Newton's Laws of Motion Explained with Real-Life Examples

in this video we're going to talk about Newton's law of motion and there's three laws that we're going to go over let's

talk about the first law so what exactly does Newton's First Law of Motion state well one part States this an

object at rest will remain at rest unless acted on by a force particularly in our imbalance

Force so let's say if we have a surface and if there's a box on its surface if we don't apply a force this

box will not move all the forces that are currently acting on this box cancel they're balanced forces for

example you have the weight force of the Box let's say the box has a mass of 10 kg to calculate the weight Force it's

equal to M * g m is the mass in kilogram G is the gravitational acceleration

so m is 10 kg G is 9.8 m per second squ that is the

acceleration due to gravity so the weight force is simply 10 * 9.8 so it's equal to 98

Newtons gravity exerts a downward weight force on any object now the block is not accelerating

downward it's at rest so the must be some other force that keeps it at rest the force that the ground exerts on a

box is known as the normal force and it has to balance the weight force in order to keep the block where it is and so the

normal force is also 98 so as you can see these are balanced forces the net force on his box is equal

to zero and so it remains at rest unless we apply an unbalance Force then the block May begin to

move we may have to overcome static friction but if we apply Force then it can move so an object at rest will

remain at rest unless acted on by net force so that's the first part of Newton's uh first law of

motion now what about the second part of it Newton's Second Law also states that an object in motion will continue in

motion unless acted on by a net force it's basically a statement of the law of inertia now let's think about

this let's say if we have a surface with let's say it's a rough surface let's use a carpet for

example if you try to roll a ball on a carpet for the most part the ball is going to quickly come to a stop it's not

going to move very far and the reason why that happens even though this object is in motion

there's a lot of friction between the surface of the ball and the carpet and friction opposes motion and so because

there's a net force this object will not continue in motion it's going to come to rest and that's what we see in real life

if you roll a ball eventually comes to a stop it doesn't continue forever but Newton's first law of motion states that

an object in motion will continue in motion unless acted on by force now if you think about it what will happen if

we can get rid of friction will the object continue to move forever now imagine if you have a smooth

surface let's say like ice now if we take a puck and slide it across the ice it's going to move for a

very very large distance it's not going to come to rest like the ball on the carpet the ball on the carpet is going

to stop after a very short distance but this Puck is going to slide across the ice for a long

time now let's say if we use a ball and we roll it on ice let's say if you put it on a frozen

lake and you roll it across the lake it's going to roll for a very very long time

until it comes to rest it's going to take a long time for it to come to rest now why is

that why is it that if we roll a ball on a rough surface it's it takes a very short time to come to rest it comes to

stop it comes to a stop quickly but if you take a ball and put it on an icy surface it will roll for a longer time

the reason for that is because there's more friction between a ball and a rough carpet but between the ball and the icy

surface there's less friction and so because there's less friction this ball will continue to travel for a much

longer time now what's going to happen if we can complete completely get rid of friction will the object continue to

move forever think about it now keep this in mind even though there's very little

friction between the icy surface and the ball you also have air resistance as the ball is moving

forward the air molecules can slow it down so you have air resistance and if it's moving fast this can be a Air drag

as well but where can we find a place where there's virtually no

friction the best place where there's almost no friction is outer space in outer space there's virtually no air

it's almost non-existing you might have a few molecules here and there but for the most part the pressure is extremely

extremely low if you think about it we know that the Earth revolves

around the Sun and the Earth is an object in motion and the Earth has been revolving around

the Sun for a very very very long time Millions perhaps billions of years and it continues to keep

moving and it makes sense because in space there's virtually no friction it's not enough to slow the

