Impulse Calculator Using Vector Subtraction Problem

Impulse Equation:

\[ \vec{I} = m \times (\vec{v_f} - \vec{v_i}) \]

Mass (m):

Initial Velocity X-component (v_ix):

m/s

Initial Velocity Y-component (v_iy):

m/s

Final Velocity X-component (v_fx):

m/s

Final Velocity Y-component (v_fy):

m/s

Impulse (I):

X-component (I_x):

Y-component (I_y):

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1. What is Impulse in Physics?

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:

\[ \vec{I} = m \times (\vec{v_f} - \vec{v_i}) \]

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 impulse.

3. Importance of Impulse Calculation

Details: Impulse calculations are crucial in analyzing collisions, rocket propulsion, sports mechanics, and any scenario where forces act over time to change an object's motion.

4. Using the Calculator

Tips: Enter mass in kilograms and velocity components in meters per second. Positive x is typically rightward, positive y upward in standard coordinate systems.

5. Frequently Asked Questions (FAQ)

Q1: How is impulse related to force?
A: Impulse equals the average force multiplied by the time over which it acts (I = F_avg × Δt).

Q2: What are typical units for impulse?
A: The SI unit is kg·m/s, which is equivalent to N·s (newton-seconds).

Q3: Can impulse be negative?
A: Yes, impulse components can be negative, indicating direction opposite to the positive coordinate axis.

Q4: How does impulse relate to momentum?
A: Impulse equals the change in momentum (Δp) of an object.

Q5: What's the difference between impulse and impact force?
A: Impulse is the product of force and time, while impact force is the instantaneous force during collision. Longer impact times reduce peak force for the same impulse.