what is the total momentum of the system before collision
What is the total momentum of the system before collision?
Answer:
The concept of momentum is fundamental in physics, particularly in understanding collisions. Momentum \mathbf{p} of an object is the product of its mass m and its velocity \mathbf{v}:
\mathbf{p} = m \mathbf{v}
To find the total momentum of a system before a collision, you must consider the momentum of each object involved in the collision and then sum these momenta vectorially.
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Identify the Components:
- Assume we have two objects, Object 1 and Object 2, participating in a collision.
- Let m_1 and \mathbf{v}_1 represent the mass and velocity of Object 1, and m_2 and \mathbf{v}_2 represent the mass and velocity of Object 2.
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Calculate Individual Momenta:
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Calculate the momentum of Object 1:
\mathbf{p}_1 = m_1 \mathbf{v}_1 -
Calculate the momentum of Object 2:
\mathbf{p}_2 = m_2 \mathbf{v}_2
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Sum the Momenta:
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The total momentum of the system before the collision is the vector sum of the individual momenta:
\mathbf{P}_{\text{total, before}} = \mathbf{p}_1 + \mathbf{p}_2
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Example Calculation:
To make things more concrete, let’s consider a numerical example:
- Suppose Object 1 has a mass of 3 \, \text{kg} and is moving with a velocity of 4 \, \text{m/s} in the positive x-direction.
- Suppose Object 2 has a mass of 5 \, \text{kg} and is moving with a velocity of 2 \, \text{m/s} in the positive x-direction.
First, we calculate the individual momenta:
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Object 1:
\mathbf{p}_1 = (3 \, \text{kg}) \times (4 \, \text{m/s}) = 12 \, \text{kg}\cdot\text{m/s} -
Object 2:
\mathbf{p}_2 = (5 \, \text{kg}) \times (2 \, \text{m/s}) = 10 \, \text{kg}\cdot\text{m/s}
Next, we sum the momenta:
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Total momentum:
\mathbf{P}_{\text{total, before}} = \mathbf{p}_1 + \mathbf{p}_2 = 12 \, \text{kg}\cdot\text{m/s} + 10 \, \text{kg}\cdot\text{m/s} = 22 \, \text{kg}\cdot\text{m/s}
Final Answer:
The total momentum of the system before the collision is \boxed{22 \, \text{kg}\cdot\text{m/s}}.