1. What is the Impulse-Momentum Theorem?

Definition: The impulse-momentum theorem states that the impulse (J) applied to an object equals the change in momentum (Δp) of that object.

Purpose: This principle is fundamental in physics for analyzing collisions, impacts, and motion changes.

2. How Does the Formula Work?

The theorem is expressed as:

Where:

• \( J \) — Impulse (Newton seconds, N·s)
• \( \Delta p \) — Change in momentum (kg·m/s)
• \( m \) — Mass of the object (kilograms, kg)
• \( \Delta v \) — Change in velocity (meters per second, m/s)

Explanation: The impulse equals the product of mass and velocity change, showing how force over time affects motion.

3. Importance of Impulse-Momentum

Details: This principle is crucial for understanding car safety (airbags, crumple zones), sports (catching balls), and rocket propulsion.

4. Using the Calculator

Tips: Enter the object's mass in kg and its velocity change in m/s. Mass must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between impulse and momentum?
A: Momentum is mass times velocity (p = mv), while impulse is the change in momentum caused by a force over time (J = FΔt).

Q2: Why are the units for impulse and momentum the same?
A: Both represent the same physical quantity - 1 N·s = 1 kg·m/s, demonstrating dimensional equivalence.

Q3: How is this related to Newton's Second Law?
A: F = ma can be rewritten as F = Δp/Δt, showing force equals rate of momentum change.

Q4: What if velocity decreases?
A: Use a negative Δv value - this indicates momentum decrease (deceleration).

Q5: How does this apply to real-world collisions?
A: Longer collision times (Δt) reduce impact forces (F) for the same Δp, which is why airbags increase collision duration.