Two fun-loving otters are sliding toward each other on a muddy (and hence frictionless) horizontal surface. One of them, of mass 7.50 kg, is sliding to the left at 5.00 m/s, while the other, of mass 5.75 kg, is slipping to the right at 6.00 m/s. They hold fast to each other after they collide. How much mechanical energy dissipates during this play?

검증된 단계별 안내

Identify the type of collision: This is an inelastic collision because the two otters stick together after the collision. In such collisions, momentum is conserved, but mechanical energy is not.

Calculate the total initial momentum of the system: Use the formula for momentum, \( p = mv \), where \( m \) is mass and \( v \) is velocity. Assign positive and negative signs to velocities based on direction (e.g., left is negative, right is positive). Compute the momentum of each otter and sum them.

Determine the final velocity of the combined system: Since momentum is conserved, set the total initial momentum equal to the total final momentum. Use the formula \( p_{\text{initial}} = p_{\text{final}} \), where \( p_{\text{final}} = (m_1 + m_2)v_{\text{final}} \). Solve for \( v_{\text{final}} \).

Calculate the initial mechanical energy: Use the kinetic energy formula \( KE = \frac{1}{2}mv^2 \) for each otter before the collision. Add their kinetic energies to find the total initial mechanical energy.

Calculate the final mechanical energy and the energy dissipated: After the collision, the combined mass moves with the final velocity. Use \( KE = \frac{1}{2}(m_1 + m_2)v_{\text{final}}^2 \) to find the final mechanical energy. Subtract the final mechanical energy from the initial mechanical energy to find the energy dissipated.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

11m

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주요 개념

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

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. In this scenario, the momentum of the two otters before they collide can be calculated and must equal the momentum of the combined mass after they hold onto each other.

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion, calculated using the formula KE = 0.5 * m * v², where m is mass and v is velocity. In this problem, the kinetic energies of both otters before the collision must be determined to assess how much energy is lost during the collision.

Mechanical Energy Dissipation

Mechanical energy dissipation refers to the loss of kinetic energy during a collision, often transformed into other forms of energy, such as heat or sound. Inelastic collisions, like the one described, result in some kinetic energy being converted to other forms, which can be calculated by comparing the total kinetic energy before and after the collision.