Bite 7: Momentum. Mechanics: Momentum 1

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1 Bite 7: Momentum It s time for the last lesson of mechanics. After all this time, you now have a good working knowledge of the rules that govern almost all movement on this planet and beyond!! This lesson we get to learn about things crashing into one another!! Isn t physics fun?! We are going to learn about impulse and momentum. Momentum Let s start with momentum. Momentum can be defined as inertia in motion. Something must be moving to have momentum. Momentum is how hard it is to get something to stop or to change directions. A moving train has a whole lot of momentum. A moving ping pong ball does not. You can easily stop a ping pong ball, even at high speeds. It is difficult, however, to stop a train even at low speeds. Mathematically, momentum is mass times velocity, or Momentum=mv. The heavier something is and/or the faster it s moving the more momentum it has. The more momentum something has, the more force it takes to get it to change velocity and the more force it can apply if it hits something. Impulse Now let s discuss impulse. Impulse is a measure of force and time. Remember, force is a push or a pull, right? Well, impulse is how much force is applied for how much time. Mathematically it s impulse equals force x time or impulse = Ft. Think about baseball. When you hit a baseball, do you just smack it with the bat or do you follow through with the swing? You follow through right? Do you see how impulse relates to your baseball swing? If you follow through with your swing, the bat stays in contact with the ball for a longer period of time. This causes the ball to go farther. Follow through is important in golf, bowling, tennis and many sports for the same reason. The longer the force is imparted, the farther and faster your ball will go. Impulse and Momentum Ok, let s add impulse and momentum together and see what we get. Impulse changes momentum. If an object puts an impulse on another object, the momentum of both objects will change. If you continue to push on your stalled car, you will change the momentum of the car right? If you are riding Mechanics: Momentum 1

2 your bike while not paying any attention and crash into the back of a parked car, you will put an impulse on the car and you and the car s momentum will change. (As a kid, I did this pretty often. That s what you get when you ride and wonder at the same time. Believe me when I tell you that my momentum changed a lot more than the car s did!!) In fact, there is a mathematical formula about this impulse and momentum thing. Impulse = change in momentum or Ft = change in mv. Force x time = mass x velocity. Does that sound familiar to anyone? It s awfully similar to Newton s second law (F=ma) isn t it? In fact it s the same thing. (Alert, alert serious math here, feel free to skip this. Ft=mv. Now if we divide both sides by t we get F=mv/t. Another way to say v is d/t (distance over time). So now we have F=m(d/t)/t. Those two t s together are the same as t 2 and d/t 2 is a. So what we have now is F=ma! Phew, a little mathematical mumbo jumbo for you.) This Ft = mv is very important, in fact, it can save your life. Seat belts, air bags, crumple zones and other car safety features are based on this formula. When you want to shrink the force of impact, you want to increase the time the impact takes. This is called the collision time. The longer the collision time the longer it takes your momentum to come to zero. Here s the math. If you are in a 1000 kg vehicle moving at 30 km/h your momentum is 1000 x 30 or 30,000. Now, lets say you hit a brick wall so your momentum goes from 30,000 to 0 in.5 seconds. Ft=mv so F(.5) = 30,000 so F= 60,000N! (N is for Newton which is a unit of force. It takes about 1 Newton to lift an apple so this car hits with the force of 60,000 apples! Talk about apple sauce!) That s gonna leave a mark! Now lets say that instead of hitting a brick wall you hit a mound of hay and so the impact takes 3 seconds. Now the formula looks like this: F(3)=30,000 or F= 10,000N. See the difference, 60,000N versus 10,000N of force. All those safety features, seat belts, helmets, air bags, are designed to increase how long it takes your momentum to come to zero. Newton s laws to the rescue! Let s do a couple of experiments here to help this information have more impact (pun intended!). Mechanics: Momentum 2

3 Experiment 1 Hitting a Brick Wall You need: A pillow A wall Your fist I hope I don t have to say this but take it easy with this one! I don t want anyone getting hurt out there so don t get carried away! 1. Find a wall. 2. Hit it with your bare fist. Take it easy, just hit it with enough force that you feel the impact. 3. Now put a pillow in front of the wall and hit it with about the same force as you hit it before. 4. With the pillow in front of the wall, you can hit it a little harder if you like but again, don t go nuts! What did the pillow do? It slowed the time of impact. Remember our formula Ft=mv. When the momentum of your moving fist struck the wall directly, the momentum was cut to zero instantly and so you felt enough force to hurt a bit. When the pillow was in the way it took longer for your momentum to come to zero. So you could hit the pillow fairly hard without feeling much force. Basically a bike helmet is like a pillow for you head. It slows the time of impact, so when you fall off your bike, there is much less force on your head. Just be glad your mom doesn t make you wear a pillow on your head! Mechanics: Momentum 3

