Impulse

Summary

In this AP Physics essentials video, Mr. Andersen explores the concept of impulse, defined as the product of force and the time over which it acts. He uses the example of a baseball to illustrate how impulse changes momentum. The video compares the impact of two spheres dropped on a table, demonstrating that impulse is equivalent to the change in momentum. Mr. Andersen then relates impulse to Newton's second law, showing how to calculate it and the force experienced during a car crash. The video concludes with a practical problem-solving exercise, emphasizing the importance of time in reducing force during collisions, which is crucial for safety in modern cars.

Takeaways

• 😀 Impulse is defined as the product of the force applied and the time over which it is applied.
• 🏐 In the context of a baseball hit, the impulse from the bat causes a dramatic change in the ball's momentum.
• 🔄 The change in momentum and the impulse are equivalent, always yielding the same value.
• 🎾 When two spheres with the same mass and velocity fall onto a table, they experience the same change in momentum and impulse, despite different interaction times with the table.
• 🚗 Cars have been designed to be safer by increasing the time it takes for the vehicle to come to a stop during a crash, thereby reducing the force experienced by the occupants.
• 📐 Newton's second law, F = ma, can be used to derive the relationship between impulse and momentum change by considering acceleration as Δv/Δt.
• ⏱️ The time of interaction is crucial in determining the force experienced; a longer interaction time results in a smaller force.
• 🧮 To calculate impulse, use the formula Impulse = m × Δv, where m is mass and Δv is the change in velocity.
• 🔢 To find the force, divide the impulse by the time of interaction, as shown in the example with the car crash scenario.
• 💡 The concept of impulse is not only fundamental in physics but also critical in safety engineering, such as in car design to protect passengers during collisions.

Q & A

What is impulse in the context of physics?

Impulse in physics is the product of the force applied and the time over which it is applied, which can be mathematically represented as Impulse = Force × Time.

How is impulse related to the change in momentum of an object?

The impulse experienced by an object is equivalent to the change in its momentum. This means that the impulse and the change in momentum will always give the same value.

What is the significance of the impulse-momentum relationship in physics?

The relationship between impulse and change in momentum is significant because it allows for the calculation of forces and changes in motion in various physical scenarios, such as collisions and impacts.

How does the time over which a force is applied affect the force experienced?

The longer the time over which a force is applied, the less force is experienced. This is because the impulse (which is the product of force and time) remains constant, so if the time increases, the force must decrease.

Why are modern cars designed to crumple in a crash?

Modern cars are designed to crumple in a crash to increase the time over which the forces are applied during an impact, thereby reducing the force experienced by the occupants and improving safety.

What is the difference between the impulse experienced by a '57 Chevy and a Honda Civic during a crash?

The '57 Chevy would experience a much shorter time of impact, resulting in a higher force during the crash. In contrast, the Honda Civic is designed to extend the time of the impact, reducing the force experienced by the occupants.

How can the principles of impulse and momentum be used to analyze a car crash?

The principles of impulse and momentum can be used to analyze a car crash by calculating the change in momentum of the car and the occupants, and then using this information to determine the forces involved during the crash.

What is the formula for calculating the impulse experienced by an object?

The impulse experienced by an object can be calculated using the formula Impulse = Mass × Change in Velocity.

How can you determine the force applied to an object if you know the impulse and the time?

If you know the impulse and the time over which it was applied, you can determine the force by dividing the impulse by the time: Force = Impulse / Time.

What is the practical application of understanding impulse and momentum in car safety?

Understanding impulse and momentum is crucial in car safety as it helps in designing vehicles that can distribute the forces of a crash over a longer period, reducing the impact on passengers and potentially saving lives.

Outlines

00:00

🏏 Impulse and Momentum in Physics

Mr. Andersen introduces the concept of impulse in AP Physics essentials video 50. Impulse is defined as the product of force and the time over which it acts. He uses a baseball scenario to explain how impulse changes the momentum of an object, emphasizing that the change in momentum is equivalent to the impulse applied. The video then compares two spheres dropped on a table, illustrating that while both experience the same change in momentum, the time over which they interact with the surface differs, affecting the force applied. The concept is further explained through the safety features of modern cars, which are designed to extend the time of impact to reduce the force experienced by passengers during a crash.

