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Question
The blocks of masses 10 kg and 20 kg moving at speeds of 10 m s−1 and 20 m s−1respectively in opposite directions, approach each other and collide. If the collision is completely inelastic, find the thermal energy developed in the process.
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Solution
Given:-
Mass of the first block, m1 = 10 kg
Mass of the second block, m2 = 20 kg
Initial velocity of the first block, u1 = 10 m/s
Initial velocity of the second block, u2 = 20 m/s
Let the velocity of the blocks after collision be v.
Applying conservation of momentum, we get
m2u2 − m1u1 = (m1 + m2)v
⇒ 20 × 20 − 10 × 10 = (10 + 20)v
⇒ 400 − 100 = 30 v
⇒ 300 = 30 v
⇒ v = 10 m/s
Initial kinetic energy is given by
`K_i=1/2m_1u_1^2+1/2m_2u_2^2`
`K_i=1/2xx10xx(10)^2+1/2xx20xx(20)^2`
`K_i=500+4000=4500`
Final kinetic energy is given by
`K_f=1/2(m_1+m_2)"v"^2`
`K_f=1/2(10+20)(10)^2`
`K_f=(30/2)xx100=1500`
∴ Total change in KE = 4500 J − 1500 J = 3000 J
Thermal energy developed in the process = 3000 J
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