Earth down and so it continues to move in its orbit and thus we can see Newton's first

law of motion in action here an object in motion will continue in motion unless acted on by a net unbalanced

force now you might be wondering all of this information is great but how can I apply this information in a problem How

will I see a question on a test well there's some things that you need to know if an object remains at rest the

net force aced on the object is equal to zero make sure you understand that concept the second thing is if an object

is in motion let's say if it's moving with constant velocity then the net force acting on

that object is equal to zero make sure you understand that if the net force is not

zero then there is a net acceleration but when the net force is zero the acceleration in that direction

is also equal to zero which means that the velocity is constant keep in mind acceleration is defined as the change in

velocity that is the final velocity minus the initial velocity divided by the change in

time so at constant velocity VF and V will be the same if you take a number and subtract it by the

same number you're going to get zero so in constant velocity VF minus V is 0 0/ t is0 now according to Newton SE law the

net force is equal to the product of the mass and the

acceleration so if the acceleration is constant and if you increase the mass of the object the net force will increase

so the net force is proportional to the mass of the object now let's say if you keep the mass constant and if you

increase the magnitude of the acceleration the net force will increase as well so the net force is also

directly proportional to the acceleration now what if we keep the net force constant what is the relationship

between the mass and the acceleration if you increase the mass the acceleration will decrease provided

if the force Remains the Same if you decrease the mass the acceleration will increase under constant force

conditions now let's put some numbers to it if you you double the mass while keeping the acceleration constant what

effect will it have on the force by what factor will the force increase by to answer these questions simply plug

in the values if you double the mass replace it with two if the acceleration is held constant replace it with one so

the force will increase by a factor of two if we triple the mass and keep the acceleration constant the force will

increase by a factor of three now what if we double the acceleration and triple the

mass what effect will it have on the force so if you triple the mass and double the acceleration 3 * 2 a six the

force will increase by a factor of six if you quadruple the mass triple the acceleration the force will increase by

a factor of 12 so Newton's Second Law basically states that the net force is equal to

the mass time the acceleration now you can also describe Newton's second law of

motion using something else so let's start with the equation f is equal to ma that is the net force is equal to the

mass time the acceleration now we said that the acceleration is the change in velocity V

final minus V initial which we can write as Delta V the triangle represents change

is the change in velocity divid by the change in time so Delta V over delta T is the same

as saying V final minus V initial over T where this T represents a change in time now what is mass times

velocity Mass multili velocity is equal to to momentum indicated by the symbol lowercase p momentum is mass in motion

an object at rest has zero momentum an object that's moving has momentum so let's say

if here's the question for you which object has more momentum a car moving at 30 miles per

hour or a train moving at 30 miles per hour if both objects are moving with the same

speed then the one that has more mass will have more momentum the train has a lot of momentum

it's very difficult to stop a train it's much easier to stop a car than a train so momentum is the product of mass

and velocity so an object with a lot of mass and with a lot of speed has a lot of

momentum now if MV V is equal to P then that means that M Delta V has to be equal to Delta P that is the

change in momentum so let's replace this term with Delta P so we could say that the net

force is equal to the rate of change of the momentum with respect to

time so this is another variation of Newton seconds law the net force is the change in momentum ID by the change in

time by the way if you start from this equation and if you multiply both sides by delta

T you're going to get another important theorem the force multiplied by the change in time is equal to the mass

times the change in velocity the product of the force and a time is known as

impulse and mass times the change in velocity is known as the change in momentum so this is known as the impulse

momentum theorem the impulse is equal to the change in momentum now what about Newton's third

law of motion what exactly does that state the third law states that for

every action there is an equal and opposite reaction so f is equal to FB so if you apply a force there's going

to be a reaction force applied to you both forces will have the same magnitude but the direction of the two forces will

be opposite to each other so let's go through some examples examp let's say if a person jumps in the

air and throws a basketball as the basketball moves in that direction he applies a force on it

but he also while in the air he's going to move back so there like a recoil of force applied to

him now because the mass of the ball is less than the mass of the person the ball's going to travel

a further distance away from the person because the ball will experience a greater

acceleration remember for the same Force if you decrease the mass the acceleration increases these two are

inversely related but the force exerted on the ball and on the person is the same so let's put numbers to this so you

