Introduction to Impulse & Momentum - Physics

Summary

This educational video delves into the concepts of impulse and momentum in physics. Momentum is defined as mass times velocity, indicating mass in motion. It's a vector quantity with both magnitude and direction. The video explains how to calculate momentum with examples, including direction considerations. Impulse, the integral of force over time, is also explored, along with the Impulse-Momentum Theorem. The theorem links impulse to changes in an object's momentum and is used to calculate final velocities and momenta with a practical example involving a force applied to a block.

Takeaways

• 📚 Momentum is defined as the product of an object's mass and velocity.
• 🚄 Objects in motion possess momentum; a train has significant momentum due to its large mass, while a sports car has momentum due to its high velocity.
• ✈️ An object at rest, like an airplane, has zero momentum because it is not moving.
• 📏 Momentum is a vector quantity, possessing both magnitude and direction, derived from the scalar mass and vector velocity.
• 🔢 The units of momentum are typically kilograms times meters per second (kg·m/s).
• 📉 The direction of an object's momentum aligns with its direction of motion; rightward motion is positive, and leftward is negative.
• 💥 Impulse is calculated as the product of force and the time over which it acts, with units of newtons times seconds (N·s).
• 🔄 The impulse-momentum theorem states that the impulse applied to an object is equal to the change in its momentum.
• 📉 Force can be defined as the rate of change of an object's momentum over time, mathematically expressed as (Δp / Δt).
• 📐 Newton's second law connects force, mass, and acceleration, where the net force on an object equals its mass times acceleration.

Q & A

What is momentum?

Momentum is a vector quantity that represents the mass of an object in motion, calculated by multiplying the object's mass by its velocity.

What is the formula for calculating momentum?

The formula for calculating momentum is given by p = mv, where p represents momentum, m is the mass, and v is the velocity of the object.

Why is momentum considered a vector quantity?

Momentum is considered a vector quantity because when you multiply a scalar (mass) by a vector (velocity), the result is a vector that has both magnitude and direction.

What are the units of momentum in physics?

In physics, the units of momentum are typically kilograms times meters per second (kg·m/s).

How do you determine the sign of momentum?

The sign of momentum is determined by the direction of the object's motion. If it's moving to the right (or east), the momentum is positive, and if it's moving to the left (or west), the momentum is negative.

What is impulse in physics?

Impulse in physics is the product of the force applied to an object and the time for which the force is applied, represented by the formula J = Ft, where J is impulse, F is force, and t is time.

What is the relationship between impulse and momentum?

According to the impulse-momentum theorem, the impulse applied to an object is equal to the change in the object's momentum, expressed as J = Δp.

What does the impulse-momentum theorem tell us about force?

The impulse-momentum theorem tells us that force is the rate at which the momentum of an object changes, which can be expressed as F = Δp/Δt.

How is impulse related to Newton's second law?

Impulse is related to Newton's second law through the concept that the net force acting on an object is equal to the mass of the object times its acceleration, which can also be viewed as the rate of change of momentum.

Can you provide an example of calculating impulse and change in momentum from the script?

Yes, in the example provided, a force of 200 newtons is applied for 5 seconds to a 50 kg block initially moving at 10 m/s east. The impulse is calculated as 200 N × 5 s = 1000 N·s. The change in momentum is also 1000 kg·m/s, assuming the force is in the same direction as the initial velocity.

What is the final velocity of the object in the example problem if the force increases its momentum?

In the example, the final velocity is calculated by adding the change in velocity to the initial velocity: v_f = v_i + Δv = 10 m/s + 20 m/s = 30 m/s.

How is the final momentum of the object calculated in the example?

The final momentum is calculated by multiplying the final velocity by the mass of the object: p_f = m × v_f = 50 kg × 30 m/s = 1500 kg·m/s.

Outlines

00:00

🚀 Understanding Momentum

This paragraph introduces the concept of momentum in physics, emphasizing its relationship with mass and velocity. Momentum, represented by the lowercase 'p', is defined as the product of an object's mass and its velocity, indicating the quantity of motion. The paragraph explains that any moving object possesses momentum and uses examples such as a train and a sports car to illustrate this point. It also clarifies that while mass is a scalar, velocity is a vector, and thus the product results in a vector quantity for momentum, which includes both magnitude and direction. The units for momentum are discussed, typically kilograms times meters per second. An example is provided to calculate the momentum of a 10 kg block moving at 5 m/s to the east, resulting in a momentum of 50 kg*m/s to the east. The paragraph also covers how to determine the sign of momentum based on the direction of motion.

05:01

🔧 Impulse and Its Relation to Momentum

The second paragraph delves into the concept of impulse, defined as the product of force and the time over which it is applied. It contrasts impulse with momentum, noting that while both have units of newton-seconds, they represent different physical quantities. The Impulse-Momentum Theorem is introduced, stating that the impulse applied to an object is equal to the change in its momentum. The paragraph then explores the relationship between force, momentum change, and time, leading to the definition of force as the rate of change of momentum. An example problem is presented where a 50 kg block is subjected to a 200 N force for 5 seconds, and the viewer is prompted to calculate the impulse, the change in momentum, and the final momentum and velocity of the block. The paragraph concludes with a teaser for additional resources on related topics and an encouragement to subscribe to the channel for more content.

