state newtons second law of motion. Prove that F=ma
Answers
Answer:
ɴᴇᴡᴛᴏɴ’s sᴇᴄᴏɴᴅ ʟᴀᴡ ᴏғ ᴍᴏᴛɪᴏɴ ᴄᴀɴ ʙᴇ sᴛᴀᴛᴇᴅ ᴀs ᴛʜᴇ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ ᴏғ ᴀɴ ᴏʙᴊᴇᴄᴛ ᴀs ᴘʀᴏᴅᴜᴄᴇᴅ ʙʏ ᴀ ɴᴇᴛ ғᴏʀᴄᴇ ɪs ᴅɪʀᴇᴄᴛʟʏ ᴘʀᴏᴘᴏʀᴛɪᴏɴᴀʟ ᴛᴏ ᴛʜᴇ ᴍᴀɢɴɪᴛᴜᴅᴇ ᴏғ ᴛʜᴇ ɴᴇᴛ ғᴏʀᴄᴇ, ɪɴ ᴛʜᴇ sᴀᴍᴇ ᴅɪʀᴇᴄᴛɪᴏɴ ᴀs ᴛʜᴇ ɴᴇᴛ ғᴏʀᴄᴇ, ᴀɴᴅ ɪɴᴠᴇʀsᴇʟʏ ᴘʀᴏᴘᴏʀᴛɪᴏɴᴀʟ ᴛᴏ ᴛʜᴇ ᴍᴀss ᴏғ ᴛʜᴇ ᴏʙᴊᴇᴄᴛ.
ʟᴇᴛ ᴜs ᴄᴏɴsɪᴅᴇʀ ᴀɴ ᴏʙᴊᴇᴄᴛ ᴏғ ᴍᴀss ᴍ, ᴍᴏᴠɪɴɢ ᴀʟᴏɴɢ ᴀ sᴛʀᴀɪɢʜᴛ ʟɪɴᴇ ᴡɪᴛʜ ᴀɴ ɪɴɪᴛɪᴀʟ ᴠᴇʟᴏᴄɪᴛʏ ᴜ. ʟᴇᴛ ᴜs sᴀʏ, ᴀғᴛᴇʀ ᴀ ᴄᴇʀᴛᴀɪɴ ᴛɪᴍᴇ ᴛ, ᴡɪᴛʜ ᴀ ᴄᴏɴsᴛᴀɴᴛ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ, ᴛʜᴇ ғɪɴᴀʟ ᴠᴇʟᴏᴄɪᴛʏ ʙᴇᴄᴏᴍᴇs ᴠ.ʜᴇʀᴇ ᴡᴇ sᴇᴇ ᴛʜᴀᴛ, ᴛʜᴇ ɪɴɪᴛɪᴀʟ ᴍᴏᴍᴇɴᴛᴜᴍ
ᴘ = ᴍ × ᴜ
ᴛʜᴇ ғɪɴᴀʟ ᴍᴏᴍᴇɴᴛᴜᴍ
ᴘ = ᴍ × ᴠ
ᴛʜᴇ ᴄʜᴀɴɢᴇ ɪɴ ᴍᴏᴍᴇɴᴛᴜᴍ ɪs
ᴘ – ᴘ = (ᴍ × ᴠ) – (ᴍ × ᴜ)
ᴘ – ᴘ = ᴍ (ᴠ – ᴜ)
ᴛʜᴇ ʀᴀᴛᴇ ᴏғ ᴄʜᴀɴɢᴇ ᴏғ ᴍᴏᴍᴇɴᴛᴜᴍ ᴡɪᴛʜ ʀᴇsᴘᴇᴄᴛ ᴛᴏ ᴛɪᴍᴇ ɪs ᴘʀᴏᴘᴏʀᴛɪᴏɴᴀʟ ᴛᴏ ᴛʜᴇ ᴀᴘᴘʟɪᴇᴅ ғᴏʀᴄᴇ. ᴛʜᴇ ᴀᴘᴘʟɪᴇᴅ ғᴏʀᴄᴇ ɪs
ғ ∝ ᴍ (ᴠ – ᴜ)/ᴛ
ᴏʀ
ғ ∝ ᴍ × ᴀ
ᴀ = ʀᴀᴛᴇ ᴏғ ᴄʜᴀɴɢᴇ ᴏғ ᴠᴇʟᴏᴄɪᴛʏ/ᴛɪᴍᴇ
ғ = ᴋ × ᴍ × ᴀ
ᴋ = ᴘʀᴏᴘᴏʀᴛɪᴏɴᴀʟɪᴛʏ ᴄᴏɴsᴛᴀɴᴛ.
ʜᴇɴᴄᴇ ғʀᴏᴍ ᴛʜᴇ sᴇᴄᴏɴᴅ ʟᴀᴡ ᴏғ ᴍᴏᴛɪᴏɴ, ᴡᴇ ɢᴇᴛ ғᴏʀᴄᴇ ɪs ᴛʜᴇ ᴘʀᴏᴅᴜᴄᴛ ᴏғ ᴍᴀss ᴀɴᴅ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ ɪ.ᴇ ғ = ᴍᴀ.
Explanation:
Newton's second law of motion states that the force applied to the system is equal to the time rate of change of momentum. So, F=dtdP. But P=mv. So, F=dtd(mv) Or F=mdtdv.
state newtons second law of motion.
Newton's second law states that the acceleration of an object is directly related to the net force and inversely related to its mass. ... So, the force/mass ratio (from the equation acceleration = force/mass) is the same for each. Therefore, the acceleration is the same and they reach the ground at the same time.
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Prove that F=ma
Newton's second law of motion states that the force applied to the system is equal to the time rate of change of momentum.
So, F= dt dP
But P=mv
So, F= dt d(mv)
Or F=m dt dv
⟹ F=ma