in this video I'm going to do a quick review of impulse and momentum we're going to go over the key formulas that you need to pass your next exam by the way for those of you who want example problems including a practice test on this topic feel free to check out the links in the description section below so let's begin the first Formula you need to be familiar with is this momentum is mass times velocity as a vector you could describe it this way momentum is a vector mass is scalar but velocity is a vector so let's say if you have a block that rests across a horizontal floor and let's say this is a 10 kgam block and it's moving at a speed of 6 m/ second the momentum of this block is going to be 10 kg that's the mass times the velocity of 6 m/s and so the momentum is going to be 60 with the units kilog time m/s so that's how you can calculate momentum it's simply mass time velocity think of it as mass in motion so make sure you write this down this is the first equation that you want to know for your test now the next thing you need to know how to calculate is impulse now some textbooks may use the letter J for impulse sometimes I've used J sometimes I use I I for impulse but also I could represent inertia too so but impulse is equal to force multiplied by time that's how you calculate impulse so imagine if you have a block and if you apply a force of 100 Newtons for a time period of 8 seconds in previous chapters you've learned about forces but in this chapter with impulse now we've Incorporated time with Force how long is the force being applied to an object because that's important so here we have a force of 100 Newtons being applied on its object for 8 seconds the impulse imparted to this object is going to be F delta T so it's 100 Newtons * 8 seconds which is 800 Newton seconds so that's how you can calculate impulse impulse tells you how much force is being applied to an object for a certain amount of time period so an Impulse of 800 can mean many things it could be you're applying a force of 100 Newtons for 8 seconds or you're applying a large force of a th000 new for 8 seconds so it just tells you you know how much force you're applying for the amount of time period combined now impulse and momentum they're related impulse is equal to the change in momentum and here's how we can derive that so according to Newton's Second Law force is equal to mass time acceleration and we know that the acceleration is the rate at which velocity changes with respect to time acceleration is the change in velocity divided by the change in time perhaps you remember this equation V final is equal to V initial plus a t if you solve for acceleration it will be V final minus V initial over time in other words it's the change in velocity with respect to time now if we multiply both sides by delta T we get that F delta T is equal to M Delta V on the left Force multiplied by time gives us impulse on the right we know that masstimes velocity is momentum so mass times the change in velocity is the change in momentum so this is related to the impulse momentum theorem now typically the formula that you need to use when solving problems with this topic is this equation this is the form of the equation that's going to be most helpful so that is the impulse momentum theorem so make sure you know these three equations number one momentum is mass times velocity number two impulse is force multiplied by time number three the impulse momentum theorem F delta T is equal to M Delta V now going back to Newton's Second Law particularly this form there's a there's a lot of other equations that we can get from this form so I'm going to adjust this equation let's say if you have a person and he has a water hose in his hand and out of it he's going to shoot out water let's say water is coming out of the hose at a speed of 20 m/ second so that's how fast it's coming out and then we need to talk about the quantity of water coming out there's something called the mass flow rate so let's say water is leaving at a mass flow rate of 5 kg per second this equation can help us to calculate the force that this fluid will exert on an object let's say if you're blasting out water from the host on a block we can calculate the force exerted by the water on this block so I'm going to move delta T to this position under M so we can describe forces as being the mass flow rate Delta M over delta T time V so instead of the change in velocity we have the change in mass in this case the velocity of water coming out of the Hol is is going to be relatively constant so in this problem the mass flow rate is 5 kg per second so every second 5 kog of water is coming out of that hose now the speed of the water is 20 m/s when we combine these two we get a force of 100 Newtons that's going to be the force exerted by the water on the Block so that's another way in which you can calculate the force that a fluid exerts on an object this could be a fluid like water it could be a fluid like air as long as you know the mass flow rate and the speed at which that fluid is moving you can calculate the force I should really highlight this equation so this is the fourth equation you want to know force is equal to mass flow rate multiplied by the velocity now for those of you who are taking calculus with physics the next Formula is going to be more applicable to you so going back to this equation instead of trying to get the mass flow rate from this equation we're going to focus on this part we know that masstimes velocity is momentum so mass times the change in velocity is the change of momentum so this is another way to describe force force can also be described as the rate at which momentum is changing in other words force is the derivative of the momentum function with respect to time so if you know the function for momentum you can get the function for force with respect to time so F of T this is force as a function of time is the derivative of the momentum function so these are some other ways in which you can calculate the force acting on an object if you know the momentum function so I would write these equations number five and number six you can add those to your notes now let's talk about the conservation of momentum so let's say we have a horizontal frictionless floor and we have block one let's say block one is moving at a speed of 2 m/s and it strikes block two afterward the two blocks they stick together and they're moving at the same speed and you want to find out what this final speed is here we have what is known as an inelastic collision whenever you have two objects colliding if they stick together it's a collision but it's in elastic because you're going to have loss of kinetic energy for elastic collisions both momentum and energy is conserved kinetic energy but for inelastic collisions only momentum is conserved so this is an example of an inelastic collision anytime they stick together and they don't bounce off you're dealing with an inelastic collision momentum is conserved but kinetic energy is not conserved for for an in inelastic collision so before the Collision we have the momentum of object one M1 V1 Plus momentum of object two after the Collision we're going to have the momentum of both objects as well so this is the conservation of momentum formula you want to make sure you write this down the basic idea behind this equation is that the total momentum of the system before the Collision is equal to the total momentum of the system after the Collision assuming no external forces are acting on a system because if there are external forces they will change the total momentum of the system so this only holds true if there are no external forces acting on the system so make sure you add this equation this is number seven now for this particular problem because they stick together V1 final and V2 final they're the same they just equal V F so for this particular situation you could shorten this equation to this form it's going to be M1 + M2 times the final speed because they stick together so they move at the same final speed so for any conservation of momentum problem you could use equation 7 but if they stick together at the end the two objects after they Collide you could use equation 8 to solve it now let's say if we have a ball moving at a speed of 6 m/ second and then strikes ball two which was initially moving at 2 m/ second and then they bounce off each other ball one goes back in this direction let's say at 3 m/ second and you're trying to find out the speed at which ball two uh moves in the to the right in other words you're trying to find V2 final a lot of times not always if they bounce off each other it could be an elastic Collision but you want to make sure the problems specify that so if it's a perfectly elastic Collision that means that kinetic energy is conserved as well as momentum so for this problem you would need to use equation 7 to solve it so you have the conservation of momentum equation now you're also let's say if you don't know this speed because if you know V1 final you can probably just use this equation to get the answer but if you don't know V1 final you need another equation to solve this so this is when you need to use conservation of energy that is the total initial energy is equal to the total final energy so this would be K initial or K1 plus ke2 equals K1 final plus K2 final now this form of the equation this going to be a lot of work a lot of algebra if you use it but if you want to get the answer faster you could use the simplified equation that comes from this equation and that equation is this which we'll describe as number 10 V1 plus V1 final is equal to V2 plus V2 final so if you have an elastic Collision where you're missing the final speeds of both objects you need to use equation seven and equation 8 to solve it so you need to write a system of equations to figure that problem out if you're given V1 final but not V2 you could just use equation 7 but if you're missing two variables you have to use two equations to solve two variables so you'll need equation 7 and 10 I do have example problems on this on my other videos on YouTube so uh feel free to take a look at that when you get a chance and you might see this also on my practice test too so that's basically it for this video those are the main equations you need for this chapter on impulse and momentum as well as elastic collisions and in elastic collisions thanks for watching