m1v1=m2v2
The Correct Answer and Explanation is:
The equation m1v1=m2v2m_1v_1 = m_2v_2m1v1=m2v2 is a mathematical representation of the principle of conservation of momentum. This principle states that in a closed system, the total momentum before an event (like a collision) must equal the total momentum after the event, provided no external forces act on the system.
In this equation:
- m1m_1m1 is the mass of the first object before the interaction,
- v1v_1v1 is the velocity of the first object before the interaction,
- m2m_2m2 is the mass of the second object after the interaction, and
- v2v_2v2 is the velocity of the second object after the interaction.
Explanation:
Momentum is a vector quantity, meaning it has both magnitude and direction. The total momentum of a system is calculated as the sum of the momentum of all the individual objects in the system. For a single object, momentum is given by the product of its mass and velocity, represented by:p=mvp = mvp=mv
If we apply this to two objects in an isolated system (no external forces), the momentum before the interaction must equal the momentum after:m1v1=m2v2m_1v_1 = m_2v_2m1v1=m2v2
This can be seen in various scenarios, like in elastic collisions (where kinetic energy is conserved) or inelastic collisions (where some energy is transformed into heat or deformation). For example, if two objects collide and one of them moves in the opposite direction after the impact, the momentum transferred between the objects will still satisfy the equation.
This relationship allows us to predict the behavior of objects involved in collisions or interactions, making it a foundational concept in physics, especially in mechanics and engineering. By knowing the masses and velocities of objects before the interaction, you can determine their velocities afterward, assuming no external forces like friction or air resistance interfere.
