Impulse and Momentum Calculator Graph

J = area under F-t graph, Impulse graph.

\[ J = \int_{t_1}^{t_2} F(t) dt \]

Impulse (J):

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1. What is Impulse?

Impulse (J) is the product of a force (F) and the time interval (Δt) over which it acts. It equals the change in momentum of an object and is represented by the area under a force-time graph.

2. How Does the Calculator Work?

The calculator uses the impulse equation:

\[ J = F \times \Delta t \]

Where:

\( J \) — Impulse (N·s)
\( F \) — Average force (N)
\( \Delta t \) — Time interval (s)

Explanation: For constant force, impulse is simply force multiplied by time. For varying force, it's the integral of force over time (area under F-t curve).

3. Importance of Impulse Calculation

Details: Impulse-momentum theorem is fundamental in physics, explaining how forces affect motion over time. Applications include vehicle safety (airbags), sports, and rocket propulsion.

4. Using the Calculator

Tips: Enter force in newtons (N) and time in seconds (s). For non-constant force, use average force value.

5. Frequently Asked Questions (FAQ)

Q1: How is impulse related to momentum?
A: Impulse equals change in momentum (J = Δp = mΔv). Same impulse can produce different momentum changes depending on mass.

Q2: What are typical impulse values?
A: Varies widely - from tiny impulses in atomic collisions to massive ones in rocket launches (10^6 N·s or more).

Q3: Why use N·s units?
A: N·s is dimensionally equivalent to kg·m/s, the unit of momentum, showing the direct relationship.

Q4: How does this apply to car crashes?
A: Safety features increase collision time (Δt) to reduce peak force (F) for same impulse, protecting passengers.

Q5: Can impulse be negative?
A: Yes, if force direction opposes positive reference direction. Negative impulse reduces momentum.