1. What is Impulse?

Impulse is a vector quantity that represents the change in momentum of an object when a force is applied over a time interval. It is equal to the product of the average force and the time duration of the force application.

2. How Does the Calculator Work?

The calculator uses the impulse-momentum theorem:

Where:

• \( \vec{I} \) — Impulse vector (kg m/s)
• \( m \) — Mass of the object (kg)
• \( \vec{v_f} \) — Final velocity vector (m/s)
• \( \vec{v_i} \) — Initial velocity vector (m/s)

Explanation: The calculator computes the vector difference between final and initial velocities, then multiplies by mass to get the impulse vector.

3. Importance of Impulse Calculation

Details: Impulse calculations are crucial in physics and engineering for analyzing collisions, rocket propulsion, sports mechanics, and safety system design (like airbags and crumple zones).

4. Using the Calculator

Tips: Enter mass in kilograms and velocity components in meters per second. All values must be valid (mass > 0). The calculator handles both positive and negative velocity components.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between impulse and momentum?
A: Momentum is mass times velocity (\( \vec{p} = m\vec{v} \)), while impulse is the change in momentum (\( \vec{I} = \Delta\vec{p} \)).

Q2: How is impulse related to force?
A: Impulse equals the average force multiplied by the time interval over which it acts (\( \vec{I} = \vec{F}_{avg} \times \Delta t \)).

Q3: What are typical units for impulse?
A: The SI unit is kilogram meter per second (kg m/s), which is equivalent to the newton-second (N s).

Q4: Can impulse be negative?
A: Yes, impulse components can be negative as they are vectors. The sign indicates direction along each axis.

Q5: How is impulse used in real-world applications?
A: Applications include designing safer vehicles, analyzing sports impacts, understanding rocket propulsion, and studying particle collisions.