Challenge !!A block of mass 2.0 kg is moving on a frictionless horizontal surface with a velocity of 1.0 m/s (figure 9-E12) towards another block of equal mass kept at rest. The spring constant of the spring fixed 100 N/ m find the maximum compression of the spring.#Don't spam. Created by BrainlyUniverse. Math

Answer:ᴍᴀss ᴏғ ᴇᴀᴄʜ ʙʟᴏᴄᴋ ᴍᴀ ᴀɴᴅ ᴍʙ = 2kg. ɪɴɪᴛɪᴀʟ ᴠᴇʟᴏᴄɪᴛʏ ᴏғ ᴛʜᴇ sᴛ ʙʟᴏᴄᴋ, (ᴠ) = 1m/s VA = 1 m/s, VB = 0 m/s sᴘʀɪɴɢ ᴄᴏɴsᴛᴀɴᴛ ᴏғ ᴛʜᴇ sᴘʀɪɴɢ = 100 N/m. ᴛʜᴇ ʙʟᴏᴄᴋ ᴀ sᴛʀɪᴋᴇs ᴛʜᴇ sᴘʀɪɴɢ ᴡɪᴛʜ ᴀ ᴠᴇʟᴏᴄɪᴛʏ 1m/s ᴀғᴛᴇʀ ᴛʜᴇ ᴄᴏʟʟɪsɪᴏɴ, ɪᴛ’s ᴠᴇʟᴏᴄɪᴛʏ ᴅᴇᴄʀᴇᴀsᴇs ᴄᴏɴᴛɪɴᴜᴏᴜsʟʏ ᴀɴᴅ ᴀᴛ ᴀ ɪɴsᴛᴀɴᴛ ᴛʜᴇ ᴡʜᴏʟᴇ sʏsᴛᴇᴍ (ʙʟᴏᴄᴋ ᴀ + ᴛʜᴇ ᴄᴏᴍᴘᴏᴜɴᴅ sᴘʀɪɴɢ + ʙʟᴏᴄᴋ ʙ) ᴍᴏᴠᴇ ᴛᴏɢᴇᴛʜᴇʀ ᴡɪᴛʜ ᴀ ᴄᴏᴍᴍᴏɴ ᴠᴇʟᴏᴄɪᴛʏ. Let that velocity be V. Using conservation of energy, (ᴡʜᴇʀᴇ x = ᴍᴀx. ᴄᴏᴍᴘʀᴇssɪᴏɴ ᴏғ sᴘʀɪɴɢ) ᴀs ᴛʜᴇʀᴇ ɪs ɴᴏ ᴇxᴛᴇʀɴᴀʟ ғᴏʀᴄᴇ ɪɴ ᴛʜᴇ ʜᴏʀɪᴢᴏɴᴛᴀʟ ᴅɪʀᴇᴄᴛɪᴏɴ, ᴛʜᴇ ᴍᴏᴍᴇɴᴛᴜᴍ sʜᴏᴜʟᴅ ʙᴇ ᴄᴏɴsᴇʀᴠᴇᴅ.Putting in equation (1)

m find the maximum compression of the spring.#Don't spam...

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Answer:

ᴍᴀss ᴏғ ᴇᴀᴄʜ ʙʟᴏᴄᴋ ᴍᴀ ᴀɴᴅ ᴍʙ = 2kg.

ɪɴɪᴛɪᴀʟ ᴠᴇʟᴏᴄɪᴛʏ ᴏғ ᴛʜᴇ sᴛ ʙʟᴏᴄᴋ, (ᴠ) = 1m/s

VA = 1 m/s,
VB = 0 m/s

sᴘʀɪɴɢ ᴄᴏɴsᴛᴀɴᴛ ᴏғ ᴛʜᴇ sᴘʀɪɴɢ = 100 N/m.

ᴛʜᴇ ʙʟᴏᴄᴋ ᴀ sᴛʀɪᴋᴇs ᴛʜᴇ sᴘʀɪɴɢ ᴡɪᴛʜ ᴀ ᴠᴇʟᴏᴄɪᴛʏ 1m/s

ᴀғᴛᴇʀ ᴛʜᴇ ᴄᴏʟʟɪsɪᴏɴ, ɪᴛ’s ᴠᴇʟᴏᴄɪᴛʏ ᴅᴇᴄʀᴇᴀsᴇs ᴄᴏɴᴛɪɴᴜᴏᴜsʟʏ ᴀɴᴅ ᴀᴛ ᴀ ɪɴsᴛᴀɴᴛ ᴛʜᴇ ᴡʜᴏʟᴇ sʏsᴛᴇᴍ (ʙʟᴏᴄᴋ ᴀ + ᴛʜᴇ ᴄᴏᴍᴘᴏᴜɴᴅ sᴘʀɪɴɢ + ʙʟᴏᴄᴋ ʙ) ᴍᴏᴠᴇ ᴛᴏɢᴇᴛʜᴇʀ ᴡɪᴛʜ ᴀ ᴄᴏᴍᴍᴏɴ ᴠᴇʟᴏᴄɪᴛʏ.

Let that velocity be V.