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Impulse Calculator

Calculate impulse ($J$), force ($F$), change in time ($\Delta t$), or change in momentum ($\Delta p$).

Impulse from Force & Time ($J = F \Delta t$)

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Impulse from Change in Momentum ($J = \Delta p$)

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What is Impulse?

In physics, impulse ($J$) is a measure of the change in momentum of an object. It is a vector quantity, meaning it has both magnitude and direction. Impulse is produced when a force ($F$) acts on an object for a certain period of time ($\Delta t$).

A large impulse can be delivered in two main ways: by applying a very large force for a short time (like a baseball bat hitting a ball) or by applying a smaller force for a longer time (like the retro-thrusters on a spaceship).

The Impulse Formulas

Impulse is defined by two primary formulas which are linked by the Impulse-Momentum Theorem.

1. Impulse from Force and Time

The first formula defines impulse as the product of the average force applied and the time interval over which it is applied.

  • $J$: Impulse, measured in Newton-seconds (N·s).
  • $F$: Average force applied, measured in Newtons (N).
  • $\Delta t$: The time interval the force is applied, measured in seconds (s).

2. Impulse as Change in Momentum

The Impulse-Momentum Theorem states that the impulse applied to an object is exactly equal to the change in that object's momentum ($\Delta p$).

  • $J$: Impulse, measured in kilogram-meters per second (kg·m/s).
  • $\Delta p$: Change in momentum.
  • $m$: Mass of the object, measured in kilograms (kg).
  • $v_f$: Final velocity of the object, in meters per second (m/s).
  • $v_i$: Initial velocity of the object, in meters per second (m/s).

Note: The units N·s and kg·m/s are equivalent and interchangeable ($1 \text{ N} \cdot \text{s} = 1 \text{ (kg} \cdot \text{m/s}^2 \text{)} \cdot \text{s} = 1 \text{ kg} \cdot \text{m/s}$).

Real-World Examples of Impulse

The impulse-momentum theorem ($F \Delta t = \Delta p$) is crucial for understanding and engineering safety and performance in many fields.

  • Car Safety (Airbags & Crumple Zones): When a car crashes, its change in momentum ($\Delta p$) is fixed (it goes from a high velocity to zero). The goal of safety features is to reduce the force ($F$) on the passengers. To do this, airbags and crumple zones *increase the time* ($\Delta t$) of the impact. By spreading the collision over a longer time, they dramatically reduce the peak force, making the crash survivable.
  • Sports (Hitting a Ball): In sports like baseball or golf, the goal is the opposite. The player wants to cause the largest possible change in momentum ($\Delta p$) to the ball. They do this by applying the maximum possible force ($F$) and "following through" with their swing to keep the bat or club in contact with the ball for the longest possible time ($\Delta t$), thereby maximizing the impulse.
  • Catching an Egg: If you try to catch a raw egg by holding your hands stiff, the time of impact ($\Delta t$) is very short, resulting in a large force ($F$) that breaks the egg. If you "give" with the catch, moving your hands backward, you increase the time ($\Delta t$) it takes to stop the egg. This reduces the force ($F$) and allows you to catch it without it breaking.