can see how it works so let's say the ball has a mass of 2 kg and the person has a mass of 80

kg actually let's say 100 100 is a nice number now let's say that the person applies a

force of 200 newtons on a ball the person is going to fill a reaction force of 200 Newtons in the

opposite direction now what is the acceleration of the person and the

ball now we know that according to Newton's Second Law f is equal to Ma so the acceleration is the force divided by

the mass so if we take 200 / 2 the acceleration will be equal to positive 100 m/s

squared now for the person 200 divid 100 is only two so the acceleration is negative 2 m/s squ

acceleration is a vector and vectors have magnitude and Direction because the person feels a force directed towards

the left his Force should be negative and therefore his acceleration is negative

force and acceleration and velocity are vector quantities direction is important speed is a scal of quantity speed has

magnitude only but as you can see the object with less Mass experiences a a much larger

acceleration the person with more mass experiences a smaller acceleration however the forces are

equal according to Newton's third law for every action force there is an equal but opposite reaction

force now here's another situation imagine if you're in the ocean on a boat

let's say this is you and you have a ball in your hand I want you to imagine the situation so just think of yourself

being on a boat in the ocean and if you throw the ball towards the right what do you think is going to

happen to you and the boat in what direction will you move now intuitively you know that if

you apply a force to throw the ball towards the right you're going to feel a force that's going to push you and the

boat towards the left but because the ball has less Mass it will have a greater acceleration and so it's going

to travel a greater distance now because the combined mass of you and the boat is so much more larger than the

ball you won't feel the acceleration as much you might move a little but the distance that the boat moves towards the

left is insignificant towards the right but it does move according to Newton's thirdd LW for

every action force there is an equal and option reaction force now let's go over one more example

so let's say this is the Earth and over here we have the

moon which is much smaller than the earth and let's say you're an astronaut somewhere in

space and you have a ball in your hand okay let's redraw the picture my drawing is

terrible I didn't want to draw the stick figure too big but sometimes bigger is

better so this person has the ball on his hand now he's in space floating in space

imagine if you're this person and you're floating in space now you don't want to drift deep into outter space you want to

get back to planet Earth in what direction should you throw the

ball now remember you want to throw the ball in a certain direction so that you will be accelerated towards the

Earth so here are your options do you want to throw the ball fall in this direction towards the moon towards the

Earth or above you where should you throw the ball now if you throw the ball let's say

towards the Earth you're going to feel a force that's going to push you towards the

moon which is not where you want to go if you throw the ball South with you you're going to fill a force that's

going to put isue away from the earth and the moon maybe towards the sun which is not good

either so what you want to do is you want to throw the ball towards the moon because if you throw it this way you're

going to feel an opposite force that will push you this way that is towards the

Earth and so once you throw the ball away from the earth you're you're going to fill a force that's going to

push you towards the Earth and while you're in space there's not much friction so the velocity that you

acquired as you throw the ball towards the right that velocity will remain constant and so you'll slowly fall

towards the Earth getting back to uh where you belong so understanding that principle

can help you to travel in space if you want to go towards the Moon throw the ball towards the Earth and

you're going to be pushed towards the moon so basically whatever Direction you want to go throw the ball opposite in

that direction so if you want to go north throw the ball South if you want to go East throw the ball West and vice

versa so now we're going to work on some problems feel free to pause the video and work on each problem that you see

from this point on a car travels on the road with a constant velocity what is the horizontal net

force acting on the car so what do you think the answer is to that question what is the net force

now if you recall anytime an object is moving with constant velocity the net force is always equal to

zero now what about the acceleration of the car well according to Newton's Second Law f is equal to Ma so if the

force is zero the acceleration must also be equal to zero now part C if the frictional force

acted on the car is 1500 Newtons what force is applied to the car by the engine so let's draw a picture I'm just

going to draw a box because it's easy to draw and this box represents the car so let's say the car is moving to

