# Ok, I got an impulse problem here

• alberto
In summary, the conversation discusses the concept of impulse and how it relates to closing an open door using a bouncy ball or sticky mud. The experts explain that while the speed may be the same for both objects, the direction and sign of the momentum is important. The ball exerts an impulse in the opposite direction, while the mud's momentum is in the same direction as the door's closing. This means that the mud will result in the door closing with a greater speed. The experts also clarify that the time factor is not significant in this scenario.

#### alberto

Ok, here the problem my teacher gave:

The goal is to close an open door in the best possible manner. You have two objects, a bouncy ball and a big chunk of sticky mud. You decide to throw one of these objects at the door to close it. The bouncy ball will bounce off the door with the same speed as it struck the door. The mud will stick to the door. Which of these two scenarios will result in the door closing with a larger speed? Use the concept of impulse in your answer.

So at first I was like "the ball", since with Impulse being the change in momentum = force x time, with the ball hitting the door and bouncing off really fast, time would have to go down in the equation, thus, force would have to go UP to compensate. But then I rationalized that if the ball is coming back off the door in the opposite direction at the same speed, it’s momentum was pretty much conserved and therefore not much was transferred to the door to shut. The mud on the other hand isn’t bouncing away, thus all of its momentum will strike the door and continue to push on the door in the same direction that the door needs to go in order to shut.

so there is definitely something wrong with one of these lines of thought...help! and thanks!

But then I rationalized that if the ball is coming back off the door in the opposite direction at the same speed, it’s momentum was pretty much conserved and therefore not much was transferred to the door to shut.
Now, remember that momentum is a VECTOR quantity. While the speed is the same, the velocity and therefore momentum of the ball is entirely different. Not only did the ball exert an impulse on the door to stop moving, but it also exerted an impulse to give the ball an momentum in the opposite direction.

So in terms of my 1st answer, the ball would then be applying greater force than the mud since its time in contact with the door would be less than the mud, right? (thanks for the quick reply!)

No, that's not what he's saying. When he alludes to the vector character of momentum, he is getting at the fact that the sign is important. When the mud hits the door, its momentum changes from p to approximately zero (I say approximately because the mud moves with the door after impact). On the other hand, when the ball hits the door its momentum changes from p to -p.

Can you take it from there?

Also, the time thing is a red herring. While the force exerted by the ball would be greater, the time taken to exert the force would be smaller. These cancel each other out.

Hitting someone with kilo of steel would hurt more than a kilo of bean bags, but it would knock them back by the same amount.

whoa whoa whoa...
I understand regarding the kilo of steel vs. kilo of bean bags, and I get how the time of the impulse is less so the effect of the force is not experianced to the same extent. So is the answer that because the momentum of the mud is in the same direction (with an additive effect) as the way the door is going to close, that this would result in the door closing with greater speed? My line of thinking is that the door's mass + the mass of the mud (since it sticks) means that the door would have to go from an initial velocity of 0 (while it's open) to some final velocity when the mud hits (when it's shutting)that would be greater than the ball hitting since the ball doesn't stick...I think I'm confusing myself (again)...

thanks again for the replies!

Ok... let's try this again.

conservation of momentum states that mu = mv + Mw

m = mass of ball, u = initial velocity of ball, v = final velocity of ball, M = mass of door, w = final velocity of door. All velocities are positive in the same direction.

now, with mud...

mu = (m + M) * w
or, Mw = mu - mw

Since the ball is now the same velocity as the door.

with the other ball...

mu = Mw + m * (-u)
since the ball is travel at the same velocity in the opposite direction to what it was before.

Rearranging...
Mw = 2 * mu

Obviously, Mw(momentum of door) is now greater. Do you see?

That explanation was perfect! I get it! thank you soooooo much! When I sat down and did the algebra, it made sense. Thanks again, good karma to you!

## 1. What is an impulse problem?

An impulse problem is a sudden, short-lived change in the state or behavior of a system. It can be caused by an external force or stimulus that acts on the system, resulting in a rapid change in its motion or behavior.

## 2. How do you identify an impulse problem?

An impulse problem can be identified by observing a sudden and significant change in the system's state or behavior. This change is usually short-lived and occurs in response to an external force or stimulus.

## 3. What are some common causes of impulse problems?

Impulse problems can be caused by a variety of factors, including external forces such as collisions, sudden changes in pressure or temperature, and abrupt changes in the system's environment.

## 4. What are the potential consequences of an impulse problem?

The consequences of an impulse problem can vary depending on the system and the magnitude of the impulse. In some cases, it may cause damage to the system or its surroundings, while in other cases it may lead to changes in the system's behavior or motion.

## 5. How can impulse problems be addressed or solved?

There are a few approaches to addressing and solving impulse problems, depending on the specific situation. Some solutions may involve adjusting the system's design or environment to minimize the impact of impulses, while others may involve implementing control measures to reduce the likelihood of impulses occurring in the first place.

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