In FIGURE EX11.5, what value of Fmax gives an impulse of 6.0 N s?

검증된 단계별 안내

Step 1: Recall the formula for impulse, which is given by \( J = F \cdot \Delta t \), where \( J \) is the impulse, \( F \) is the force, and \( \Delta t \) is the time interval during which the force acts.

Step 2: From the graph, observe that the force \( F_{\text{max}} \) acts over a time interval \( \Delta t \) from \( t = 4 \, \text{s} \) to \( t = 10 \, \text{s} \). Calculate \( \Delta t \) as \( \Delta t = 10 - 4 = 6 \, \text{s} \).

Step 3: Substitute the given impulse \( J = 6.0 \, \text{N} \cdot \text{s} \) and the time interval \( \Delta t = 6 \, \text{s} \) into the formula \( J = F \cdot \Delta t \). Rearrange the formula to solve for \( F \): \( F = \frac{J}{\Delta t} \).

Step 4: Perform the substitution: \( F = \frac{6.0}{6} \). This will give the value of \( F_{\text{max}} \).

Step 5: Interpret the result: The calculated \( F_{\text{max}} \) represents the maximum constant force that acts over the time interval \( \Delta t \) to produce the given impulse.

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.

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 force and the time duration for which the force acts. In this context, the impulse is given as 6.0 N·s, indicating the total effect of the force applied over the specified time interval.

Force-Time Graph

A force-time graph visually represents how force varies with time. The area under the curve of this graph corresponds to the impulse experienced by an object. In the provided graph, the force is constant at Fmax for a certain duration, allowing for straightforward calculation of impulse by multiplying Fmax by the time interval during which the force is applied.

Calculating Fmax

To find the maximum force (Fmax) that results in a specific impulse, one can use the relationship between impulse, force, and time. Given the impulse (6.0 N·s) and the duration of the force application (which can be inferred from the graph), Fmax can be calculated using the formula: Impulse = Fmax × time. This allows for determining the required force to achieve the desired impulse.