Understanding Impulse and Momentum Concepts

In this video, we're going to talk about impulse and momentum. But let's begin our discussion with momentum. What is momentum? I know you heard of this word, but what really is it? Here's the formula for momentum. Momentum, represented by the lowercase p symbol, is mass times velocity. Now let's think about what that means. Momentum is basically mass in motion. Any object that is moving has momentum. A train, for example, that's moving has a lot of momentum because it has a lot of mass. A sports car, which may not have as much mass but it's moving fast, also has a lot of momentum. An airplane at rest has no momentum because it's not moving. So momentum is basically mass in motion. Now, is momentum a scalar quantity or a vector quantity? What would you say? Mass is a scalar quantity and velocity is a vector quantity. If you recall, vectors have both magnitude and direction. There's no direction with mass. Now, what happens when we multiply a scalar by a vector? A scalar times a vector. will give you another factor that factor could be greater or smaller in magnitude but it will give you another factor so momentum is a factor it has both magnitude and direction now let's talk about the units of momentum in physics mass is typically in kilograms velocity is usually in meters per second some momentum will have the units kilograms times meters per second. At least this is the most common unit that you'll see for momentum. Now let's work on an example problem. Let's say we have a 10 kilogram block sliding along a horizontal frictionless surface at a speed of 5 meters per second east. So the speed is 5 meters per second but the velocity is 5 meters per second east. What is the momentum of the block? Well, momentum is mass times velocity. So the mass is 10 kilograms, the velocity is 5 meters per second east, so the momentum will be positive 50 kilograms times meters per second. The reason why it's positive is because the object is moving to the right. Now what if the object was moving to the left? So let's say we have a 20 kilogram object moving at 3 meters per second to the left. What is the momentum? Well, momentum is mass times velocity. The mass is 20 kilograms. And what is the velocity? Is it positive or negative 3 meters per second? Because the block is moving to the west, to the negative x direction, the velocity is negative. So it's negative 3 meters per second, which means the momentum is negative 60 kilograms times meters per second. So when dealing with momentum, if you have an object that's moving to the right, the momentum should be positive. If it's moving to the left, the momentum should be negative. Now let's talk about impulse. What is impulse? In physics, impulse is force multiplied by time. Now be careful because sometimes you'll see I, which may represent inertia in physics. But in this example, I'm using I as impulse. So it's force multiplied by time. The unit for force is the Newton, and for time it's typically in seconds. So impulse will have the units Newtons times seconds. Now there's something known as the impulse momentum theorem. According to the impulse momentum theorem, the impulse is equal to the change in the momentum of the object. So a force acting on an object for a given time interval is equal to the mass times the change in the velocity of the object. So this is the impulse momentum theorem. Now, we know the unit for impulse. is Newtons times seconds, and the unit for momentum kilograms times meters per second. So these units are equivalent but when you see newtons times seconds typically corresponds to impulse and if you see kilograms times meters per second that usually corresponds to momentum but those units they're equivalent though. Now there is an important point to mention regarding impulse and momentum. So we said that impulse is equal to the change in momentum. And impulse is equal to force multiplied by time, or the change in time, or the time that the force has been acting on the object for. Now, if we divide both sides by delta t, we get something interesting, and that is the true definition of a force. So a force is really the rate at which the momentum of the object changes. It's delta P over delta T. So if you know how fast the momentum of the object is changing, you basically know the net force acting on that object. And so this is another way in which you could define a force in physics. Now this equation is related to Newton's second law. Momentum is mass times the change in velocity. And what do you know about the change in velocity over the change in time? So that is V final minus V initial divided by T. This is equal to the acceleration. The acceleration of the object, or of any object rather, is the rate at which the velocity changes. And so what we could do is replace delta V over delta T with acceleration. And so we get mass times acceleration. And so according to Newton's second law, the net force acting on an object is equal to the mass of the object times the acceleration of the object. And it's related to this expression. A force acting on the object is equal to the rate at which the momentum changes for that object. Now let's work on an example problem. So here we have a horizontal frictionless surface, and we have a block with a mass of 50 kilograms. And we're going to apply a force of 200 N on this block. And we're only going to apply this force for a specific time period. And that is, that force will be active on this object for only 5 seconds. And now let's say that before the force acted on the object, let's say that the initial velocity of the object is 10 m per second east. So I want you to find a few things. Calculate the impulse acting on the object and then part B, calculate the change in momentum of the object. Part C, calculate the final momentum of the object and then part D, calculate the final velocity of the object. So using the formulas that we talked about, see if you can calculate these things. Feel free to pause the video. If you want to. Now before we get started on this problem, I want to mention a few things. That is, first of all, for those of you who want more problems on impulse, momentum, elastic collisions, inelastic collisions, conservation of momentum, and stuff like that, check out the links in the description section below. I'm going to post some more videos on those topics. And whatever you do, don't forget to subscribe to this channel, if of course you like this video. So let's go ahead and begin. How can we calculate the impulse acting on this object? The impulse is simply the force multiplied by the time in which the force is active. So it's 200 newtons multiplied by 5 seconds. So that gives us, I'm going to write the answer here, 1000 newtons times seconds. So that's part A. Now, part B, what is the change in the momentum? According to the impulse momentum theorem, the impulse is equal to the change in momentum. Now, here's a question for you. Is the force increasing the momentum of the object or decreasing the momentum of the object? Notice that the force vector and the velocity vector are in the same direction. So, therefore, the force is accelerating the object. It's making it move faster. Therefore, it's going to increase the momentum. So the change in momentum is positive because it could be negative. This could be negative 1000 instead of positive 1000. Another way in which you could look at this is that the force is a vector and it's directed to the right. So it has to be positive, which means the impulse is positive. And so the momentum is going to be positive. So it's 1000 kilograms times meters per second. But I'm out of space, so I didn't write it there. Now let's calculate the final momentum. So we know that the change in momentum is the mass times the change in velocity. And the change in velocity is the final velocity minus the initial velocity. And delta P is 1000. Now we have a block with a mass of 50 kilograms. The initial speed is 10, and so we can get the answer. Let's begin by dividing both sides by 50. And so 1,000 divided by 50, that's the same as 100 divided by 5, which is 20. And now all we need to do is add 10 to both sides. Well, that will give us the final velocity, which is part d. So I might as well write that answer now. So the final velocity is 30. I need to calculate the final momentum, which I could just use this formula. The final momentum is simply the mass times the final velocity. So we have a mass of 50 and a final velocity of 30 meters per second. And so if we multiply 5 times 3, that's 15. And then add in the two zeros, that gives us 1500. So it's 1500 kilograms. times meters per second. So now I'm going to stop the video here and hopefully it gave you a decent understanding of impulse and momentum and how they're related. So thanks again for watching and don't forget to check out the links below and subscribe to this channel.

