GCSE Physics - Momentum Part 1 of 2 - Conservation of Momentum Principle #59

Summary

This educational video explores the concept of momentum, a vector quantity defined as mass times velocity. It illustrates momentum with examples of a charging dinosaur and a moving car, emphasizing directionality. The script then delves into the conservation of momentum, using a collision scenario to demonstrate how total momentum remains constant. It concludes with applications, such as a gun's recoil, showing how initial and final momentums balance to zero. The video is designed to educate and engage viewers on the fundamental principles of physics.

Takeaways

• 🌟 Momentum is a property of all moving objects and is calculated as the product of an object's mass and velocity.
• 🦖 A 4500 kg dinosaur moving at 12 m/s has a momentum of 54,000 kg m/s.
• 🚗 A 1200 kg car traveling at 25 m/s has a momentum of 30,000 kg m/s.
• 📐 Momentum is a vector quantity, meaning it has both magnitude and direction.
• ➡️ The forward direction is considered positive, so the dinosaur has positive momentum, while the car has negative momentum.
• 🔄 The conservation of momentum principle states that the total momentum in a closed system remains constant before and after an event, like a collision.
• 🤝 After a collision, the combined momentum of the dinosaur and car is the sum of their individual momenta.
• 🧮 The velocity after a collision can be found by dividing the total momentum by the combined mass of the objects involved.
• 🔁 If the initial momentum is zero, the total momentum after an event must also be zero, as seen with a gun firing a bullet.
• 🔍 The recoil velocity of the gun can be calculated using the conservation of momentum, where the gun's momentum is equal and opposite to the bullet's momentum.
• 🔤 The symbol for momentum is 'p', and the equation is written as p = m * v.

Q & A

What is the definition of momentum according to the video?

Momentum is a property that all moving objects have, and it is calculated by multiplying the mass of an object by its velocity.

How do you calculate the momentum of an object?

Momentum is calculated using the equation: momentum = mass × velocity.

What is the momentum of a 4,500 kg dinosaur moving at 12 meters per second?

The momentum of the dinosaur is 4,500 kg × 12 m/s = 54,000 kg·m/s.

How is momentum a vector quantity?

Momentum is a vector quantity because it has both magnitude (size) and direction. For example, in the video, the dinosaur's momentum is considered positive because it moves to the right, while the car's momentum is negative because it moves to the left.

What is the principle of conservation of momentum?

The conservation of momentum principle states that in a closed system, the total momentum before an event, such as a collision, is equal to the total momentum after the event.

How can you find the velocity of two objects after a collision?

To find the velocity after a collision, you first calculate the total momentum before the collision, then divide it by the combined mass of the two objects to get their shared velocity.

What is the combined velocity of a 4,500 kg dinosaur and a 1,200 kg car after they collide?

After the collision, the combined velocity is calculated as 24,000 kg·m/s (total momentum) divided by 5,700 kg (combined mass), which gives a velocity of 4.4 m/s to the right.

How does momentum behave in a system where the total initial momentum is zero?

In a system where the initial momentum is zero, such as a stationary object, the total momentum after an event (like firing a gun) must still be zero. This means the momentum of one object will be balanced by the opposite momentum of another.

How do you calculate the recoil velocity of a gun when it fires a bullet?

You calculate the momentum of the bullet, then set up an equation where the gun's momentum plus the bullet's momentum equals zero. Solve for the gun's velocity (v) to find its recoil speed.

What does a negative velocity in momentum calculations indicate?

A negative velocity indicates that the object is moving in the opposite direction. For example, if a gun recoils after firing a bullet, the negative sign indicates the gun moves in the opposite direction to the bullet.

Outlines

00:00

🦖 Momentum and Conservation of Momentum

This paragraph introduces the concept of momentum, which is defined as the product of an object's mass and its velocity. It uses the examples of a dinosaur and a car to illustrate how to calculate momentum. The paragraph also explains that momentum is a vector quantity, having both magnitude and direction. It then discusses the conservation of momentum principle, which states that the total momentum in a closed system remains constant before and after an event, such as a collision. An example is given where a dinosaur and a car collide, and the calculation shows that their combined momentum after the collision is the sum of their individual momenta, resulting in a shared velocity to the right.

