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.

검증된 단계별 안내

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.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

10m

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.