Impulsive Forces

Overview

Engineering reference data for Impulsive Forces in dynamics.

Key Formulas

Newton's Second Law

$F = ma$

Force = mass × acceleration.

Kinetic Energy

$E_k = \frac{1}{2}mv^2$

Energy of motion.

Momentum

$p = mv$

Mass × velocity.

Work

$W = Fd\cos\theta$

Force × displacement × cos(angle).

Variables

Definition of Impulse and Impulsive Force

Impulse is the product of a force and the time duration over which it acts. It is equal to the change in momentum produced by that force.

$$I = \int F \, dt = \Delta M$$

For a constant force, this simplifies to:

$$I = F \cdot \Delta t = \Delta M$$

A force that acts for a very short duration is called an impulsive force. The effect of such a force is measured by its impulse.

Example: Resulting Velocity After a Constant Force

Problem: A constant force of 1000 N acts on a car with a mass of 1000 kg for 10 seconds. Assuming the car starts from rest, calculate the resulting velocity.

Solution:

1. Calculate the Impulse (Change in Momentum): The impulse $I$ delivered to the car is:

   $$I = F \cdot \Delta t = (1000 \, \text{N}) \cdot (10 \, \text{s}) = 10{,}000 \, \text{N·s}$$

   This impulse equals the change in momentum ($\Delta M$) of the car.

2. Relate Momentum Change to Velocity: Momentum ($M$) is mass times velocity. Since the car starts from rest, its initial momentum is zero. The final momentum is:

   $$\Delta M = m \cdot v$$

   Therefore:

   $$10{,}000 \, \text{kg·m/s} = (1000 \, \text{kg}) \cdot v$$

3. Solve for Final Velocity:

   $$v = \frac{10{,}000 \, \text{kg·m/s}}{1000 \, \text{kg}} = 10 \, \text{m/s}$$

   The final velocity is $10 \, \text{m/s}$ or $36 \, \text{km/h}$.

References

• Original Source