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Ch 11: Impulse and Momentum
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796당신이 사용하는 게 아니라요?교과서 변경
11장, 문제 14

A 10,000 kg railroad car is rolling at 2.0 m/s when a 4000 kg load of gravel is suddenly dropped in. What is the car’s speed just after the gravel is loaded?

검증된 단계별 안내
1
Identify the principle involved: This is a conservation of momentum problem. The total momentum of the system (railroad car + gravel) before the gravel is dropped must equal the total momentum of the system after the gravel is dropped, assuming no external forces act on the system.
Write the equation for conservation of momentum: \( m_1 v_1 + m_2 v_2 = (m_1 + m_2) v_f \), where \( m_1 \) is the mass of the railroad car, \( v_1 \) is its initial velocity, \( m_2 \) is the mass of the gravel, \( v_2 \) is the initial velocity of the gravel (which is 0 since it is dropped vertically), and \( v_f \) is the final velocity of the system.
Substitute the known values into the equation: \( (10,000 \text{ kg})(2.0 \text{ m/s}) + (4,000 \text{ kg})(0 \text{ m/s}) = (10,000 \text{ kg} + 4,000 \text{ kg}) v_f \).
Simplify the equation: Calculate the total momentum on the left-hand side and the total mass on the right-hand side. This will leave you with an equation in terms of \( v_f \), the final velocity.
Solve for \( v_f \): Divide the total momentum by the total mass to find the final velocity of the railroad car and gravel system.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
3m

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 must equal the total momentum after the event, provided no external forces act on it. In this scenario, the momentum of the railroad car and the gravel must be calculated before and after the gravel is dropped to find the new speed of the car.
추천 영상:
가이드 코스
05:58
Conservation Of Momentum

Momentum Calculation

Momentum is defined as the product of an object's mass and its velocity (p = mv). To solve the problem, we need to calculate the initial momentum of the railroad car and the gravel separately, and then combine them to find the final momentum of the system after the gravel is added.
추천 영상:
가이드 코스
05:17
Intro to Momentum

Final Velocity Determination

After applying the conservation of momentum, the final velocity of the railroad car can be determined using the formula for momentum. By setting the total initial momentum equal to the total final momentum, we can solve for the final speed of the railroad car after the gravel is added, ensuring that we account for the combined mass of the car and the gravel.
추천 영상:
가이드 코스
7:27
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