A 1500 kg car is rolling at 2.0 m/s. You would like to stop the car by firing a 10 kg blob of sticky clay at it. How fast should you fire the clay?

검증된 단계별 안내

Step 1: Identify the principle of conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision, assuming no external forces act on the system.

Step 2: Write the equation for the conservation of momentum. Before the collision, the car has momentum \( p_{car} = m_{car} \cdot v_{car} \), and the clay has momentum \( p_{clay} = m_{clay} \cdot v_{clay} \). After the collision, the car and clay stick together, so their combined momentum is \( p_{combined} = (m_{car} + m_{clay}) \cdot v_{final} \).

Step 3: Set up the equation for conservation of momentum: \( m_{car} \cdot v_{car} + m_{clay} \cdot v_{clay} = (m_{car} + m_{clay}) \cdot v_{final} \).

Step 4: Solve for \( v_{clay} \), the speed at which the clay must be fired. Rearrange the equation to isolate \( v_{clay} \): \( v_{clay} = \frac{(m_{car} + m_{clay}) \cdot v_{final} - m_{car} \cdot v_{car}}{m_{clay}} \).

Step 5: Substitute the given values into the equation: \( m_{car} = 1500 \; \text{kg}, \; v_{car} = 2.0 \; \text{m/s}, \; m_{clay} = 10 \; \text{kg}, \; v_{final} = 0 \; \text{m/s} \). Perform the algebraic simplifications to find \( v_{clay} \).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

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

Conservation of Momentum

The conservation of momentum states that in a closed system, the total momentum before an event must equal the total momentum after the event. In this scenario, the car and the clay blob form a system where the momentum of the car before the collision must equal the combined momentum of the car and clay after they stick together.

Momentum Calculation

Momentum is calculated as the product of an object's mass and its velocity (p = mv). For the car, its momentum can be calculated using its mass (1500 kg) and its velocity (2.0 m/s). The clay's momentum will depend on its mass and the velocity at which it is fired, which we need to determine to achieve the desired outcome.

Inelastic Collision

An inelastic collision occurs when two objects collide and stick together, resulting in a loss of kinetic energy but conservation of momentum. In this case, when the clay hits the car, they will move together as one mass, and we can use the conservation of momentum principle to find the required speed of the clay to stop the car.