05:04

🚗 Calculating Impulse and Force in a Car Crash

In the second paragraph, Mr. Andersen demonstrates how to calculate the impulse and force on a car and its occupant during a crash. He uses a video of a 2013 Honda Civic Hybrid crashing into a wall at 35 miles per hour to show the difference in time it takes for the car and the crash test dummy to come to rest. The video provides the mass of the car and the person, the initial velocity, and the change in velocity. Mr. Andersen guides viewers through the process of calculating the impulse using the formula mass times change in velocity. He then shows how to determine the force by dividing the impulse by the time of impact. The video concludes with a problem for viewers to practice calculating the impulse and force experienced by the car and the person, emphasizing the importance of understanding these concepts in physics.

Keywords

💡Impulse

Impulse is defined as the product of the force applied to an object and the time over which that force is applied. In the context of the video, impulse is central to understanding how a baseball's momentum changes when hit by a bat, or how a car and its occupants experience forces during a crash. The video script uses the example of a baseball to illustrate how the impulse from the bat changes the ball's momentum, and also discusses how different durations of impact can lead to different forces experienced, as seen in the comparison between the '57 Chevy and the Honda Civic during a crash.

💡Momentum

Momentum is the product of an object's mass and its velocity. The video script explains that when an object's momentum changes, it is due to an impulse being applied to it. The change in momentum and the impulse are equivalent, which is a key concept in physics. The script uses the example of two spheres dropped on a table to demonstrate that even though they have the same mass and velocity, the change in momentum is the same for both, hence the impulse is the same, despite the different times over which they come to rest.

💡Force

Force is the push or pull acting on an object, and it is a vector quantity, meaning it has both magnitude and direction. In the video, force is discussed in relation to impulse, where the force applied over time results in an impulse. The script also explains that by increasing the time over which a force is applied, the force experienced can be reduced, which is a principle utilized in car safety design to reduce the impact on passengers during a crash.

💡Velocity

Velocity is a measure of the speed of an object in a specific direction. The video script uses velocity to describe the state of the baseball moving towards the batter and how it changes direction after being hit. It also discusses the change in velocity of a car and its occupants as they go from a speed of 35 miles per hour to a stop, which is a crucial factor in calculating the impulse and force experienced during a crash.

💡Acceleration

Acceleration is the rate of change of velocity with respect to time. In the video, acceleration is broken down as the change in velocity over time, which is used to derive the relationship between force, mass, and impulse. The script uses Newton's second law to connect acceleration with force and momentum change, showing how these concepts are interrelated in physics.

💡Mass

Mass is a measure of the amount of matter in an object and is an intrinsic property that determines the object's resistance to acceleration. The video script provides the mass of the car and the person as essential data for calculating the impulse and force experienced during a crash. Understanding mass is fundamental to applying the principles of physics to real-world scenarios, such as the safety of vehicles and their occupants.

💡Time

Time is a measure in seconds of the duration over which a force is applied. In the context of the video, the time of the impulse is crucial in determining the force experienced by the car and its occupants during a crash. The script illustrates how a longer time of impact can reduce the force experienced, which is a critical factor in modern car safety design.

💡Significant Digits

Significant digits are the digits in a number that carry meaning contributing to its precision. The video script mentions the importance of reducing the number of significant digits in calculated results to match the precision of the given data, such as the time of the car's impact, which has only two significant digits. This concept is important in scientific calculations to ensure that the results are as accurate as the input data allows.

💡Crash Test Dummy

A crash test dummy is an anthropomorphic test device used in the automotive industry to simulate the dynamics of a human body during a crash. In the video, the script uses the crash test dummy to illustrate how the force experienced by a person in a car crash can be calculated and analyzed. The concept helps to understand the real-world application of physics in ensuring the safety of vehicle occupants.

💡Newton's Second Law

Newton's second law of motion states that the force acting on an object is equal to the mass of that object multiplied by its acceleration. The video script uses this law as a foundational principle to explain the relationship between force, mass, and acceleration. It shows how this law can be used to derive the equations for momentum change and impulse, which are essential for understanding the physics of collisions and impacts.

Highlights

Impulse is the product of force applied over time.