the right so V represents the velocity where where it's

going friction opposes motion so the frictional force is 1500 Newtons now the net force is zero which

means that the applied force has to be 1500 Newtons these two forces cancel out so

the net force is zero and therefore the acceleration is zero and if the acceleration is zero the velocity is

constant keep in mind acceleration is the rate of change of velocity if the velocity changes then

there's an acceleration if the acceleration is zero the velocity will not

change a force of 200 Newtons is applied on a 10 kg box across the frictionless surface that is a horizontal frictional

surface what is the acceleration of the box so let's draw a picture and here is the 10 kg

box and we're going to apply a force of 200 NS so to calculate the acceleration we

can use this equation f is equal to ma a so F / m is a the force is 200 Newtons the mass is 10 kilg 200 ID 10

will give us an Exel acceleration of 20 m/s squ now what about Part B if the Box

accelerates from rest what will its final speed be after 8 seconds the

acceleration tells you how much the speed changes every second so let's make a

table so initially the velocity or the speed is zero every second that passes the speed will

increase by 20 so 1 second later it's going to be 20 2 seconds later 40 3 seconds later 60 4 seconds later 80 and

I'm going to continue the table here let's see if I can fit it in 5 seconds later it's going to be 100 6

seconds later 120 7 seconds later 140 8 seconds later 160 so after 8

seconds the speed of the Box will be 160 m/ second now the equation that you can use to calculate this answer is this

equation we're looking for the final speed VF the initial speed V is zero because it started from rest the

acceleration is 20 the time is 8 20 * 8 if you have 820 bills how much money do you have 8 $220 bills is $160 so 20 * 8

is 160 so you get 160 m/s now what about part

C how long will it take the box to reach a speed of 500 m/ second if it continues to accelerate at this

rate so starting from a speed of zero a is 20 let's solve for T the final speed is

500 so we got to divide both sides by 20 so what is 500 ID 20 well we can cancel zero so it becomes 50 divid by two half

of 50 is 25 so it's going to take 25 seconds for the box to accelerate from rest to a

speed of 500 m/s a force of 300 Newtons is applied across a 20 kg

box the frictional force acting on a box is 200 Newtons what is the net horizontal force on the box so let's

begin so we have an applied force of 300 Newtons so let's call it a capital f and there's a frictional

force of 200 Newtons so the net force is in this direction the net force is simply the

difference between the two forces so it's 100 Newtons directed towards the right if these two forces are in their

respective positions now what is the acceleration of the

box once you have the net force you can use this equation FAL ma to find the acceleration so the acceleration is the

net force of 100 divid by the mass of the box so the acceleration is 5 m/s

squ now what about part C how far will the Box travel after 12 seconds if it continues to accelerate at this rate

starting from rest so the initial speed is zero if it starts from rest

the time is 12 seconds our goal is to find the distance traveled so we're looking for D what

equation has v initial t d and a so make sure you review your kinematics equation you never know when those equations will

be helpful the equation that you need is the displacement is equal to the initial speed multiplied by the time plus 12

a^2 the initial speed is zero the acceleration is five and the time is

12 and let's not forget to square it so we have a half * 5 * 12 * 12 a half * 12 is

6 6 * 5 is 30 and 30 * 12 if we multiply 30 by 10 that's 300 30 * 2 is 60 so 30 * 12 is

360 so this particular box is going to travel 360 M before it's going to travel 360 m in 12

seconds that's what I wanted to say an 8 kg object speeds up from 20 m m/ second to 50 m/s in 6 seconds what is

the acceleration to find the acceleration you can use this

equation perhaps you've seen the same equation written this way a is equal to V final minus V initial / T these two

equations are the same but you can solve for a and it's going to look like that so let's use the equation on the right

side so the acceleration is the change in velocity so 50 - 20 / the time which is 6 50 - 20 is 30 30 ID 6 is 5 so the

acceleration is 5 m/s squ now Part B what is the net horizontal force acting on the object

