Impulse and Momentum Calculator

Mass (m):

Initial Velocity (v₁):

Final Velocity (v₂):

1. What is an Impulse and Momentum Calculator?

Definition: This calculator determines the impulse required to change the momentum of an object, based on its mass and the change in velocity.

Purpose: It is used in physics to analyze scenarios involving collisions, stopping objects, or changing their motion, such as stopping a ball or calculating the force in a collision.

2. How Does the Calculator Work?

The calculator uses the following formula:

Impulse: $J = m \times (v_{2} - v_{1})$ Where:

$J$ : Impulse (N·s, kN·s, kg·m/s, lb·ft/s, lbf·s)
$m$ : Mass (mg, g, kg, oz, lb)
$v_{2}$ : Final velocity (m/s, km/h, ft/s, mph, kn, ft/min)
$v_{1}$ : Initial velocity (m/s, km/h, ft/s, mph, kn, ft/min)

Unit Conversions:

Mass Units (m): mg, g, kg, oz, lb
Velocity Units (v₁, v₂): m/s, km/h, ft/s, mph, kn, ft/min
Impulse Units (J): N·s, kN·s, kg·m/s, lb·ft/s, lbf·s

Steps:

Enter the mass (m), selecting the unit (mg, g, kg, oz, lb)
Enter the initial velocity (v₁), selecting the unit (m/s, km/h, ft/s, mph, kn, ft/min)
Enter the final velocity (v₂), selecting the unit (m/s, km/h, ft/s, mph, kn, ft/min)
Convert mass to kg and velocities to m/s for calculation
Calculate the impulse using the formula
Select the desired unit for the impulse and view the converted value

3. Importance of Impulse and Momentum Calculation

Calculating impulse and momentum is crucial for:

Physics Education: Understanding the relationship between force, time, and change in momentum.
Safety Analysis: Designing safety systems like airbags, which reduce the impulse during a collision.
Sports and Engineering: Analyzing the impact in sports (e.g., hitting a ball) or engineering applications (e.g., crash testing).

4. Using the Calculator

Examples:

Example 1: For a mass $m = 160 g$ , initial velocity $v_{1} = 2.5 m/s$ , final velocity $v_{2} = 0 m/s$ :
- Mass in kg = $160 \times 0.001 = 0.160 kg$
- Impulse = $0.160 \times (0 - 2.5) = - 0.400 N·s$
- In lb·ft/s = $- 0.400 \times 0.224809 = - 0.090 lb·ft/s$
Example 2: For a mass $m = 1 lb$ , initial velocity $v_{1} = 20 mph$ , final velocity $v_{2} = 10 mph$ :
- Mass in kg = $1 \times 0.453592 = 0.453592 kg$
- Initial velocity in m/s = $20 \times 0.44704 = 8.941 m/s$
- Final velocity in m/s = $10 \times 0.44704 = 4.470 m/s$
- Impulse = $0.453592 \times (4.470 - 8.941) = - 2.027 N·s$
- In kN·s = $- 2.027 \times 0.001 = - 0.002 kN·s$

5. Frequently Asked Questions (FAQ)

Q: What is impulse?
A: Impulse ( $J$ ) is the change in momentum of an object, calculated as $J = m \times (v_{2} - v_{1})$ , and is equal to the force applied over a period of time ( $J = F \times Δ t$ ).

Q: What is momentum?
A: Momentum ( $p$ ) is the product of an object's mass and velocity, calculated as $p = m \times v$ , and is a measure of how difficult it is to stop a moving object.

Q: Why is impulse negative in some cases?
A: A negative impulse indicates that the force is applied in the opposite direction of the object's initial motion, which is necessary to slow down or stop the object.