Impulse and change in momentum are equivalent; they yield the same value.

When two spheres of the same mass and velocity are dropped, both experience the same change in momentum and impulse.

The difference between two falling spheres lies in the time over which they interact with the table, affecting the force applied.

A larger force over a shorter time versus a smaller force over a longer time can result in the same momentum change.

In car safety, modern cars like the Honda Civic are designed to slow down over a longer period of time during a crash, reducing the force experienced.

Newton's second law (force = mass × acceleration) underpins the relationship between force, time, and impulse.

Momentum change can be expressed as mass × change in velocity, while impulse is force × time.

In a crash scenario, increasing the time over which the momentum changes reduces the force on the car and passengers.

Impulse can be calculated using mass and change in velocity, and force can be derived by dividing impulse by time.

In a 2013 Honda Civic crash, the impulse on the car is calculated to be 20,200 newtons-seconds.

By dividing the impulse by the crash time (0.072 seconds), the force on the car is found to be 280,000 newtons.

For the passenger in the car, the impulse is calculated as 1,220 newtons-seconds.

The force on the passenger, derived from the impulse and the time (0.112 seconds), is approximately 11,000 newtons.

Modern cars increase crash time, reducing the force on passengers and making crashes survivable.

Transcripts

Hi. It's Mr. Andersen and this AP Physics essentials video 50. It is on impulse which

is simply the product of the force being applied times the time over which that force is being

applied. And so let me give you a scenario. Imagine we have a baseball here that is moving

from the left towards the right. And so it has momentum towards the batter. And let's

say he hits it. Well what is going to happen to the momentum? It is going to change dramatically.

It is going to go in the opposite direction. What is causing that however is the impulse.

The bat is applying a force over a given period of time. And what is interesting is that the

change in the momentum and the impulse are equivalent. What does that mean? They are

always going to give you the same value. And that makes them really valuable when we are

looking at physics. And so let's look at two spheres that are being dropped on a table.

Let's imagine that they both fall with the same velocity and they both have the same

mass. So watch what happens to the first one and then the second one. And so a good question

might be which has experienced the most dramatic change in momentum? That is kind of a trick

question. Since they both have the same mass and the same velocity and at the end they

are at rest, they have experienced the same change in momentum. Therefore their impulse

is the same. And so what is different in these two spheres is they fall to the table? Well

it is the time over which they interact with the table itself. The one on the right is

really slowing down over a longer period of time. And that means it is applying less force

to that table. And so momentum will change over time. And so if we have these two spheres,

the momentum is going to be the same between each of those. The impulse is also going to

be the same. What is they impulse? It is simply multiplying the force of an object times the

time of that object. And these are equivalent. The change in momentum and the impulse are

exactly the same thing. And so what is different in these two spheres. Well in this sphere

right here what we are getting is a really large force over a short period of time. In

this one we are getting a really short or small force over a long period of time. And

that fact is so important that it could literally save your life. Cars have gotten safer and

safer over time. And so this is a safety video. If we were to crash a '57 Chevy, an old car

into a wall at 35 miles per hour, the person inside would really be hurt because it is

going to come to a stop almost instantaneously. But watch what happens when this Honda Civic

is driven into a wall at 35 miles per hour. Again it is slowed down, but watch how long

it takes for that car to come to rest. And so it is like that squishy ball. It is taking

a longer period of time for it to change its momentum. And so we are decreasing the force

experienced by both the car and the person inside the car. And so to figure out how these

two are related it is really simple and it begins like everything in physics with Newton's

second law, which is force equal to mass times acceleration. But let's break down acceleration

which is simply going to be the change in velocity over time. Now I am going to take

both sides of this equation and I am going to multiply them times time. And so if I do

that, what do I get? The two subjects of this video. Momentum change, which is mass times

the change in velocity. That is on the right. What is on the left? That is going to be the

impulse. And these are equivalent. So we can use it to solve really difficult problems.

