2. Consider that an object?s mass is 5 kg and it is moving towards north direction with 4 m/s velocity. Another object of 3 kg is moving to the south direction with 2 m/s velocity. In any moment, the two objects interact with each other and become one object. Now determine the velocity and direction of one object.

To find the velocity and direction of the combined object after the two objects interact, we can use the principle of conservation of momentum. This principle states that the total momentum of a closed system before an interaction is equal to the total momentum after the interaction, provided no external forces act on it.

Calculating Initial Momentum

First, let's calculate the momentum of each object before they collide. Momentum is defined as the product of mass and velocity, expressed mathematically as:

Momentum (p) = Mass (m) × Velocity (v)

Object 1: 5 kg moving north

For the first object:

• Mass (m₁) = 5 kg
• Velocity (v₁) = 4 m/s (north)

The momentum of the first object (p₁) is:

p₁ = 5 kg × 4 m/s = 20 kg·m/s (north)

Object 2: 3 kg moving south

For the second object:

• Mass (m₂) = 3 kg
• Velocity (v₂) = 2 m/s (south)

The momentum of the second object (p₂) is:

p₂ = 3 kg × 2 m/s = 6 kg·m/s (south)

Considering Direction

Since the two objects are moving in opposite directions, we need to assign a positive or negative value to their momentum based on their direction. Let's consider north as positive and south as negative.

Thus, the momentum of the second object can be expressed as:

p₂ = -6 kg·m/s (south)

Finding Total Momentum

The total momentum (p_total) before the interaction is the sum of the momenta of both objects:

p_total = p₁ + p₂

p_total = 20 kg·m/s (north) - 6 kg·m/s (south) = 20 kg·m/s - 6 kg·m/s = 14 kg·m/s (north)

Calculating the Combined Mass

Next, we need to find the total mass of the combined object:

m_total = m₁ + m₂ = 5 kg + 3 kg = 8 kg

Determining the Final Velocity

Now, we can find the final velocity (v_final) of the combined object using the total momentum:

Using the formula:

p_total = m_total × v_final

We can rearrange this to solve for v_final:

v_final = p_total / m_total

Substituting the values we calculated:

v_final = 14 kg·m/s / 8 kg = 1.75 m/s

Final Direction

Since the total momentum is positive, the direction of the final velocity is north. Therefore, the final velocity of the combined object is:

1.75 m/s towards the north

This example illustrates how momentum conservation works in a system with two objects moving in opposite directions, leading to a combined object with a new velocity and direction. Understanding these principles is crucial in physics, especially in topics related to collisions and interactions.