢᴇ ɪɴ ᴍᴏᴍᴇɴᴛᴜᴍ = ᴘ2⃣⃣ – ᴘ1⃣⃣
ᴛʜᴇ ᴄʜᴀɴɢᴇ ɪɴ ᴍᴏᴍᴇɴᴛᴜᴍ = ᴍᴠ – ᴍᴜ
ᴛʜᴇ ᴄʜᴀɴɢᴇ ɪɴ ᴍᴏᴍᴇɴᴛᴜᴍ = ᴍ × (ᴠ – ᴜ).
ᴛʜᴇ ʀᴀᴛᴇ ᴏғ ᴄʜᴀɴɢᴇ ᴏғ ᴍᴏᴍᴇɴᴛᴜᴍ = ᴍ × (ᴠ – ᴜ)/ᴛ(ᴠ - ᴜ)ᴛ
ᴏʀ, ᴛʜᴇ ᴀᴘᴘʟɪᴇᴅ ғᴏʀᴄᴇ, ғ ∝ ᴍ × (ᴠ – ᴜ)/ᴛ (ᴠ - ᴜ)ᴛ
ғ = ᴋᴍ × (ᴠ – ᴜ)/ᴛ
ғ = ᴋᴍᴀ ---------------------------- (ɪ)
ʜᴇʀᴇ, ᴀ ɪs ᴛʜᴇ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ [ɪ.ᴇ., ᴀ= (ᴠ – ᴜ)/ᴛ], ᴡʜɪᴄʜ ɪs ᴛʜᴇ ʀᴀᴛᴇ ᴏғ ᴄʜᴀɴɢᴇ ᴏғ ᴠᴇʟᴏᴄɪᴛʏ. ᴛʜᴇ ϙᴜᴀɴᴛɪᴛʏ, ᴋ ɪs ᴀ ᴄᴏɴsᴛᴀɴᴛ ᴏғ ᴘʀᴏᴘᴏʀᴛɪᴏɴᴀʟɪᴛʏ.
ᴛʜᴇ sɪ ᴜɴɪᴛs ᴏғ ᴍᴀss ᴀɴᴅ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ ᴀʀᴇ ᴋɢ ᴀɴᴅ ᴍ s-2⃣⃣ ʀᴇsᴘᴇᴄᴛɪᴠᴇʟʏ. ᴛʜᴇ ᴜɴɪᴛ ᴏғ ғᴏʀᴄᴇ ɪs sᴏ ᴄʜᴏsᴇɴ ᴛʜᴀᴛ ᴛʜᴇ ᴠᴀʟᴜᴇ ᴏғ ᴛʜᴇ ᴄᴏɴsᴛᴀɴᴛ, ᴋ ʙᴇᴄᴏᴍᴇs ᴏɴᴇ. ғᴏʀ ᴛʜɪs, ᴏɴᴇ ᴜɴɪᴛ ᴏғ ғᴏʀᴄᴇ ɪs ᴅᴇғɪɴᴇᴅ ᴀs ᴛʜᴇ ᴀᴍᴏᴜɴᴛ ᴛʜᴀᴛ ᴘʀᴏᴅᴜᴄᴇs ᴀɴ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ ᴏғ 1⃣⃣ ᴍ s-2⃣⃣ ɪɴ ᴀɴ ᴏʙᴊᴇᴄᴛ ᴏғ 1⃣⃣ ᴋɢ ᴍᴀss. ᴛʜᴀᴛ ɪs,
1⃣⃣ ᴜɴɪᴛ ᴏғ ғᴏʀᴄᴇ = ᴋ × (1⃣⃣ ᴋɢ) × (1⃣⃣ ᴍ s-2⃣⃣).
ᴛʜᴜs, ᴛʜᴇ ᴠᴀʟᴜᴇ ᴏғ ᴋ ʙᴇᴄᴏᴍᴇs 1⃣⃣.
ғʀᴏᴍ ᴇϙ. (ɪ)
ғ = ᴍᴀ
ᴛʜᴇ ᴜɴɪᴛ ᴏғ ғᴏʀᴄᴇ ɪs ᴋɢ ᴍ s-2⃣⃣ ᴏʀ ɴᴇᴡᴛᴏɴ, ʀᴇᴘʀᴇsᴇɴᴛᴇᴅ ᴀs ɴ.
ʜᴏᴘᴇ ɪᴛ ʜᴇʟᴘs ʏᴏᴜ
Azikhan:
may I ask u one question dear user?
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Answered by
12
Hey friend ☺ here is the answer __________________________
The formula can be proven by using dimension method
As we know
Force = mass × acceleration
F = ma
LHS :-
Dimension of F = [ MLT^-2 ]
RHS :-
Dimension of ma = [M] × [LT^-2] = [MLT^-2]
LHS = RHS
Hence proved
Hope this helps you.
The formula can be proven by using dimension method
As we know
Force = mass × acceleration
F = ma
LHS :-
Dimension of F = [ MLT^-2 ]
RHS :-
Dimension of ma = [M] × [LT^-2] = [MLT^-2]
LHS = RHS
Hence proved
Hope this helps you.
Hmm ....thnx
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