A 300 g bird flying along at 6.0 m/s sees a 10 g insect heading straight toward it at a speed of 30 m/s. The bird opens its mouth wide and enjoys a nice lunch. What is the bird’s speed immediately after swallowing?

검증된 단계별 안내

Step 1: Identify the principle of conservation of momentum, which states that the total momentum of a system before and after a collision remains constant if no external forces act on the system.

Step 2: Write the equation for conservation of momentum. The total momentum before the collision is the sum of the bird's momentum and the insect's momentum: \( p_{initial} = m_{bird} v_{bird} + m_{insect} v_{insect} \). After the collision, the bird and insect move together, so \( p_{final} = (m_{bird} + m_{insect}) v_{final} \).

Step 3: Substitute the given values into the equation. The bird's mass \( m_{bird} \) is 300 g (convert to kg: \( 0.300 \, \text{kg} \)), its velocity \( v_{bird} \) is \( 6.0 \, \text{m/s} \), the insect's mass \( m_{insect} \) is 10 g (convert to kg: \( 0.010 \, \text{kg} \)), and its velocity \( v_{insect} \) is \( -30 \, \text{m/s} \) (negative because it is moving toward the bird).

Step 4: Solve for \( v_{final} \), the bird's speed immediately after swallowing the insect. Rearrange the conservation of momentum equation: \( v_{final} = \frac{m_{bird} v_{bird} + m_{insect} v_{insect}}{m_{bird} + m_{insect}} \).

Step 5: Perform the calculation using the substituted values to find \( v_{final} \). Ensure units are consistent throughout the calculation (mass in kilograms and velocity in meters per second).

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주요 개념

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Conservation of Momentum

The conservation of momentum states that in a closed system, the total momentum before an event must equal the total momentum after the event, provided no external forces act on it. In this scenario, the bird and the insect collide, and their combined momentum will be conserved during the interaction.

Momentum Calculation

Momentum is calculated as the product of an object's mass and its velocity (p = mv). For the bird and the insect, we will calculate their individual momenta before the bird swallows the insect, and then use these values to find the final momentum of the bird-insect system after the event.

Final Velocity Determination

To find the final velocity of the bird after swallowing the insect, we can use the formula derived from the conservation of momentum. By setting the total initial momentum equal to the total final momentum, we can solve for the bird's new speed after the collision, taking into account the combined mass of the bird and the insect.