In this video, we're going to talk about impulse and momentum. But let's begin our discussion with momentum. What is momentum?

I know you heard of this word, but what really is it? Here's the formula for momentum. Momentum, represented by the lowercase p symbol, is mass times velocity. Now let's think about what that means.

Momentum is basically mass in motion. Any object that is moving has momentum. A train, for example, that's moving has a lot of momentum because it has a lot of mass.

A sports car, which may not have as much mass but it's moving fast, also has a lot of momentum. An airplane at rest has no momentum because it's not moving. So momentum is basically mass in motion. Now, is momentum a scalar quantity or a vector quantity? What would you say?

Mass is a scalar quantity and velocity is a vector quantity. If you recall, vectors have both magnitude and direction. There's no direction with mass. Now, what happens when we multiply a scalar by a vector? A scalar times a vector.

will give you another factor that factor could be greater or smaller in magnitude but it will give you another factor so momentum is a factor it has both magnitude and direction now let's talk about the units of momentum in physics mass is typically in kilograms velocity is usually in meters per second some momentum will have the units kilograms times meters per second. At least this is the most common unit that you'll see for momentum. Now let's work on an example problem. Let's say we have a 10 kilogram block sliding along a horizontal frictionless surface at a speed of 5 meters per second east.

So the speed is 5 meters per second but the velocity is 5 meters per second east. What is the momentum of the block? Well, momentum is mass times velocity.

So the mass is 10 kilograms, the velocity is 5 meters per second east, so the momentum will be positive 50 kilograms times meters per second. The reason why it's positive is because the object is moving to the right. Now what if the object was moving to the left? So let's say we have a 20 kilogram object moving at 3 meters per second to the left. What is the momentum?

Well, momentum is mass times velocity. The mass is 20 kilograms. And what is the velocity? Is it positive or negative 3 meters per second? Because the block is moving to the west, to the negative x direction, the velocity is negative.

So it's negative 3 meters per second, which means the momentum is negative 60 kilograms times meters per second. So when dealing with momentum, if you have an object that's moving to the right, the momentum should be positive. If it's moving to the left, the momentum should be negative. Now let's talk about impulse.

What is impulse? In physics, impulse is force multiplied by time. Now be careful because sometimes you'll see I, which may represent inertia in physics.

But in this example, I'm using I as impulse. So it's force multiplied by time. The unit for force is the Newton, and for time it's typically in seconds.