the net force is simply the product of the mass and the acceleration so the mass is eight the

acceleration is five the net force is 40 Newtons now what about part

C if the frictional force is 35 Newtons what is the applied force so here's the frictional

force the net force is 40 Newtons what number minus 35 is 40 the applied

force has to be 75 as you can see 75 minus 35 is 40 in order for the object to accelerate

the applied force has to be greater than 35 it can't be less to get the applied force you have

to add 35 + 40 and that will give you 75 if you subtract 35 and 40 you'll get neg5 and that's not going to be the

apply force and an 80 kg astronaut in space throws a 2 kg package with an

acceleration of pos4 m/s squared what force did the astronaut

exert on a package so let's draw a picture so let's say this is the astronaut he's in

space and he throws a package towards the right the mass of the package is 2 kg

the mass of the as is 80 kg and the package has an acceleration of 4 m/s squ to calculate

the force that the astronaut exerted on a package we can use this equation f is equal to ma the package has a mass of

two and an acceleration of four so the force applied to it is 8 Newtons now what force does the package

exert on the astronom well according to Newton's third law for every action force there is an equal but

opposite reaction force so if 8 Newtons of force was exerted on a package 8 Newtons of force will be

exerted on the astronom but because it's in the opposite direction let's put a negative

sign to it now let's calculate the acceleration so the acceleration is the force divid by the mass it's A8 / by 80

is .1 so this is the acceleration acting on the astronaut as

you can see the object with less Mass has a larger acceleration whenever the force is

constant which it is as you can see these two forces are the same according to Newton's third

law now for the object with a larger Mass it experiences a much smaller acceleration the 80 kilogram

person has more mass than the 2 kilogram package and so the acceleration of the 80 kg person is much less than the

acceleration of the package 0.1 is much less than four a 120 kg skater pushes against an

80 kg skater after contact the 80 kg skater was given an acceleration of 1.5 m/s

squ what is the acceleration of the 120 kgam scater well according to Newton's third

law for every action force there is an equal and opposite reaction force so F A equals negative

FB so fa we're just going to say is the mass times the acceleration let's say M1 * A1

FB let's call it M2 * A2 now all we got to do is plug in the information the mass of the heavy skater

is 120 kg we don't know the acceleration of the heavy skater we need to find it the mass

of the light skater is 80 kilg and his acceleration is

1.5 now 80 * 1.5 is 120 and if we divide both sides by

120 we can see that the acceleration of the 120 kg skater is1 the negative sign simply tells you

that his acceleration is opposite to the other skater but since he has a larger Mass

his acceleration should be less than the scale with less Mass the skater with less mass will experience a larger

acceleration now what force was exerted on each skater to calculate the force is simply

f is equal to Ma so we can multiply the mass of the 120 kg skater by1 that will give us a

force of -20 or we could take the mass of the 80 kilogram skater and multiply by his acceleration of

1.5 which is also uh 120 but positive so these two forces they're equal in magnitude but opposite in

direction so what we're going to do now is a quick review of everything that we've learned so Newton's first law of

motion an object at rest will continue to be at rest unless acted on by a net force or an unbalanced

force also an object in motion will continue in motion unless acted on by net force so keep this in mind if an

object is moving with a constant velocity the acceleration is zero and therefore the net force acting on the

object is zero and the reverse statement is true if the net force is zero then the object has a constant velocity and

also constant speed now Newton's Second Law f is equal to Ma

the net force is the product of the mass times the acceleration whenever the force is

constant if you increase the mass the acceleration decreases and if you decrease the mass the acceleration

increases so heavy objects don't move much the light objects are easy to push they they will it's easy to give a light

object a large acceleration heavy objects tend to have small accelerations so this equation describes

Newton's Second Law now Newton's third law every action force for every action force I meant to say there is an equal

but opposite reaction force so you could say M1 * A1 is equal to M2 * A2 and so that is it for this

video now if you want to find more physics videos feel free to check out my Channel or even take a look at my

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