Like could you calculate the impulse and the force on both the car as it crashes into the

wall and then the crash test dummy on the inside of the car? Well you will be able to

and we will work through a few problems likes that. And so if you want to figure out what

we need to solve a problem like that it is all given in the equations up here. Mass times

change in velocity, force times time. But we are just watching a video here. So you

do not see any force in the video. And so we are going to have to solve for that in

a little bit of an indirect kind of a way. And so what would be the first things that

we can figure out? Well we have to figure out the mass. And so I could just give you

the mass. The mass of this car, which is a 2013 Honda Civic Hybrid is 1301 kilograms.

And the mass of the person inside the car is around 78 kilograms. What else could I

tell you? Well we know this car is going at 35 miles per hour and at the end it is going

to be going 0. And so we could see a change in velocity of 15.6 meters per second. What

else do we have to figure out? Well it would important for us to figure out time. This

information right here is enough for us to figure the momentum change and the impulse,

but if we want to get at the force being applied to the car and the crash test dummy we also

have to know the time. And so let's watch the video and let me show you how you could

figure this out. So we have the car crashing into the wall. I am going to grab the video

right here. And you can see here that right at this point, at time 0 it is impacting the

car. And we have reset our time to 0. And so what I want you to do is let's watch a

section of the car. Let's watch this section of the car right here. And let's see how long

it takes for that car to come to rest. And so again we will go back to 0. So it is now

at 0. So we are at 0 here and so just watch the car and figure out how long it takes for

that car to completely come to rest. Let me keep moving. So right about there. So right

about there the car has stopped moving and so we could say that that change in time is

0.072 seconds. I am getting that right here. But if I keep playing the video you will see

that that person continues to move. They are still moving forward. And they do not come

to a stop until around here. And so we could say their time of impulse is going to be 0.112

seconds. And so let me give you a simple problem. What I want you to figure out is calculate

the impulse and the force being applied to both the car and the man sitting within the

car. And what I would encourage you to do is pause the video right here. You have everything

you need right up here. I would grab a piece of paper and try to work this out. Again you

are going to have four values when you are done. Impulse of the car, force on the car,

impulse on the man and force on the man. And so pause the video. Try to work that out.

But I am going to show you how to do it right now. And so what you would do, if we are trying

to figure out the impulse on the car, all you need is the mass of the car and then that

change in velocity. And so impulse is equal to the mass times the change in velocity.

So I am simply putting in the mass right here, 1301 kilograms, the change in velocity, 15.6

meters per second. And so my impulse is going to be this, newtons per second. Now how did

I get that? Well since it is a force times a time it is going to be newtons times seconds.

You can see here that this number has way too many significant digits. And so I could

reduce that so that it has three significant digits and that is the answer of the impulse

on that car. Now how do we figure out the force being applied? Well since I showed you

the time, 0.072 seconds, if we want to figure out the impulse all we do is simply divide

by the time. So if we divide it by the time it is going to give us the force that is being

applied. So I am going to take that impulse, which is right here. I am going to include

all those significant digits. And then I am going to divide it by the time which is 0.072

seconds. And it is going to give me a force of that. And then again, too many significant

digits. I could figure out my force, which is only going to have 2 significant digits.

And so it is going to be 2.8 times 10 to the 5 newtons. Why is that? Because 0.072 only

has 2 significant digits. And so that is a massive force that is being applied to that

car. But since the time is greater than it would be with an old car, it is actually going

to be a much smaller force you would experience in a new age car. Let's say we were to look

at the person inside it. How do we figure that out again? Again you could stop right

now and if you want to try to solve this one, you sure could. We are going to start with

an impulse which is simply going to be the mass times the change in velocity. And so

I could figure it out like that with significant digits. It is going to be 1.2 times 10 to

the 3 newtons seconds. That is going to be the impulse. If I want to figure out the force

all I am going to do is going to be to divide by the time. And so that is going to give

me a value of around 1.1 times 10 to the 4 newtons. And so that is going to be the force

that is applied to that person. Now that is not a deadly force, and the reason why is

that we have increased that amount of time even though the momentum and the impulse stay

the same, by increasing the time we can decrease the force. And so did you learn to justify

this selection of data if you want to figure out the impulse or if you want to figure out

the force? And then finally could you predict, analyze and design a plan for collecting data?

In this case we used a video to look at the change in that momentum over time. But you

could use a ticker tape. You could use a motion sensor to figure this out. So that is impulse.

Again, product of force times time. And I hope that was helpful.