What impulse does the force shown in FIGURE EX11.3 exert on a 250 g particle?

검증된 단계별 안내

Step 1: Recall the formula for impulse, which is the integral of force over time: \( J = \int F_x \, dt \). Impulse can also be calculated as the area under the force-time graph.

Step 2: Analyze the graph provided. The force \( F_x \) increases linearly from 0 N to 15 N over a time interval of 12 ms. The graph forms a triangle with a base of 12 ms and a height of 15 N.

Step 3: Calculate the area of the triangle to determine the impulse. The area of a triangle is given by \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \). Here, the base is 12 ms (convert to seconds: \( 12 \times 10^{-3} \) s), and the height is 15 N.

Step 4: Substitute the values into the area formula: \( \text{Area} = \frac{1}{2} \times (12 \times 10^{-3}) \times 15 \). This area represents the impulse exerted on the particle.

Step 5: The impulse calculated from the area is in units of \( \text{N} \cdot \text{s} \). This impulse is the total change in momentum of the 250 g particle due to the force applied.

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주요 개념

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

Impulse

Impulse is defined as the change in momentum of an object when a force is applied over a period of time. It is mathematically represented as the product of the average force and the time duration during which the force acts. In the context of the given question, the impulse can be calculated by finding the area under the force vs. time graph.

Force vs. Time Graph

A force vs. time graph visually represents how force changes over time. The area under the curve of this graph corresponds to the impulse experienced by an object. In the provided graph, the shape consists of a triangle and a rectangle, which can be used to calculate the total impulse exerted on the 250 g particle.

Mass and Weight

Mass is a measure of the amount of matter in an object, typically measured in kilograms (kg), while weight is the force exerted by gravity on that mass. In this question, the mass of the particle is given as 250 g, which is equivalent to 0.25 kg. Understanding the relationship between mass, weight, and impulse is crucial for analyzing the motion of the particle after the force is applied.