IDNLearn.com offers a unique blend of expert answers and community-driven insights. Ask anything and receive prompt, well-informed answers from our community of experienced experts.

two gliders are set in motion on a horizontal air track. a light spring of force constant k is attached to the back end of the second glider. both gliders are having the same mass m. the first glider moves to the right with speed v1 and the second is at rest. when the first glider collides with the spring attached to the second glider, the spring compress by a distance xmax, and the gliders then move apart again. in terms of v1, m, and k, find

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

https://brainly.com/question/24131537

#SPJ4

Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Your questions deserve accurate answers. Thank you for visiting IDNLearn.com, and see you again for more solutions.