Question

An object of mass 1 kg travelling in a straight line with a velocity of 10 m/s collides with, and sticks to, a stationary wooden block of mass 5 kg. Then, they both move off together in the same straight line. Calculate the total momentum just before the impact. *

a) 10 kgm/s

b) 5 kgm/s

c) 15 kgm/s

d) 20 kgm/s

​

Answer 1

Answer:

Mass of the body = m1 = 1 kg.

Velocity of the body = v1 = 10 m/s.

Mass of other stationary body = m2 = 5 kg.

Momentum is said to be the product of mass and velocity.

Hence, Momentum before collision = m1v1 + m2v2

⇒ m1v1 + m2v2

⇒ 1×10 + 5×0

⇒ 10 kgm/s

So, let us find the velocity of both the bodies after collision.

Hence, the momentum of the body after collision = (m1 + m2)v = 10 kgm/s.

⇒ (1 + 5)v = 10

⇒ 6v = 10

⇒ v = 10/6

⇒ v = 5/3 m/s

Hence, the answer to your question : a) 10 kgm/s.

Answer 2

GIVEN :-

• Aɴ ᴏʙᴊᴇᴄᴛ ᴏғ ᴍᴀss 1 ᴋg .

• Tʜᴇ ᴏʙᴊᴇᴄᴛ ᴡᴀs ᴛʀᴀᴠᴇʟʟɪɴɢ ɪɴ ᴀ sᴛʀᴀɪɢʜᴛ ʟɪɴᴇ ᴡɪᴛʜ ᴀ ᴠᴇʟᴏᴄɪᴛʏ ᴏғ 10ᴍ/s .

• Tʜᴇ ᴏʙᴊᴇᴄᴛ ᴄᴏʟʟɪᴅᴇs ᴡɪᴛʜ ᴀɴᴅ sᴛɪᴄᴋs ᴛᴏ, ᴀ sᴛᴀᴛɪᴏɴᴀʀʏ ᴡᴏᴏᴅᴇɴ ʙʟᴏᴄᴋ ᴏғ ᴍᴀss 5ᴋg .

• Tʜᴇɴ ᴛʜᴇʏ ʙᴏᴛʜ ᴍᴏᴠᴇs ᴛᴏɢᴇᴛʜᴇʀ ɪɴ ᴛʜᴇ sᴀᴍᴇ sᴛʀᴀɪɢʜᴛ ʟɪɴᴇ .

TO FIND :-

• Tʜᴇ ᴛᴏᴛᴀʟ ᴍᴏᴍᴇᴍᴛᴜᴍ ᴊᴜsᴛ ʙᴇғᴏʀᴇ ᴛʜᴇ ɪᴍᴘᴀᴄᴛ .

SOLUTION :-

Fᴏʀ ғɪʀsᴛ ᴏʙᴊᴇᴄᴛ :-

• ᴍᴀss ᴏғ ᴛʜᴇ ᴏʙᴊᴇᴄᴛ = $\bf\pink{m_1}$ = 1 kg

• ᴠᴇʟᴏᴄɪᴛʏ ᴏғ ᴛʜᴇ ᴏʙᴊᴇᴄᴛ ʙᴇғᴏʀᴇ ᴄᴏʟʟɪsɪᴏɴ = $\bf\pink{v_1}$ = 10ᴍ/s .

Fᴏʀ sᴇᴄᴏɴᴅ ᴏʙᴊᴇᴄᴛ :-

• ᴍᴀss ᴏғ ᴛʜᴇ sᴛᴀᴛɪᴏɴᴀʀʏ ᴡᴏᴏᴅᴇɴ ʙʟᴏᴄᴋ = $\bf\pink{m_2}$ = 5 Kg

• ᴠᴇʟᴏᴄɪᴛʏ ᴏғ ᴛʜᴇ ᴡᴏᴏᴅᴇɴ ʙʟᴏᴄᴋ ʙᴇғᴏʀᴇ ᴄᴏʟʟɪsɪᴏɴ = $\bf\pink{v_2}$ = 0 ᴍ/s

☯︎ Tᴏᴛᴀʟ ᴍᴏᴍᴇɴᴛᴜᴍ ʙᴇғᴏʀᴇ ᴄᴏʟʟɪsɪᴏɴ ᴄᴏʟʟɪsɪᴏɴ,

➪ $\bf\red{m_1\:v_1}$ + $\bf\red{m_2\:v_2}$

➪ 1 × 10 + 5 × 0

➪ 10 + 0

➪ $\bf\purple{10\:kg.m.s^{-1}\:}$

$\rule{200}2$

✰ Iᴛ ɪs ɢɪᴠᴇɴ ᴛʜᴀᴛ ᴀғᴛᴇʀ ᴄᴏʟʟɪsɪᴏɴ, ᴛʜᴇ ᴏʙᴊᴇᴄᴛ ᴀɴᴅ ᴛʜᴇ ᴡᴏᴏᴅᴇɴ ʙʟᴏᴄᴋ sᴛɪᴄᴋ ᴛᴏɢᴇᴛʜᴇʀ .

✯ Tʜᴇ ᴛᴏᴛᴀʟ ᴍᴀss ᴏғ ᴛʜᴇ ᴄᴏᴍʙɪɴᴇᴅ sʏsᴛᴇᴍ ɪs,

• $\bf\red{m_1}$ + $\bf\red{m_2}$

✯ Vᴇʟᴏᴄɪᴛʏ ᴏғ ᴛʜᴇ ᴄᴏᴍʙɪɴᴇᴅ ᴏʙᴊᴇᴄᴛ ɪs,

• $\bf\red{v}$

Aᴄᴄᴏʀᴅɪɴɢ ᴛᴏ ᴛʜᴇ ʟᴀᴡ ᴏғ ᴄᴏɴsᴇʀᴠᴀᴛɪᴏɴ ᴏғ ᴍᴏᴍᴇɴᴛᴜᴍ,

$\huge\orange\star$ Tᴏᴛᴀʟ ᴍᴏᴍᴇɴᴛᴜᴍ ʙᴇғᴏʀᴇ ᴄᴏʟʟɪsɪᴏɴ = Tᴏᴛᴀʟ ᴍᴏᴍᴇɴᴛᴜᴍ ʙᴇғᴏʀᴇ ᴄᴏʟʟɪsɪᴏɴ .

➟ $\bf\pink{m_1\:v_1}$ + $\bf\pink{m_2\:v_2}$ = ($\bf\red{m_1}$ + $\bf\red{m_2}$) $\bf\pink{v}$

➪ $\bf\purple{10\:kg.m.s^{-1}\:}$ = (1 + 5) × ᴠ

➪ 10 = 6 × ᴠ

➪ ᴠ = 10/6

➪ ᴠ = 5/3 m/s

$\rule{200}2$

$\huge\bf\red{\therefore}$ Tʜᴇ ᴛᴏᴛᴀʟ ᴍᴏᴍᴇᴍᴛᴜᴍ ᴊᴜsᴛ ʙᴇғᴏʀᴇ ᴛʜᴇ ɪᴍᴘᴀᴄᴛ ɪs "10 ᴋg.m/s" .