Ch 11: Impulse and Momentum

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 11: Impulse and Momentum

Problem 18

Chapter 11, Problem 18

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?

Verified step by step guidance

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).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

Recommended video:

Guided course

7:27

Escape Velocity

Related Practice

Textbook Question

Three identical train cars, coupled together, are rolling east at speed v₀. A fourth car traveling east at 2v₀ catches up with the three and couples to make a four-car train. A moment later, the train cars hit a fifth car that was at rest on the tracks, and it couples to make a five-car train. What is the speed of the five-car train?

views

Textbook Question

A 30 g dart traveling horizontally hits and sticks in the back of a 500 g toy car, causing the car to roll forward at 1.4 m/s. What was the speed of the dart?

Textbook Question

A 1500 kg car is rolling at 2.0 m/s. You would like to stop the car by firing a 10 kg blob of sticky clay at it. How fast should you fire the clay?

views

Textbook Question

Fred (mass 60 kg) is running with the football at a speed of 6.0 m/s when he is met head-on by Brutus (mass 120 kg), who is moving at 4.0 m/s. Brutus grabs Fred in a tight grip, and they fall to the ground. Which way do they slide, and how far? The coefficient of kinetic friction between football uniforms and Astroturf is 0.30.

Textbook Question

A 10-m-long glider with a mass of 680 kg (including the passengers) is gliding horizontally through the air at 30 m/s when a 60 kg skydiver drops out by releasing his grip on the glider. What is the glider's velocity just after the skydiver lets go?

views

Textbook Question

A 10,000 kg railroad car is rolling at 2.0 m/s when a 4000 kg load of gravel is suddenly dropped in. What is the car’s speed just after the gravel is loaded?

views