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Ch. 09 - Linear Momentum
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoGiancoli Douglas 5th editionCh. 09 - Linear MomentumProblema 42a
Capitolo 9, Problema 42a

A 144-g baseball moving 28.0 m/s strikes a stationary 4.85-kg brick resting on small rollers so it moves without significant friction. After hitting the brick, the baseball bounces straight back, and the brick moves forward at 1.10 m/s. What is the baseball’s speed after the collision?

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Convert the mass of the baseball from grams to kilograms. Since 1 gram = 0.001 kilograms, the mass of the baseball is \( m_1 = 144 \times 10^{-3} \, \text{kg} = 0.144 \, \text{kg} \).
Apply the principle of conservation of momentum. The total momentum before the collision equals the total momentum after the collision. The equation is: \( m_1 v_{1i} + m_2 v_{2i} = m_1 v_{1f} + m_2 v_{2f} \), where \( m_1 \) and \( m_2 \) are the masses of the baseball and brick, \( v_{1i} \) and \( v_{2i} \) are their initial velocities, and \( v_{1f} \) and \( v_{2f} \) are their final velocities.
Substitute the known values into the momentum equation. The initial velocity of the baseball is \( v_{1i} = 28.0 \, \text{m/s} \), the initial velocity of the brick is \( v_{2i} = 0 \, \text{m/s} \), the final velocity of the brick is \( v_{2f} = 1.10 \, \text{m/s} \), and the masses are \( m_1 = 0.144 \, \text{kg} \) and \( m_2 = 4.85 \, \text{kg} \). The equation becomes: \( (0.144)(28.0) + (4.85)(0) = (0.144)v_{1f} + (4.85)(1.10) \).
Simplify the equation to isolate \( v_{1f} \), the final velocity of the baseball. Rearrange the terms to solve for \( v_{1f} \): \( v_{1f} = \frac{(0.144)(28.0) - (4.85)(1.10)}{0.144} \).
Perform the calculations step by step to find \( v_{1f} \), ensuring that the units are consistent throughout. Note that the result will be the baseball's speed after the collision, and it will have a negative sign if the baseball bounces back in the opposite direction.

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Conservation of Momentum

The principle of conservation of momentum states that in a closed system, the total momentum before a collision is equal to the total momentum after the collision. This is crucial for analyzing collisions, as it allows us to set up equations based on the masses and velocities of the objects involved.
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Percorso guidato
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Conservation Of Momentum

Elastic and 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 scenario described involves an inelastic collision since the baseball bounces back, indicating some energy is lost.
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Percorso guidato
08:56
Intro To Elastic Collisions

Velocity and Speed

Velocity is a vector quantity that includes both speed and direction, while speed is a scalar quantity that only measures how fast an object is moving. Understanding the difference is essential for solving the problem, as the direction of the baseball's velocity changes after the collision, affecting the final calculations.
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Percorso guidato
05:35
Intro to Velocity and Speed
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