The maximum height to which block 1 rises after the collision is 0.56m
<h3>What is mechanical energy?</h3>
The mechanical energy is the sum of kinetic energy and the potential energy of an object at any instant of time.
M.E = KE +PE
A block of mass m1 = 5.00kg is released from A. It makes a head-on elastic collision at B with a block of mass m2= 10.0 kg that is initially at rest.
The conservation of energy principle states that total mechanical energy remains conserved in all situations where there is no external force acting on the system.
Kinetic energy before collision = Potential energy after collision
1/2 mu² =mgh
The velocity at the bottom, when the height h = 5m, is
u= √2gh
u = √2x 9.81 x5
u = 9.9 m/s
For elastic head on collision, final velocity of block 1 after collision is
v₁ = (m₁ -m₂)/ (m₁ +m₂) x u
Putting the values, we get
v₁ = -3.3 m/s
The final velocity of block 2 after collision is
v₂ = 2m₁ / (m₁ +m₂) x u
Putting the values, we get
v₂ =6.6 m/s
For block 1, after collision kinetic energy is converted to potential energy, then the maximum height rises
h' = v₁²/2g
h' = (-3.3)²/(2x9.81)
h' = 0.56 m
Thus, the height gained by the block after collision is 0.56 m.
Learn more about mechanical energy.
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