4 Experiment 2 Egg Safety (A movie of this is available at You need An egg or two Stuff you have handy, popsicle sticks, tissue, rubber bands, napkins, etc. A ladder or a chair Newspaper This could get messy so make sure you have an adult s permission for this one. Besides, they will probably want to try this with you anyway! Your goal here is to drop the egg from at least 8 feet up and not have the egg break. If you dropped an egg from this height unprotected it would break, right? So you need to create a safety cage for your egg! Keep our new formula in mind, Ft = mv. The less velocity your egg has, the safer it will be. The longer it takes the egg to go from full momentum to zero, the safer it will be. Your goal is to make the force the egg hits the ground with less than the force required to break the egg. Once you ve made your contraption, get up on a ladder or a chair and drop it. Please be careful on the ladder or the chair. I would also recommend putting newspaper on the ground to help clean up any messes. This is fun to try with water balloons instead of eggs too. Good luck!!! Conservation of Momentum So let s go back to momentum for a minute. Momentum is inertia in motion. It is how much force it takes to get something to slow down or change direction. One more concept I d like to give you this month, is conservation of momentum. This is basically momentum equals momentum or mathematically mv=mv. (Momentum is mass times velocity.) When objects collide, the momentum that both objects have after the collision, is equal to the amount of momentum the objects had before the collision. Let s take a Mechanics: Momentum 4

5 look at this with this experiment. (Also see the Newton s Swing video at for a good example of this concept.) Experiment 3 Crashing Presidents You need: Several coins Smooth flat table 1. Put one penny on the table. 2. Put another penny on the table about 6 inches away from the first one. 3. Now, slide one penny fairly fast towards the first penny. 4. What you want to have happen, is that the moving penny strikes (or gives impulse to) the stationary penny head on. The moving penny should stop and the stationary penny will move. 5. Now, try that with other coins. Make big ones hit small ones and vice versa. It s also fun to put a line of 5 coins all touching one another. Then strike the end of the line with a moving penny. This is conservation of momentum. If you were able to strike the penny head on, you should have seen that the penny that was moving, stopped, and the penny that was stationary moved with about the same speed of the original moving penny. Conservation of momentum is mv = mv. Once the moving penny struck the other, all the moving penny s momentum transferred to the second penny. Since the pennies weighed the same, the v (velocity) of the first penny is transferred to the second penny and the second penny moves with the same velocity as the first penny. What happens if you use a quarter and a penny? Make the quarter strike the penny. That penny should really zip! Again mv=mv. The mass of the quarter is much greater then the mass of Mechanics: Momentum 5

6 the penny. So for momentum to be conserved, after impact, the penny had to have a much greater velocity to compensate for its lower mass. Mathematically it would look like this (the masses are not accurate to make the math easier to see.) After collision Mass of Quarter x Velocity of Quarter = Mass of Penny x Velocity of Penny 5g x 10m/s = 1g x v 50 = 1 x v 50/1 = v 50m/s = v or 5g x 10m/s = 1g x 50 m/s 50 momentum = 50 momentum After the collision, the penny is moving at 50 m/s, 5 times faster then the quarter was moving because the penny is 5 times lighter then the quarter. Mechanics: Momentum 6

7 Experiment 4 Super Rocket Bus (A movie of this is available at If this looks familiar, it s because we did it during the last lesson as well. We re going to do a little more with it this time. This experiment will pop a cork out of a wine bottle and make it go 20 to 30 feet, while the bus moves in the other direction! This is an outdoor experiment. Be careful with this. The cork comes out with a good amount of force. Don t point it at anyone or anything. Don t point it at yourself. What you need: Wine bottle Cork (be careful that the corkscrew didn t go all the way through it) Baking Soda Vinegar Paper towel Fairly large Toy Car, Truck or Bus Duct Tape Flat Sidewalk or Driveway 1. Strap the wine bottle to the top of the toy bus with the duct tape. You want the opening of the bottle to be facing the back of the bus. 2. Put about one inch of vinegar into the bottle. 3. Shove a wad of paper towel as far into the neck of the bottle as you can. Make sure the wad is not too tight. It needs to stick into the neck of the bottle but not too tightly. 4. Pour baking soda into the neck of the bottle. Fill the bottle from the wad of paper all the way to the top of the bottle. 5. Now put the cork into the bottle fairly tightly. Mechanics: Momentum 7

