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 23

Chapter 11, Problem 23

A 50 g marble moving at 2.0 m/s strikes a 20 g marble at rest. What is the speed of each marble immediately after the collision?

Verified step by step guidance

Identify the type of collision: Since the problem does not specify whether the collision is elastic or inelastic, assume it is an elastic collision (as is common in such problems unless stated otherwise). In an elastic collision, both momentum and kinetic energy are conserved.

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

m

₁v₁i + m₂v₂i = m₁v₁f + m₂v₂f, where

m

₁ and

m

₂ are the masses of the marbles,

v

₁i and

v

₂i are their initial velocities, and

v

₁f and

v

₂f are their final velocities.

Write the equation for conservation of kinetic energy: Since the collision is elastic, the total kinetic energy before the collision equals the total kinetic energy after the collision. Use the formula:

1/2 m

₁v₁i² + 1/2 m₂v₂i² = 1/2 m₁v₁f² + 1/2 m₂v₂f².

Substitute the given values into the equations: Use

m

₁ = 50 \(\text{ g}\) = 0.050 \(\text{ kg}\),

m

₂ = 20 \(\text{ g}\) = 0.020 \(\text{ kg}\),

v

₁i = 2.0 \(\text{ m/s}\), and

v

₂i = 0 \(\text{ m/s}\). Solve the system of equations for

v

₁f and

v

₂f.

Solve the system of equations: Use algebraic methods to solve the two equations (momentum and kinetic energy conservation) simultaneously. This will yield the final velocities

v

₁f and

v

₂f for the two marbles.

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Key Concepts

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

Conservation of Momentum

The principle of conservation of momentum states that in a closed system, the total momentum before an event (like a collision) is equal to the total momentum after the event. This means that the momentum lost by one object is gained by another, allowing us to set up equations to solve for unknown velocities after the collision.

Elastic vs. Inelastic Collisions

Collisions can be classified as elastic or inelastic. In elastic collisions, both momentum and kinetic energy are conserved, while in inelastic collisions, momentum is conserved but kinetic energy is not. The problem does not specify the type of collision, but understanding this distinction is crucial for determining how to approach the calculations.

Mass and Velocity Relationship

The relationship between mass and velocity is fundamental in physics, particularly in momentum calculations. Momentum (p) is defined as the product of mass (m) and velocity (v), expressed as p = mv. This relationship allows us to analyze how changes in mass or velocity affect the overall momentum of the system during collisions.

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