Why does impulse equal the change in momentum

It just doesn't make sense to me! Now, often times when I make this argument to people, they immediately jump to the conclusion that I think the two are the same because they always have the same value, and because mathematically they are the same. Personally, I think that mathematically proving that two things are the same is enough to say that they are the same. But, quite frankly, even ignoring the fact that, mathematically, impulse and change in momentum are the same, I still think that conceptually they are the same, and I think that for the reasons given above.

So here, really, lies my question: Is there even a point to arguing about this? Is this a controversial topic in physics? Surely I am not the only one who thinks that these two concepts ought to be treated as one? So far, no argument that has been presented to me has been enough to convince me that it is practical, or even conceptually enlightening to keep them separate. If anything, I think it is beautiful that they are the same, and that considering them to be separate actually prevents a deeper conceptual understanding of the universe and mathematics as a whole.

Am I crazy for thinking that? This is the historic and common point of view, I believe. But I wouldn't say this means that impulse and change of momentum are the same concepts , because they are introduced in a different way with different name and symbol. So either way, I think it is safe to say that both are different concepts, while having the same value, either approximately if 2nd law is taken as approximate law of physics or exactly if it is taken as a definition of force.

Except that it isn't. Have you taken a Statics course yet? Don't forget, in the equation. Also, there are alternate formulations of mechanics, e. We recognize the left hand side as the time rate of change of momentum and the right hand side as the negative of the spatial rate of change of the potential energy. But, on the Newtonian view, the right hand side is the force on the mass due to the spring, not the left hand side. So, I don't think one can successfully sustain "Force really is the derivative of momentum.

Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Just to restate, momentum is conserved in all three kinds of collisions. Begin typing your search term above and press enter to search.

Press ESC to cancel. Skip to content Home Essay Why is impulse equal to the change in momentum? Ben Davis February 10, Why is impulse equal to the change in momentum? Is it correct to say that impulse equals momentum or impulse equals a change in momentum? How are impulse and momentum related quizlet? Does impulse and momentum have same dimension?

What is the impulse momentum theorem? When would you use impulse-momentum theorem? Is momentum directly proportional to mass? For which system does the law of momentum hold true? Why is momentum not conserved? Is momentum always conserved in a collision? How do you know if momentum is conserved? What is an example of the law of conservation of momentum from everyday life?

Next, we choose a reasonable force function for the impact event, calculate the average value of that function Figure , and set the resulting expression equal to the calculated average force. This enables us to solve for the maximum force.

For simplicity, assume the meteor is traveling vertically downward prior to impact. In that case, its initial velocity is. From Figure ,. This is the average force applied during the collision. Notice that this force vector points in the same direction as the change of velocity vector. Next, we calculate the maximum force. The impulse is related to the force function by. We need to make a reasonable choice for the force as a function of time.

We define. Then we assume the force is a maximum at impact, and rapidly drops to zero. A function that does this is. The graph of this function contains important information. Notice that the area under each plot has been filled in. For the plot of the constant force.

As for the plot of F t , recall from calculus that the area under the plot of a function is numerically equal to the integral of that function, over the specified interval; so here, that is.

Thus, the areas are equal, and both represent the impulse that the meteor applied to Earth during the two-second impact. The average force on Earth sounds like a huge force, and it is. Nevertheless, Earth barely noticed it.

The acceleration Earth obtained was just. That said, the impact created seismic waves that nowadays could be detected by modern monitoring equipment. The collision with the building causes the car to come to a stop in approximately 1 second. The driver, who weighs N, is protected by a combination of a variable-tension seatbelt and an airbag Figure. In effect, the driver collides with the seatbelt and airbag and not with the building. The airbag and seatbelt slow his velocity, such that he comes to a stop in approximately 2.

Impulse seems the right way to tackle this; we can combine Figure and Figure. The negative sign implies that the force slows him down. For perspective, this is about 1. Same calculation, just the different time interval:. Big difference! Significance You see that the value of an airbag is how greatly it reduces the force on the vehicle occupants. For this reason, they have been required on all passenger vehicles in the United States since , and have been commonplace throughout Europe and Asia since the mids.

The change of momentum in a crash is the same, with or without an airbag; the force, however, is vastly different. Recall Figure :. This gives us the following relation, called the impulse-momentum theorem or relation. The impulse-momentum theorem is depicted graphically in Figure. An impulse does not cause momentum; rather, it causes a change in the momentum of an object. Thus, you must subtract the final momentum from the initial momentum, and—since momentum is also a vector quantity—you must take careful account of the signs of the momentum vectors.

The most common questions asked in relation to impulse are to calculate the applied force, or the change of velocity that occurs as a result of applying an impulse. The general approach is the same. Equate these and solve for the desired quantity. Example Moving the Enterprise Figure 9. Assuming this maneuver is completed in 60 s, what average force did the impulse engines apply to the ship? We are asked for a force; we know the initial and final speeds and hence the change in speed , and we know the time interval over which this all happened.

In particular, we know the amount of time that the force acted. This suggests using the impulse-momentum relation. To use that, though, we need the mass of the Enterprise. An internet search gives a best estimate of the mass of the Enterprise in the movie as. Because this problem involves only one direction i. Solving for the magnitude of the force and inserting the given values leads to. This is an unimaginably huge force. It goes almost without saying that such a force would kill everyone on board instantly, as well as destroying every piece of equipment.

How much time must the Enterprise spend accelerating if the humans on board are to experience an average of at most 10 g s of acceleration? Assume the inertial dampeners are offline. Apple released its iPhone 6 Plus in November According to many reports, it was originally supposed to have a screen made from sapphire, but that was changed at the last minute for a hardened glass screen.

Reportedly, this was because the sapphire screen cracked when the phone was dropped.