lawsite

welcome back. we're now ready for newton'ssecond law. and newton's second law cansimply be stated-- and you've probably seen this before asforce is equal to mass times acceleration. this is probably, if not themost famous formula in all of time or all of physics,it's up there. it's probably up there withe equals mc squared. but that one's a littlebit more complicated.

so what does this tell us? this tells us that the force,the net force upon an object, is equal to the object's masstimes its acceleration. so let's stay in the metricsystem because most of what you'll do in physic class is inthe metric system, and that tends to be because the metricsystem makes more sense. so let's say that i havea 1 kilogram object. so its mass is 1 kilogram. and it's being pulled downat-- let's say its

it's being accelerated downwardat 9.8 meters per second squared. these kind of units should befamiliar with you from all the projectile motion problems. so the force applied on thatobject in order to get this type of acceleration would be--you just multiply mass times acceleration. the force would have had to be9.8 kilogram times the meter. kilogram.

times meter oversecond square. that's the force appliedon the object. and you're saying, sal,this is very messy. i don't like writing kilogrammeters per second squared. and you are in luck becausethere is a unit and that unit is the newton. 1 newton is equal to 1 kilogram meter per second squared. so if i'm pulling down on anobject at 9.8 newtons, that's

just this, right? this is 1 newton. if i'm pulling down at 9.8newtons on an object that is 1 kilogram, its acceleration isgoing to be 9.8 meters per second squared down. and notice i said the word down,but i didn't write it anywhere in the formula. and i guess we can imply thatboth force and acceleration have direction by writingthis in the formula.

that force is a vector andacceleration is a vector. and so we could have written9.8 newtons-- i don't know. you'll never see thisconvention. we could say newtons down isequal to 1 kilogram times 9.8 meters per second down. so what can we do withthis formula? well we can solve problems.so let's say that i have an object. so my object weighs--not weighs.

the mass of my object. and i'll differentiate betweenweight and mass in a second. let's say the mass of someobject is-- i don't know-- 50 kilograms. that's how much anormal person might weigh or a light person. mass weighs 50 kilograms. andlet's say we're in an inertial frame of reference. we're in deep space, so we don'thave all these other-- the force of wind andthe force of gravity

acting on us, et cetera. my force, let's say i applyit to the right. so we know that forceis a vector. let's say i apply a force of--i don't know-- 100 newtons. and let's say i applyit to the right. so this is the object, 50kilograms. and i'm applying a force to the rightof 100 newtons. so what's going to happento this object? well, let's use the formula.

force is equal to masstimes acceleration. the force is 100 newtons. 100 newtons is equalto the mass. the mass is 50 kilograms.50 kilograms times the so we can divide both sides by50 and you get 100 newtons over 50 kilograms is equalto the acceleration. and it's 100 newtonsto the right. i'll use this littlearrow here. that's not a traditionalconvention, but that's how we

know it's to the right. so it's 100 divided by 50. so it's 2. we get this weird units here,newtons per kilogram is equal to the accelerationto the right. this is also going to be tothe right because the direction of the force is goingto be the same as the direction of the acceleration. so what is this, 2 newtonsper kilogram?

well, if you remember-- well youcould just guess that the unit of acceleration is metersper second squared. but let's show that thissimplifies to that. so we said earlier that-- letme just switch colors. that a newton is kilogram meterper second squared. and we're taking this newtonover this kilogram over kilogram, right? so that will cancel out withthat and you get meters per and you wouldn't have to do thison a test. essentially,

if you did everything right, youwould know that the unit acceleration is metersper second squared. so you would have theacceleration-- i'm just switching the two sides--is equal to 2 meters per second squared. and it'll be to the right. so that's useful. we just figured out based on howhard i push something, how fast it's going to acceleratewhile i push it.

and you could use thesame formula to figure out other things. let's say i know that an objectis accelerating-- let's say my acceleration is3 meters per second squared to the right. let's say to the left, justto switch things. and let's say that i know theforce being applied on it is-- i don't know-- 30 newtonsto the left. and i want to figureout the mass.

well you use the same thing. you say force, 30 newtons tothe left is equal to mass times 3 meters per secondsquared to the left. divide both sides by the 3meters per second and you get 30 newtons over 3 metersper second squared is equal to the mass. 30 divided by 3 is 10. you can figure out that newtonsis kilogram meters per so you're just left with10 kilograms is

it's very important that if yousee a problem where the answer's given in-- i don'tknow-- kilometers per second squared or you know, instead ofgiving it in kilograms it's giving it in grams or decagrams,you should convert back to kilograms or meters justso you make sure you're using the right units. and that tends to be frankly,i think, the hardest thing for people. and we'll do all of that whenwe tackle harder problems.

i think now is a good time backto actually differentiate between mass and weight. and you've probably thought thetwo were interchangeable, but they're not. mass is how much of anobject there is. you can almost view it as howmuch of the stuff there is or you can almost it view it--how many atoms there are. but even atoms have mass. so just how muchstuff there is.

and another way to view mass is,how much does the object resist change? and that actually fallsout of f equals ma. because if our mass is bigger,it's going to take a lot more force to make it acceleratea certain amount. if the mass is smaller it'lltake less force. so mass can be viewed as howmuch stuff there is, of an object there is. or you can view it as how hardis it to change what that

object is doing. if it's stationary, how hardis it to accelerate it? if it's moving, how hardis it to maybe stop it? which would essentiallybe decelerating. how hard is it to acceleratean object? weight is actually how muchis-- what is the force of earth upon an object? so you're weight would actuallychange if you go from one planet to another becausethe force of gravity changes.

so your weight is 1/6 on themoon as it is on earth because the pull of gravity is 1/6. but your mass doesn't change. there's still the same amountof sal on earth as there is on the moon. so your weight really-- when youask someone in europe and they say hey, you know, i weigh50 kilograms. you should say, no, you don't weigh 50kilograms. you weigh whatever 50 times 9.8 is.

that's like 400 something--you weigh 490 newtons or something. this is mass. and it's interesting because inthe english system, and all of us americans, we usethe english system. when we say that we weigh 10pounds, we're actually using the correct terminologybecause pounds are a unit of force. we're saying, if i weigh-- andi do weigh about 150 pounds.

that means the earth is thispulling on me with 150 pounds of force. and actually, turns out thatmy mass is measured in the unit called a slug, whichwe might discuss later. actually, we'll do some problemswhere we do it in the metric system and theenglish system. and i'll see you in thenext presentation.