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 19

Chapter 11, Problem 19

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?

Verified step by step guidance

Step 1: Identify the principle of conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision, assuming no external forces act on the system.

Step 2: Write the equation for the conservation of momentum. Before the collision, the car has momentum \( p_{car} = m_{car} \cdot v_{car} \), and the clay has momentum \( p_{clay} = m_{clay} \cdot v_{clay} \). After the collision, the car and clay stick together, so their combined momentum is \( p_{combined} = (m_{car} + m_{clay}) \cdot v_{final} \).

Step 3: Set up the equation for conservation of momentum: \( m_{car} \cdot v_{car} + m_{clay} \cdot v_{clay} = (m_{car} + m_{clay}) \cdot v_{final} \).

Step 4: Solve for \( v_{clay} \), the speed at which the clay must be fired. Rearrange the equation to isolate \( v_{clay} \): \( v_{clay} = \frac{(m_{car} + m_{clay}) \cdot v_{final} - m_{car} \cdot v_{car}}{m_{clay}} \).

Step 5: Substitute the given values into the equation: \( m_{car} = 1500 \; \text{kg}, \; v_{car} = 2.0 \; \text{m/s}, \; m_{clay} = 10 \; \text{kg}, \; v_{final} = 0 \; \text{m/s} \). Perform the algebraic simplifications to find \( v_{clay} \).

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. In this scenario, the car and the clay blob form a system where the momentum of the car before the collision must equal the combined momentum of the car and clay after they stick together.

Momentum Calculation

Momentum is calculated as the product of an object's mass and its velocity (p = mv). For the car, its momentum can be calculated using its mass (1500 kg) and its velocity (2.0 m/s). The clay's momentum will depend on its mass and the velocity at which it is fired, which we need to determine to achieve the desired outcome.

Inelastic Collision

An inelastic collision occurs when two objects collide and stick together, resulting in a loss of kinetic energy but conservation of momentum. In this case, when the clay hits the car, they will move together as one mass, and we can use the conservation of momentum principle to find the required speed of the clay to stop the car.

Recommended video:

Guided course

04:18

Completely Inelastic Collisions

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

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 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?

views

Textbook Question

A proton is traveling to the right at 2.0 x 10⁷ m/s. It has a head-on perfectly elastic collision with a carbon atom. The mass of the carbon atom is 12 times the mass of the proton. What are the speed and direction of each after the collision?

views