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Impulse and Momentum Calculator Calculus

Impulse Equation:

\[ J = \int F \, dt \]

N
s

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1. What is Impulse?

Impulse (J) is the integral of force (F) with respect to time (t). It equals the change in momentum of an object when a force is applied. The SI unit of impulse is the newton second (N·s).

2. How Does the Calculator Work?

The calculator uses the impulse equation:

\[ J = \int F \, dt \]

For constant force, this simplifies to: \[ J = F \times \Delta t \]

Where:

Explanation: The impulse delivered to an object equals the force applied multiplied by the time over which it acts.

3. Importance of Impulse Calculation

Details: Impulse is crucial in understanding collisions, rocket propulsion, sports mechanics, and any situation where forces act over time intervals.

4. Using the Calculator

Tips: Enter force in newtons (N) and time interval in seconds (s). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: How is impulse related to momentum?
A: Impulse equals the change in momentum (J = Δp). This is known as the impulse-momentum theorem.

Q2: What's the difference between impulse and force?
A: Force measures instantaneous interaction, while impulse measures the cumulative effect of force over time.

Q3: Why is impulse important in safety engineering?
A: Safety devices like airbags increase impact time, reducing force for a given impulse (momentum change), making collisions less dangerous.

Q4: Can impulse be negative?
A: Yes, if the force direction is opposite to the reference direction, impulse can be negative, indicating momentum reduction.

Q5: How does this relate to variable forces?
A: For variable forces, impulse is calculated by integrating force over time (area under force-time curve).

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