Ch. 09 - Linear Momentum

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook

Giancoli Douglas 5th edition

Ch. 09 - Linear Momentum

Problem 42b

Chapter 9, Problem 42b

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. Find the total kinetic energy before and after the collision.

Verified step by step guidance

Convert the mass of the baseball from grams to kilograms. Since 1 gram = 0.001 kilograms, the mass of the baseball is \( m_1 = 144 \times 10^{-3} \, \text{kg} \).

Calculate the initial kinetic energy of the baseball using the formula \( KE = \frac{1}{2} m v^2 \). Here, \( m_1 = 0.144 \; \text{kg} \) and \( v_1 = 28.0 \; \text{m/s} \).

Determine the initial kinetic energy of the brick. Since the brick is stationary before the collision, its initial velocity \( v_2 = 0 \; \text{m/s} \), so its initial kinetic energy is zero.

Calculate the final kinetic energy of the baseball after the collision. Use the same formula \( KE = \frac{1}{2} m v^2 \), but substitute the final velocity of the baseball (which is not given directly in the problem but can be determined if needed).

Calculate the final kinetic energy of the brick after the collision using \( KE = \frac{1}{2} m v^2 \), where \( m_2 = 4.85 \; \text{kg} \) and \( v_2 = 1.10 \; \text{m/s} \). Add the final kinetic energies of the baseball and the brick to find the total kinetic energy after the collision.

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Key Concepts

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

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion, calculated using the formula KE = 1/2 mv², where m is the mass and v is the velocity. In this scenario, both the baseball and the brick have kinetic energy before and after the collision, which must be calculated to analyze the system's energy changes.

Conservation of Momentum

The principle of conservation of momentum states that the total momentum of a closed system remains constant if no external forces act on it. In this collision, the momentum before the impact must equal the momentum after the impact, allowing us to relate the velocities of the baseball and the brick to find their respective speeds post-collision.

Elastic vs. Inelastic Collisions

Collisions can be classified as elastic or inelastic based on whether kinetic energy is conserved. In this case, since the baseball bounces back and the brick moves forward, it suggests an inelastic collision where some kinetic energy is transformed into other forms of energy, such as sound or heat, which must be accounted for when calculating total kinetic energy before and after the collision.

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Textbook Question

The force on a bullet along the barrel of a firearm is given by the formula F = [740 ― (2.3 x 10⁵ s⁻¹ ) t] N over the time interval t = 0 to t = 3.0 x 10⁻³ s. Plot a graph of F versus t for t = 0 to t = 3.0 ms. Use the graph to estimate the impulse given the bullet.

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Textbook Question

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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