Inelastic Collision and Conservation of Momentum: A Detailed Analysis

Understanding the principles of physics, especially those governing the behavior of objects in collision, is fundamental to many fields. In this article, we will delve into the concept of an inelastic collision, focusing on how the principle of conservation of momentum can be applied to solve such problems.

Principle of Conservation of Momentum

Before diving into the specific problem, it's important to understand the principle of conservation of momentum. This principle states that in the absence of external forces, the total momentum of a closed system remains constant. This means that the sum of the momenta of all objects in the system before the collision is equal to the sum of the momenta after the collision.

Problem Setup

The problem at hand involves a 10 kg object colliding with a 5 kg object that is initially stationary. After the collision, the two objects stick together and move forward with a velocity of 4 m/s. Our goal is to find the velocity with which the 10 kg object hit the 5 kg object.

Solution Steps

Step 1: Conservation of Momentum Equation

Let us start by writing the conservation of momentum equation for this scenario. Using the principle of conservation of momentum, the total momentum before the collision must be equal to the total momentum after the collision:

(m_1 v_{1i} m_2 v_{2i} m_1 v_f m_2 v_f)

Step 2: Substitution of Known Values

Given the problem parameters:

(m_1 10 , text{kg}) (m_2 5 , text{kg}) (m_2 v_{2i} 0 , text{m/s}) (m_1 v_f 4 , text{m/s})

We can plug these values into the conservation of momentum equation:

(10 v_{1i} 5 times 0 10 times 4 5 times 4)

Step 3: Simplify the Equation

This simplifies to:

(10 v_{1i} 60)

Step 4: Solve for (v_{1i})

Dividing both sides by 10:

(v_{1i} frac{60}{10} 6 , text{m/s})

Conclusion

The velocity with which the 10 kg object hit the 5 kg object is (6 , text{m/s}).

Summary of the Solution

To summarize, the problem involved a 10 kg object colliding with a 5 kg object that was stationary. After the collision, the objects stick together and move with a velocity of 4 m/s. By applying the principle of conservation of momentum and following the steps outlined, we determined that the initial velocity of the 10 kg object was 6 m/s.

Additional Insights

Understanding inelastic collisions and the conservation of momentum is crucial in various practical applications, such as car crashes, ballistics, and sports science. These principles help us predict and analyze the behavior of objects in motion. By mastering these concepts, you can apply similar methods to solve more complex physics problems.

Related Topics

If you're interested in learning more about physics and collisions, consider exploring the following related topics:

Inelastic Collision Conservation of Momentum Physics of Collisions

References

For further reading and in-depth exploration of these concepts, you can refer to the following resources:

Resnick, Robert, and David Halliday. Physics, 2nd ed. Wiley, 1988. Cohen-Tannoudji, Claude, Bernard Diu, and Maurice Lalo?. Mecanique Quantique, 2 volumes. Hermann, 1973.