8 6. Now tap the whole contraption hard on the ground outside to force the wad of paper and the baking soda into the bottle. 7. Give the bottle a bit of a shake. 8. Set it down and watch. Do not stand behind the bus where the cork will shoot. 9. In 20 seconds or less, the cork should come popping off of the bottle. 10. Do the entire thing again, but this time make the cork heavier. I wrapped mine in duct tape and then jammed a roll of electrical tape on the end. If you wanted to tape a golf ball to the cork or tape a bunch of change to it it would work as well. Just try to make the cork a good bit heavier than it was in the first place. This is a great example of impulse as well as conservation of momentum. The impulse (Ft) is the baking soda and vinegar gas mixture creating enough pressure to force the cork off the bottle. According to Newton s Third Law, the force from that impulse has an equal and opposite reaction, so the bus goes one way and the cork goes the other. Now take that information and combine it with what you now know about conservation of momentum. The impulse is equal for the cork and the bus, so which one is going to have more velocity due to it s lighter mass? The cork. mv=mv. Just like the penny and the quarter, the lighter cork will go farther than the heavier bus. Now if you make the cork heavier and try it again, what will you see? Now the bus moves farther but the cork moves less far. Again, conservation of momentum, mv = mv. Let s try this same thing a different way. Mechanics: Momentum 8

9 Experiment 5 You re Too Pushy You need: A wagon A skateboard 2 humans You can do this with any two wagon or skateboard like things. The important part of the equipment is that you can sit on them and have your two arms relatively free. 1. Put the wagon and the skateboard close to one another. 2. Have one person sit on the skateboard while the other sits on the wagon. 3. Make sure the wheels are straight on the wagon and that the sidewalk is relatively free of stuff in the way. 4. Have one person give a good shove to the other person. Usually, it is easier for the person on the skateboard to push on the wagon. If this is true with your setup, then do it that way. Otherwise, do whatever is easiest. 5. Feel free to add more people or weight to the wagon and try it again. Can you see how this and the Rocket Bus experiment are really showing the same concept? Who went farther and faster? The lighter person on the lighter vehicle right? The impulse of the push was the same for both vehicles, so both vehicles had the same momentum. Momentum is mass and velocity so if the mass for both vehicles was the same, the speed would be the same. If the mass of one was more then the mass of the other, then the heavier one would move more slowly then the lighter one. Mechanics: Momentum 9

10 In a Nutshell Impulse is the amount of time a force is put on an object. How hard and how long something gets pushed or pulled. Ft = Impulse. Impulse affects the momentum of an object. Momentum is inertia in motion, how hard it is to get something to change directions or speed. Momentum = mv. Conservation of momentum; mv = mv. If something hits something else the momentum of the objects before the collision will equal the momentum of the objects after the collision. Mechanics: Momentum 10

11 Did You Get it? Try your hand at these questions to see if you ve got the concepts. If you re not sure of something, go back to the text above. The answers are later in this chapter. 1. What is momentum? 2. Which has more momentum, a stopped train or a moving ping pong ball? 3. What is impulse? 4. What does this formula mean? Ft = mv 5. Which would create more of a change in the momentum of a base ball. A fast ball thrown into a brick wall, or a fast ball hit by a bat? 6. What is conservation of momentum? 7. Tell me what conservation of momentum has to do with a hammer pounding in a nail. 8. If you weigh 100lbs and are on a skateboard, and you push a 300lb linebacker on another skateboard, which one of you moves farther? Assume both skateboards are exactly the same and both are at rest. 9. If you are chopping wood, why would you want a heavy ax head? 10. If mv = mv why wouldn t a baseball player want the heaviest bat he could swing to impart the most momentum possible to the ball? 11. So, what does Newton s Second Law (F=ma) have to do with question 10? Mechanics: Momentum 11

