where to use m1v1=m2v2 formula and where to use n1v1=n2v2 formula?

The equations $m_1{v}_1=m_2{v}_2$ and $n_1{v}_1=n_2{v}_2$ are both fundamental in the study of conservation laws in physics, particularly in the context of momentum and mass flow. However, they apply to different scenarios, so understanding when to use each is crucial for solving problems correctly.

Understanding the Context of Each Formula

Let's break down each formula and see where they fit in the broader picture of physics.

Momentum Conservation: $m_1{v}_1=m_2{v}_2$

This equation represents the principle of conservation of momentum. Here, $m_1$ and $m_2$ are the masses of two objects, while $v_1$ and $v_2$ are their respective velocities. This formula is typically used in collision problems, where two objects collide and exchange momentum.

• Example: Imagine two ice skaters pushing off each other. If skater A has a mass of 50 kg and moves at 2 m/s after the push, and skater B has a mass of 70 kg, you can find B's velocity after the push using the formula.

In this case, the total momentum before the push equals the total momentum after the push, allowing you to set up the equation:

Before: $0=m_1{v}_1+m_2{v}_2$ (assuming they start from rest)

After: $m_1{v}_1+m_2{v}_2=0$

Mass Flow Rate: $n_1{v}_1=n_2{v}_2$

This equation is used in fluid dynamics and relates to the conservation of mass, particularly in systems where fluids flow through different cross-sectional areas. Here, $n_1$ and $n_2$ represent the mass flow rates at two different points, while $v_1$ and $v_2$ are the velocities of the fluid at those points.

• Example: Consider a pipe that narrows down. If water flows through a wider section at a slower speed, it must flow faster in the narrower section to maintain the same mass flow rate. If the flow rate at the wider section is 5 kg/s and the velocity is 2 m/s, you can find the velocity in the narrower section using this formula.

In this scenario, the mass flow rate remains constant, so you can set up the equation:

At point 1: $n_1=\text{mass flow rate}$

At point 2: $n_2=\text{mass flow rate}$

Key Differences and Applications

To summarize, the choice between these two formulas depends on the physical situation:

• Use $m_1{v}_1=m_2{v}_2$ when dealing with collisions or interactions between two objects where momentum is conserved.
• Use $n_1{v}_1=n_2{v}_2$ when analyzing fluid flow in a system where mass is conserved across different sections of a flow path.

By understanding the context and the physical principles behind each formula, you can effectively apply them to solve a variety of problems in physics. Whether you're analyzing a collision or studying fluid dynamics, knowing when to use each equation is key to finding the right solution.