Two gliders, A and B collide on a level frictionless track. The mass of glider A is less than the mass of glider B. The final speed of glider A is greater than the final speed of glider B. After collision gliders move in opposite directions. Is the magnitude of the final momentum of glider A greater than, less than, or equal to the magnitude of the final momentum of glider B? Draw a momentum vector diagram to support answer. Circle your answer
The Correct Answer and Explanation is :
Correct Answer: The magnitude of the final momentum of glider A is less than the magnitude of the final momentum of glider B.
Explanation:
To answer this question, let’s consider the principle of momentum conservation and the given information in the problem.
1. Conservation of Momentum:
Momentum is a vector quantity, and the law of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces act on it. For this scenario, where two gliders, A and B, collide on a frictionless track, the total momentum before and after the collision must be the same.
Initially, the two gliders are moving towards each other with certain velocities and masses. After the collision, they move in opposite directions with new velocities. The total momentum is conserved, but the individual momenta may differ because of the different masses and velocities.
2. Momentum Magnitude and Direction:
The momentum of an object is calculated as:
[
p = m \times v
]
where:
- ( p ) is the momentum,
- ( m ) is the mass of the object, and
- ( v ) is the velocity of the object. Given:
- The mass of glider A is less than that of glider B (i.e., ( m_A < m_B )).
- The final speed of glider A is greater than that of glider B (i.e., ( v_A > v_B )).
- After the collision, gliders move in opposite directions. Despite glider A having a greater speed, because it has a smaller mass than glider B, the magnitude of its momentum will still be less than that of glider B. This is because the momentum depends both on the mass and the velocity, and the mass of glider B is significantly larger.
3. Momentum Vector Diagram:
- Let the initial momentum of glider A be a vector pointing in one direction, say to the right.
- The initial momentum of glider B will have the opposite direction (pointing to the left).
- After the collision, glider A’s momentum vector will point to the right with a smaller magnitude, and glider B’s momentum vector will point to the left with a larger magnitude. Since momentum is a vector quantity, and glider B’s mass is greater, the magnitude of glider B’s momentum is greater, even though glider A has a higher speed.
Conclusion:
The magnitude of the final momentum of glider A is less than the magnitude of the final momentum of glider B, primarily because glider B’s mass is larger than that of glider A, and the momentum depends on both mass and velocity.