12 Answers Answers to Did You Get It 1. Momentum can be defined as inertia in motion. Something must be moving to have momentum. Momentum is how hard it is to get something to stop or to change directions. Momentum = mass x velocity 2. The ping pong ball. If the train is not moving it has no momentum. Something must be moving to have momentum. 3. Impulse is a measure of force and time. It s a measure of how long a force is applied to an object. The larger the impulse, the more the object receiving the impulse will change its momentum. Impulse = Force x time. 4. Force x time = mass x velocity. Impulse changes momentum or a change in momentum equals an impulse. 5. A base ball would have its momentum changed more if it is hit by a bat. The impulse of the bat with a higher force and a longer time of impact would change the momentum of the ball much more than the wall who s impulse would only be for a very short time. 6. If something hits something else the momentum of the objects before the collision will equal the momentum of the objects after the collision. mv = mv 7. The hammer has a lot of momentum due to its large mass and its high velocity. When it hits the nail, momentum is conserved so the very light nail suddenly has a great velocity. This helps pound the nail into the wood. 8. You do. Since you weigh so much less and since momentum is conserved, you gain more velocity from the initial impulse and as such you move farther. (By the way, don t try this at home, I hear linebackers can get cranky.) 9. The heavier the head of the ax and the faster you swing the ax, the more Mechanics: Momentum 12

13 momentum the ax will have and the deeper the ax can sink into the wood. 10. He would...except for Newton s Second Law. Take a look at question Force = mass x acceleration. The more mass something has the more force that s required to accelerate it. If a baseball player used a tree trunk as a bat, he would have a very difficult time getting much speed out of it. Also, as the pitch comes in, the ball often moves so the player needs to adjust the trajectory of the bat as he swings it. The heavier the bat, the more momentum the bat has and as such the harder it is to change the bat s direction. In baseball, you want the heaviest bat that you can easily swing. Mechanics: Momentum 13

14 A Little Math The following math is all done in metric. I usually like doing the math in english units since most of us have a much better feeling for the english units than we do for metric units. These formula s however are dealing with Newton s. A Newton is a metric unit of force so we need to convert all the other units to metric as well. As always, the math is here in case you want it. It is not necessary to do the math section in order to get a good feeling for the concepts. Impulse = Ft 1. What impulse is put on a car if you push it with 20 N for 30 seconds? 2. If an apple takes.3 seconds to bounce off your head with one N of force, how much impulse does it put on your head? 3. What if a water melon bounced off your head with 10N of force (also.3 seconds)? Momentum = mv 4. What momentum does a 2000kg (about 2 tons) van have if it is moving at 13m/s (30 mph)? 5. What momentum does a.005kg ping pong ball have if it s moving at 13 m/s? Momentum and Impulse mv = Ft 6. How fast will a 10kg cannon ball go if it is fired with a force of 20N over 2 seconds? 7. How fast will a.2 kg base ball go if it is fired with a force of 20N over 2 seconds? Mechanics: Momentum 14

15 Conservation of Momentum mv = mv 8. If a 10kg bowling ball moving at 2 m/s collides with a 5kg bowling ball standing still, how fast will the lighter bowling ball be going after the collision? 9. If a 5kg bowling ball hits a 10 kg bowling ball that is not moving at 2m/s how fast will the bowling ball be going after the collision? 10. If a 2 kg (about 5lbs) bat moving at 18m/s (40mph) hits a.2 kg (half a pound) baseball off a tee, how fast will the baseball be going? Mechanics: Momentum 15

16 Answers to A Little Math 1. Impulse = 20N x 30sec Impulse = Impulse = 1N x.3 sec Impulse =.3 3. Impulse = 10N x.3 sec Impulse = 3 (ouch!) 4. Momentum = 2000kg x 13m/s Momentum = Momentum =.005kg x 13m/s Momentum =.065 (Big difference huh?) 6. 10kg x v = 20N x 2sec 10kg x v = 40 v = 40/10 v = 4 m/s (about 9 mph) 7..2kg x v = 20N x 2 sec.2 x v = 40 v = 40/.2 v = 200m/s or 450 mph (You might want to duck!) 8. 10kg x 2 m/s = 5kg x v 20 = 5 x v 4m/s = v 9. 10kg x v = 5kg x 2m/s 10kg x v = 10 v = 10/10 v=1 m/s kg x 18 m/s =.2 kg x v 36 =.2 x v 36/.2 = v 180 m/s (400mph) = v Mechanics: Momentum 16