05:01

🔫 Recoil and Momentum Calculation

The second paragraph delves into the concept of recoil and how it relates to momentum. It uses the example of a gun firing a bullet to demonstrate how the momentum of the bullet and the gun's recoil are equal and opposite, thus conserving the total momentum. The calculation involves finding the bullet's momentum using its mass and velocity, and then using that to calculate the gun's recoil velocity. The paragraph concludes with the formula for momentum, represented by the symbol 'p', which equals mass times velocity (p = m * v). The video ends with a call to action for viewers to like and subscribe for more content.

Keywords

💡Momentum

Momentum is a measure of the motion of an object, defined as the product of an object's mass and its velocity. In the video, momentum is central to understanding how moving objects interact. For instance, the script uses the example of a dinosaur and a car to illustrate how momentum is calculated and its vector nature, indicating direction as well as magnitude.

💡Mass

Mass is a fundamental property of matter that quantifies the amount of matter in an object. It is a scalar quantity and is used in the formula for momentum (momentum = mass x velocity). The video script mentions the mass of a dinosaur and a car to calculate their respective momenta.

💡Velocity

Velocity is a vector quantity that describes the rate of change of an object's position with respect to time, including both speed and direction. The video emphasizes the importance of velocity in calculating momentum and uses it to illustrate the conservation of momentum principle.

💡Vector Quantity

A vector quantity is a physical quantity that has both magnitude and direction. Momentum is described as a vector quantity in the video, which means it has directionality. The script explains how the dinosaur's momentum is positive (to the right), while the car's is negative (to the left).

💡Conservation of Momentum

The conservation of momentum principle states that the total momentum of a closed system remains constant if no external forces act on it. The video uses the principle to explain how to calculate the velocity of two objects after they collide, ensuring the total momentum before and after the collision remains the same.

💡Collision

A collision is the event where two or more bodies exert forces on each other for a very short period of time. The video script uses a collision between a dinosaur and a car to demonstrate the conservation of momentum and how it affects the velocities of the objects involved.

💡Recoil

Recoil is the reaction to a force exerted by an object, typically experienced when a gun is fired. The video explains how the gun's recoil velocity is calculated using the conservation of momentum principle, showing that the gun moves backward as the bullet moves forward.

💡Scalar Quantity

A scalar quantity is a simple physical quantity that has only magnitude and no direction. The video contrasts scalar and vector quantities by mentioning mass as a scalar, in contrast to momentum which is a vector.

💡Kilogram-meters per second

Kilogram-meters per second is the SI unit for momentum, indicating the product of an object's mass in kilograms and its velocity in meters per second. The video uses this unit to express the momentum of the dinosaur and the car.

💡Direction

Direction is a property of vector quantities that specifies the orientation of the quantity in space. The video script discusses how direction is crucial for understanding momentum, using the forward direction as an example to assign positive or negative values to the momentum of the dinosaur and the car.

💡Event

In the context of the video, an event refers to a specific occurrence, such as a collision, that can change the momentum of objects. The script uses the term to describe the point before and after which the total momentum is calculated.

Highlights

Momentum is a property of all moving objects.

Momentum is calculated as mass multiplied by velocity.

A 4500 kg dinosaur charging at 12 m/s has a momentum of 54,000 kg m/s.

A 1200 kg car traveling at 25 m/s has a momentum of 30,000 kg m/s.

Momentum is a vector quantity with both magnitude and direction.

The conservation of momentum principle states that total momentum in a closed system remains constant.

Total momentum before and after a collision is the same.

After a collision, objects continue moving with the total momentum they had before.

The velocity after a collision can be found using the conservation of momentum principle.

The combined velocity after a collision is the total momentum divided by the total mass.

In some cases, the total momentum before an event might be zero.

The recoil of a gun is an example of conservation of momentum in action.

The gun's recoil velocity can be calculated using the bullet's momentum and the conservation of momentum.

The letter symbol for momentum is 'p', and it can be represented as p = m * v.

