インパルス

Impulse is the product of force and the time interval over which the force is applied. It is a vector quantity with the same direction as the applied force, expressed as vector J in newton-seconds. Mathematically, impulse equals the definite integral of the force function over a time interval, represented graphically as the area under a force-time curve.

According to Newton's second law, the total impulse acting on an object over a time interval equals the change in its momentum. The impulse-momentum theorem shows that the product of force and time directly determines how an object's motion changes. This relationship allows us to calculate average force by dividing total impulse by the time interval over which it acts.

Yes. A large force acting over a shorter duration can produce the same impulse as a small force acting over a longer duration, since impulse depends on the product of both quantities. For example, stopping a truck by sudden braking or by gentle braking over a longer period can result in similar total impulse, though the forces differ significantly.

Airbags increase the collision time between a driver and the vehicle interior. Although the total change in momentum remains the same, extending the time interval reduces the average force applied to the driver. Lower force over a longer duration causes less injury than high force over a fraction of a second, which is why airbags have been mandatory in US vehicles since 1991.

Impulse is represented by the area under a force-time curve. When force varies over time, the definite integral of the force function over the time interval gives the total impulse. This graphical method allows visualization of how impulse accumulates and helps compare impulses from different force profiles acting over different durations.

The SI unit of impulse is the newton-second, derived from multiplying force in newtons by time in seconds. Since impulse is the product of force and time interval, this unit directly reflects the definition. The newton-second is equivalent to kilogram-meter per second, linking impulse to momentum change.

In collisions, impulse determines the average force experienced. A meteorite impact lasting two seconds with enormous velocity change produced an average force of approximately 3 trillion newtons on Earth. Similarly, in golf, a club delivers large impulse to a ball in less than a second, causing rapid velocity change. These examples show how impulse quantifies the force-time relationship in dynamic events.