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Sagot :
The constant velocity of center of mass when the spring is at maximum compression is V = ( [tex]m_{1} v_{1}[/tex] + [tex]m_{2} v_{2}[/tex] ) / ([tex]m_{1} + m_{2}[/tex] )
When two objects collide the momentum is always conserved no matter the type of collision. But in case of kinetic energy, it is conserved only if the collision is elastic. Here the collision is elastic due to the presence of a spring. So, in this situation kinetic energy is conserved.
At maximum compression, According to law of conservation of momentum,
Sum of linear momentum before collision = Sum of linear momentum after collision
[tex]m_{1} v_{1}[/tex] + [tex]m_{2} v_{2}[/tex] = ([tex]m_{1} + m_{2}[/tex] ) V
V = ( [tex]m_{1} v_{1}[/tex] + [tex]m_{2} v_{2}[/tex] ) / ([tex]m_{1} + m_{2}[/tex] )
where,
V = Velocity of center of mass
[tex]m_{1}[/tex] = Mass of glider 1
[tex]m_{2}[/tex] = Mass of glider 2
[tex]v_{1}[/tex] = Velocity of glider 1
[tex]v_{2}[/tex] = Velocity of glider 2
Therefore, the constant velocity of center of mass when the spring is at maximum compression is V = ( [tex]m_{1} v_{1}[/tex] + [tex]m_{2} v_{2}[/tex] ) / ([tex]m_{1} + m_{2}[/tex] )
To know more about law of conservation of momentum
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