Reken kilonewton-second [kN·s] om naar kilogram-meter per second [kg·m/s] • Impulse • Mechanica • Compacte rekenmachine • Online omrekentools voor eenheden (2024)

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The faster any object, for example, a car or football, or a particle, is moving, the harder it is to stop. This hardness is a reflection of linear momentum, a physical vector quantity that is defined as the product of object’s mass and velocity.

If a body at rest begins to move, there must be some type of force that changes its speed. Without the action of an external force, objects do not change their speed. To change an object’s speed, one must exert a net force on it that acts for some period of time. The net force is the vector sum of all forces acting on an object and Newton’s second law of motion states that this force accelerates the object, that is, it changes its speed. The product of the net force F_net and the period of time it is applied (t₂ – t₁) is called the impulse. Impulse is also defined as a change in momentum (p₂ –p₁ = Δp):

In stricter terms, the impulse I is the definite integral of the net force F(t) acting on an object over the time interval, for which it acts (t₂ – t₁):

Impulse is a vector quantity because force is a vector quantity. However, if only the average magnitude of F(t) during the time interval of its acting on an object is known, then we can determine the magnitude of the impulse in a simpler way:

Unlike inertia, which is the tendency of an object at rest to remain at rest and of an object in motion to remain in motion, momentum always involves a body in motion. If there is no motion, there will be no momentum. What both momentum and inertia have in common is mass, which is a measure of inertia indicating the resistance of an object to any change in its motion. This includes the absence of motion. Impulse, as a change in momentum, is also always associated with motion.

In SI, the unit of impulse is newton-seconds (N·s), which is dimensionally equivalent to the unit of momentum, kilogram-meter per second (kg·m/s). In the British Gravitational System, it is measured in slug-feet per second (slug·ft/s) and in English Engineering Units it is measured in pound-force-second (lbf·s).

Total and Specific Impulse

If a function for F(t) is represented in the form of a plot of force versus time, we can evaluate the impulse by finding the area under the curve. In rocketry, the term “total impulse” is used instead of the term “impulse”. For example, we want to calculate the total impulse for a model rocket motor. Thrust curves showing the motor thrust versus time in the form of a graph or a table are usually available in motor specifications, therefore it is possible to calculate not only the total magnitude of the impulse, but to plot a graph of a rocket speed and acceleration. Our calculator of a model rocket’s total impulse, maximum altitude, acceleration, and velocity can calculate the total impulse of a model rocket with a selected motor.

Suppose we want to launch a model rocket with the Estes B4-4 motor. The picture shows the thrust force F_t curve of this motor in newtons (N) as a function of time in seconds (s). The blue area under the curve represents the total impulse during the motor’s burning time during lift-off t_burn = 1.03 s). It is determined as the integral

This area is equal to the green area bounded the average thrust F_avg = 4.17 N. Therefore, the total impulse of this motor in N·s can be determined using the simple formula mentioned above:

The total impulse can be used to define a specific impulse, which is used to analyze jet and rocket engines and measure their efficiency. The specific impulse is normalized by unit of propellant expended and is commonly measured in seconds. The higher the value of the specific impulse, the more efficient is the engine. For example, the specific impulse of turbofan CFM56 engines used in Boeing 737-800 is 5740 s, the specific impulse of NPO Energomash RD-170 engine is 309 s at sea level, and the specific impulse of the F-1 rocket engine used in the Saturn V rocket at sea level is only 260 s. That is, compared to Boeing’s engines, Saturn V engines have very low efficiency, which, however, did not prevent these rockets from reaching the Moon. Specific impulse is the time in which a rocket engine consumes the amount of propellant (by weight) equal to the engine’s thrust.

Helmets, Eggs, and Impulse

It is the impulse that drives the development and selection of the proper methods and tools to ensure survival when skiing, snowboarding, and even in a car or plane crash. Here is a good example of the importance of impulse in the design of safe means of transport and safety devices like helmets and airbags.

Two eggs of the same mass were dropped from the same height of 70 cm on two different surfaces. One was dropped into an empty thick-walled glass bowl, another — into the same bowl with 1 inch of dry rice. Each egg has the same velocity at the time of the collision (we will determine it from the video footage). That means each egg has the same momentum (mass times velocity). The question is if the momentum is the same for both eggs, why are the results are so different?

The glass bottom applies a big stopping force over a very short period of the collision over a small part of the surface of the egg. When analyzing the video footage shot at a frame rate of 120 fps, we estimated its duration as half the frame period, that is, 4 milliseconds. The layer of dry rice applies a smaller stopping force over a much longer time period (42 ms in our experiment) and over a larger part of the surface of the egg.

Let us calculate the impulse and force acting on the egg in both cases. Mass of the is 61 g. We can measure the velocity at the moment of impact since we have video footage with a ruler and a known frame rate of 120 fps. The definition of velocity is shown in the picture. We can also use our Free Fall Calculator to determine the velocity of an egg dropped from 0.7 m. At the moment of impact, the speed is 3.72 m/s. From the formula above, the impulse in N·s is

The duration of the impact with a hard glass surface is 4 ms and with a layer of dry rice 42 ms. Therefore, the force of impact with the glass bottom is

As we can see, a rather large force of 45.4 N is applied over a small area of the shell, and as a result of the action of rather large pressure, it easily breaks.

Note that in both cases, the impulse of the force acting on the flying egg remains unchanged and equals 0.23 N·s. What changes is the time of action of the force and the force itself, and their product (the impulse) remains constant.

The force of impact with a dry rice layer is

As we can see, in the second case, the force is almost 10 times less and it acts on the entire lower surface of the egg. The eggshell can easily withstand this pressure and remains intact.

Now we will try to estimate the pressure acting on the shell at the moment of impact. We will see how different the pressure is in these two cases.

The impact area of the eggshell hitting the glass is approximately 0.5 sq. cm or even less. Thus, the pressure upon impact on glass is 45.4 / 0.5 = 91 N/cm², and upon impact against dry rice layer is 5.4 / 35 = 0.3 N/cm². That’s 300 times less! If you don’t wear a helmet when cycling or sledding, hopefully, this calculation will convince you not to neglect safety rules!

The same principle is used in car designs where crumple zones are provided that increase the duration of collisions. Airbags serve the same purpose. They increase the time interval during which the passenger is brought to rest, thereby decreasing the force on the passenger. They also reduce pressure during a collision because the force of the dashboard or the steering column is distributed by the airbag over a larger area. A helmet does the same thing. It reduces acceleration during the collision and distributes the force over a larger surface, thereby reducing the pressure on the passenger body.

You will find more information about impulse in our Impulse and Momentum Calculator.

Dit artikel is geschreven door Anatoly Zolotkov

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Mechanica

Mechanica is een onderdeel van de natuurkunde waarin wordt bestudeerd hoe fysieke lichamen reageren als ze worden onderworpen aan krachten of verschuivingen en wat de effecten hiervan zijn op de lichamen en hun omgeving.

Impulse

Impulse in classical mechanics is a vector physical quantity on a short time interval equal to the product of the force acting on the object and the time interval of its action. It is equivalent to the change in momentum. A stricter definition defines the impulse as the definite integral of force acting on a body over the time interval, for which it acts. It is a vector quantity because force is a vector quantity.

In SI, impulse is measured in newton-seconds (N·s), which is dimensionally equivalent to the unit of momentum, kilogram-meter per second (kg·m/s). In English Engineering Units it is measured in pound-force-second (lbf·s) and in the British Gravitational System it is measured in slug-feet per second (slug·ft/s).

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