The video concludes with a reminder to like and subscribe for more content.

Transcripts

in today's video we're going to look at

momentum which is a property that all

moving objects have

the main thing to know is that momentum

is equal to the mass of an object

multiplied by its velocity

so if we saw a four and a half thousand

kilo dinosaur

charging at 12 meters per second

then its momentum

would be 4 500

times 12.

so 54 000 kilogram meters per second

whereas if we had a 1200 kilo car

traveling at 25 meters per second

then its momentum would be 1200 times 25

so 30 000 kilogram meters per second

an important thing to remember though is

that momentum is a vector quantity

so it has both a magnitude and a

direction

so here if we consider the forward

direction to be to the right then the

dinosaur will have a positive momentum

but the car must have a negative

momentum

the next thing to know is the

conservation of momentum principle

which is the idea that in a closed

system

the total momentum before an event like

a collision

is exactly the same as the total

momentum after the

event to see how this works let's

imagine our dinosaur and our car as two

particles which are traveling towards

each other and are going to collide

after which they'll both continue moving

together at the same speed

how would we find their velocity after

the collision

well the first thing we need to do is

find their total momentum before the

collision

which we can do by adding together the

dinosaurs and the car's momentums

so 54 000

plus

negative 30 000

which gives us positive 24 000 kilograms

meters per second

then because of our conservation of

momentum principle

we know that once they've collided

their total momentum

must still be positive 24 000

and remember that in this scenario a

positive number means that it's going to

the right

so after our particles collide together

they'll both get carried to the right

because the purple one had more momentum

and because they're both moving together

we can now treat them as a single large

particle

so to work out their shared velocity

all we have to do is rearrange our

momentum equation to show that velocity

equals momentum divided by mass

and then plug in the values for this

combined particle

so 24 000

divided by their combined masses from

before

which would be four thousand five

hundred for the dinosaur

plus twelve hundred for the car

so five thousand seven hundred kilos

which gives us a velocity of four point

four meters per second to the right

so basically after the dinosaur and the

car collide

that both continue moving to the right

at a velocity of 4.4 meters per second

now in some circumstances

the momentum before an event might be

zero

like it is for stationary objects

which don't have any momentum because

they're not moving

and so in these cases the total momentum

after the event

must also be zero

for example if we imagine a gun before

it's fired

then its initial momentum would be zero

because its velocity is zero

however once the gun fires the bullet

that flies out will have a momentum in

the forward direction

and so to compensate for this

the gun has to recoil backwards with an

equal momentum

so that together the total momentum is

still zero

so if we knew that this gun had a mass

of 2 kilos

and that a 5 gram bullet was fired out

at a velocity of 120 meters per second

we should be able to work out the

velocity of the gun's recoil

the key to this is remembering that the

gun's momentum

plus the bullet's momentum

must equal zero

because it started off at zero before

the gun fired

the first thing we want to do is find

the bullet's momentum

using this bottom equation

so we do

0.005

which is its mass in kilos

times its velocity of 120

which will give us a momentum of 0.6

kilometers per second

next we want to try and find the gun's

momentum

so again we just do the mass of two

times the velocity

but because we don't know what the

velocity is yet

we can just write v for velocity

so the momentum will be two v

where two is the mass in kilos

and v stands for the gun's velocity

which we're about to find out

finally we can use these momentum values

for the gun and the bullet to rewrite

our equation

as 2v

plus 0.6

equals 0

and then we can just rearrange this

equation to find out the missing value

of v

so first we subtract 0.6 from both sides

giving us 2v equals negative 0.6

and then we divide both sides by 2

leaving us with v equals negative 0.3

meters per second

which is the gun's recoil velocity

and remember the fact that it's negative

means that it's effectively going

backwards

or in other words it's going in the

opposite direction to the bullet

the one thing we haven't mentioned yet

is that you need to know that the letter

symbol for momentum is row which looks

like a p

so the momentum equation can also be

written as p

equals m v

that's everything for this video though

so i hope you enjoyed it if you did then

give us a like and subscribe

and we'll see you next time