Understanding the Concepts
* Conservation of Momentum: In a closed system (like our gliders on an air track), the total momentum before a collision equals the total momentum after the collision.
* Momentum: Momentum is the mass of an object multiplied by its velocity (p = mv).
Solving the Problem
1. Define Variables:
* Let 'm' be the mass of each glider.
* Let 'v' be the initial speed of each glider (since they have the same speed).
2. Momentum Before Collision:
* The momentum of the first glider is 'mv' (moving to the right).
* The momentum of the second glider is '-mv' (moving to the left).
* Total momentum before the collision is 'mv - mv = 0'.
3. Momentum After Collision:
* The gliders stick together, forming a single object with a mass of '2m'.
* Let 'vf' be the final velocity of the combined object.
* The total momentum after the collision is '2m * vf'.
4. Conservation of Momentum:
* The total momentum before the collision must equal the total momentum after:
0 = 2m * vf
5. Final Velocity:
* Solving for 'vf', we get: vf = 0
Conclusion
The final velocity of the gliders after they stick together is 0. This means they come to a complete stop. This result makes sense because the gliders have equal and opposite momenta, which cancel each other out during the perfectly inelastic collision.
