Ch 11: Impulse and Momentum

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo

Knight Calc 5th Edition

Ch 11: Impulse and Momentum

Problema 25a

Capitolo 11, Problema 25a

A 50 g ball of clay traveling at speed v₀ hits and sticks to a 1.0 kg brick sitting at rest on a frictionless surface. What is the speed of the brick after the collision?

Guida verificata passo dopo passo

Step 1: Identify the type of collision. Since the ball of clay sticks to the brick after the collision, this is an inelastic collision. In such collisions, momentum is conserved but kinetic energy is not.

Step 2: Write the equation for conservation of momentum. The total momentum before the collision equals the total momentum after the collision. Use the formula:

m_{1} v_{0} + m_{2} v_{2} = (m_{1} + m_{2}) v_{f}

, where

m_{1}

and

v_{0}

are the mass and velocity of the clay,

m_{2}

and

v_{2}

are the mass and velocity of the brick, and

v_{f}

is the final velocity of the combined system.

Step 3: Substitute the given values into the momentum equation. The mass of the clay is 50 g (convert to kg: 0.05 kg), the mass of the brick is 1.0 kg, the initial velocity of the brick is 0 m/s (since it is at rest), and the initial velocity of the clay is

v_{0}

. The equation becomes:

0.05 v_{0} + 1.0 (0) = (0.05 + 1.0) v_{f}

Step 4: Simplify the equation to isolate

v_{f}

. After simplifying, the equation becomes:

v_{f} = (0.05 v_{0})/(1.05)

Step 5: Conclude that the final velocity of the brick and clay system depends on the initial velocity of the clay,

v_{0}

. To find the numerical value, substitute the value of

v_{0}

into the equation.

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Conservation of Momentum

The principle of 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 clay ball collides with the brick, and since no external forces are acting on the system, the momentum of the clay ball and brick combined must remain constant throughout the collision.

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Percorso guidato

05:58

Conservation Of Momentum

Elastic vs. Inelastic Collisions

Collisions can be classified as elastic or inelastic based on whether kinetic energy is conserved. In this case, the clay ball sticks to the brick after the collision, indicating an inelastic collision where kinetic energy is not conserved, but momentum is. This distinction is crucial for calculating the final speed of the combined mass after the collision.

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Percorso guidato

08:56

Intro To Elastic Collisions

Mass and Velocity Relationship

The relationship between mass and velocity is fundamental in determining the outcome of collisions. In this problem, the mass of the clay ball (50 g) and the brick (1.0 kg) will influence the final velocity of the combined system after the collision. Understanding how mass affects momentum allows for the calculation of the final speed using the conservation of momentum principle.

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Percorso guidato

20:32

Mass Spectrometers

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Concetti chiave

Conservation of Momentum

Elastic vs. Inelastic Collisions

Mass and Velocity Relationship

A 50 g ball of clay traveling at speed v₀ hits and sticks to a 1.0 kg brick sitting at rest on a frictionless surface. What is the speed of the brick after the collision?