So impulse will have the units Newtons times seconds. Now there's something known as the impulse momentum theorem. According to the impulse momentum theorem, the impulse is equal to the change in the momentum of the object. So a force acting on an object for a given time interval is equal to the mass times the change in the velocity of the object. So this is the impulse momentum theorem.

Now, we know the unit for impulse. is Newtons times seconds, and the unit for momentum kilograms times meters per second. So these units are equivalent but when you see newtons times seconds typically corresponds to impulse and if you see kilograms times meters per second that usually corresponds to momentum but those units they're equivalent though.

Now there is an important point to mention regarding impulse and momentum. So we said that impulse is equal to the change in momentum. And impulse is equal to force multiplied by time, or the change in time, or the time that the force has been acting on the object for. Now, if we divide both sides by delta t, we get something interesting, and that is the true definition of a force.

So a force is really the rate at which the momentum of the object changes. It's delta P over delta T. So if you know how fast the momentum of the object is changing, you basically know the net force acting on that object.

And so this is another way in which you could define a force in physics. Now this equation is related to Newton's second law. Momentum is mass times the change in velocity. And what do you know about the change in velocity over the change in time? So that is V final minus V initial divided by T.

This is equal to the acceleration. The acceleration of the object, or of any object rather, is the rate at which the velocity changes. And so what we could do is replace delta V over delta T with acceleration. And so we get mass times acceleration. And so according to Newton's second law, the net force acting on an object is equal to the mass of the object times the acceleration of the object.

And it's related to this expression. A force acting on the object is equal to the rate at which the momentum changes for that object. Now let's work on an example problem. So here we have a horizontal frictionless surface, and we have a block with a mass of 50 kilograms. And we're going to apply a force of 200 N on this block.

And we're only going to apply this force for a specific time period. And that is, that force will be active on this object for only 5 seconds. And now let's say that before the force acted on the object, let's say that the initial velocity of the object is 10 m per second east. So I want you to find a few things.

Calculate the impulse acting on the object and then part B, calculate the change in momentum of the object. Part C, calculate the final momentum of the object and then part D, calculate the final velocity of the object. So using the formulas that we talked about, see if you can calculate these things.

Feel free to pause the video. If you want to. Now before we get started on this problem, I want to mention a few things. That is, first of all, for those of you who want more problems on impulse, momentum, elastic collisions, inelastic collisions, conservation of momentum, and stuff like that, check out the links in the description section below.

I'm going to post some more videos on those topics. And whatever you do, don't forget to subscribe to this channel, if of course you like this video. So let's go ahead and begin.

How can we calculate the impulse acting on this object? The impulse is simply the force multiplied by the time in which the force is active. So it's 200 newtons multiplied by 5 seconds.

So that gives us, I'm going to write the answer here, 1000 newtons times seconds. So that's part A. Now, part B, what is the change in the momentum?

According to the impulse momentum theorem, the impulse is equal to the change in momentum. Now, here's a question for you. Is the force increasing the momentum of the object or decreasing the momentum of the object?

Notice that the force vector and the velocity vector are in the same direction. So, therefore, the force is accelerating the object. It's making it move faster. Therefore, it's going to increase the momentum. So the change in momentum is positive because it could be negative.

This could be negative 1000 instead of positive 1000. Another way in which you could look at this is that the force is a vector and it's directed to the right. So it has to be positive, which means the impulse is positive. And so the momentum is going to be positive. So it's 1000 kilograms times meters per second. But I'm out of space, so I didn't write it there.

Now let's calculate the final momentum. So we know that the change in momentum is the mass times the change in velocity. And the change in velocity is the final velocity minus the initial velocity.

And delta P is 1000. Now we have a block with a mass of 50 kilograms. The initial speed is 10, and so we can get the answer. Let's begin by dividing both sides by 50. And so 1,000 divided by 50, that's the same as 100 divided by 5, which is 20. And now all we need to do is add 10 to both sides. Well, that will give us the final velocity, which is part d.

So I might as well write that answer now. So the final velocity is 30. I need to calculate the final momentum, which I could just use this formula. The final momentum is simply the mass times the final velocity.

So we have a mass of 50 and a final velocity of 30 meters per second. And so if we multiply 5 times 3, that's 15. And then add in the two zeros, that gives us 1500. So it's 1500 kilograms. times meters per second.

So now I'm going to stop the video here and hopefully it gave you a decent understanding of impulse and momentum and how they're related. So thanks again for watching and don't forget to check out the links below and subscribe to this channel.

Transcript for:Understanding Impulse and Momentum Concepts

Transcript for:
Understanding Impulse and Momentum Concepts