10:03

📚 Calculating Impulse and Momentum

The final paragraph provides a step-by-step calculation for the example problem introduced in the previous section. It starts by calculating the impulse as the force of 200 N applied over 5 seconds, resulting in 1000 N*s. The change in momentum is then determined by applying the Impulse-Momentum Theorem, which equates the impulse to the change in momentum. The paragraph explains that since the force and velocity are in the same direction, the force increases the object's momentum, making the change positive. The calculation proceeds to find the final velocity by dividing the change in momentum by the object's mass and then adding the initial velocity, resulting in a final velocity of 30 m/s. Lastly, the final momentum is calculated by multiplying the object's mass by its final velocity, yielding 1500 kg*m/s. The paragraph concludes with a summary of the key points about impulse and momentum and an encouragement to explore further resources and subscribe to the channel.

Keywords

💡Momentum

Momentum is defined as the product of an object's mass and its velocity, represented by the formula p = mv. It is a vector quantity, meaning it has both magnitude and direction. In the video, momentum is used to describe the motion of objects such as a train, a sports car, and an airplane. The concept is central to understanding how objects move and interact, with moving objects having momentum and stationary objects having none.

💡Mass

Mass is a scalar quantity that represents the amount of matter in an object. It is typically measured in kilograms. In the context of the video, mass is a key component in calculating momentum, as it multiplies with velocity to give the momentum of an object. The video uses the example of a train to illustrate how a large mass contributes to significant momentum.

💡Velocity

Velocity is a vector quantity that describes the speed of an object in a specific direction. It is measured in meters per second. The video explains that velocity, when combined with mass, determines an object's momentum. The direction of velocity is crucial in determining the sign of momentum; for example, eastward velocity results in positive momentum, while westward velocity results in negative momentum.

💡Scalar

A scalar is a simple physical quantity that has only magnitude and no direction. In the video, mass is identified as a scalar quantity. Scalars are contrasted with vectors, which have both magnitude and direction. The video explains that when a scalar (mass) is multiplied by a vector (velocity), the result is a vector (momentum).

💡Vector

A vector is a physical quantity that has both magnitude and direction. Examples of vectors include velocity and momentum. The video emphasizes that vectors are crucial in physics for describing motion, as they provide information about both how much an object moves and the direction of that movement.

💡Impulse

Impulse is defined as the product of the force applied to an object and the time for which it is applied, represented by I = Ft. It is a vector quantity and is directly related to the change in an object's momentum. In the video, impulse is used to explain how forces can alter an object's momentum over time, with the example of a force applied to a block for a certain duration.

💡Force

Force is a vector quantity that can cause an object to change its velocity. It is measured in newtons. The video discusses how force, when applied over a period, results in impulse, which in turn can change an object's momentum. The concept is integral to understanding how objects accelerate and move under different forces.

💡Impulse-Momentum Theorem

The Impulse-Momentum Theorem states that the impulse of the resultant forces acting on an object is equal to the change in the object's momentum. This theorem is central to the video's discussion on how forces affect motion. The video uses this theorem to explain how a force applied to an object for a certain time can increase or decrease its momentum.

💡Units

Units are used to quantify physical quantities. In the video, units for momentum are kilograms times meters per second, while units for impulse are newtons times seconds. The video explains that although these units are different, they are equivalent because they both measure the same physical concept—change in momentum—just from different perspectives.

💡Acceleration

Acceleration is the rate at which an object's velocity changes over time. It is defined as the change in velocity divided by the change in time. The video connects acceleration to the concept of force by stating that force is the rate at which momentum changes, which is directly related to acceleration as per Newton's second law.

💡Newton's Second Law

Newton's Second Law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. The video uses this law to connect the concepts of force, mass, acceleration, and momentum. It shows how understanding Newton's Second Law helps in calculating the final velocity and momentum of an object when a force is applied.

Highlights

Momentum is defined as mass times velocity.

Momentum represents mass in motion.

An object at rest has no momentum.

Momentum is a vector quantity with both magnitude and direction.

The unit for momentum is kilograms times meters per second.

Momentum is positive if an object moves to the right and negative if it moves to the left.

Impulse is defined as force multiplied by time.

Impulse has units of newtons times seconds, equivalent to momentum units.

The impulse-momentum theorem states that impulse equals the change in momentum.

Force is the rate at which momentum changes, defined as delta p over delta t.

Newton's second law relates force to mass and acceleration.

An example problem involves calculating impulse, change in momentum, and final momentum and velocity.

Impulse can be calculated by multiplying force by the time the force is applied.

The direction of force and velocity determines whether the change in momentum is positive or negative.

The change in momentum can be found using the impulse-momentum theorem.

Final momentum is calculated by adding the change in momentum to the initial momentum.

Final velocity is calculated by adding the change in velocity to the initial velocity.

The video provides additional resources for further study on impulse, momentum, and collisions.

Transcripts

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 the vectors have both

magnitude and direction

there's no direction of mass

now what happens

when we multiply a scalar by a vector

a scalar times a vector will give you

another vector

that vector could be

greater or smaller in magnitude but it

will give you another vector

so momentum

is a vector

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

so 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

at three 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 three meters

per second

because the block is moving to the west

to the negative x direction the velocity

is negative

so it's negative three 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

unit for force is the newton

and for time it's typically in seconds

so impulse

will have the units

newtons

times seconds

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 newton's

time seconds

and the unit for momentum

is kilograms

times meters per second

so these units are equivalent

but when you see newton's times seconds

typically it 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

its 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 a v final minus v initial

divided by t

this is equal to the acceleration

the acceleration of the object or of any

object rather it's 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 an 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 newtons

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 five seconds

and now let's say that before the force

was

before the force acted on the object

let's say that the initial velocity

of the object is 10 meters 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 and 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 one thousand

instead of positive one thousand

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 a thousand 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 of 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 a thousand

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 a thousand

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 gonna stop the video here

and uh 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