Before we get into Newton’s Second Law, we need to get up to speed with acceleration. In physics acceleration is defined as a change in velocity. In other words, it is a change in speed or a change in direction. It is how much time it takes something to go from one velocity to another. Remember that velocity is speed and direction. If you go straight ahead on your bike at a constant speed of 5 mph you are not accelerating. Neither your speed nor your direction is changing. Now, if you are stopped at a stop light and it turns green, you are accelerating as your speed increases from 0 mph to 10 mph. The same thing happens if you are traveling at a nice even 10 mph and slow to a stop. In physics we don’t use the word deceleration. We use positive and negative acceleration. Now what happens if you are in a car and it turns a corner at a constant speed of 15 mph? Is it accelerating or not? Well, its speed is not changing but its direction is, so it is indeed accelerating. Remember back when we talked about gravity? We learned that gravity accelerates things at 32 feet per second². Now this may make a little more sense. Gravity made something continue to increase in speed so that after one second of having the force of gravity pull on something, that something has reached a speed of 32 feet per second. When that thing started falling it was at 0 velocity, after a second it’s at 32 feet per second after 2 seconds it’s at 64 feet per second and so on. It’s the old formula v=gt or velocity equals the gravitational constant (32 ft/s²) times time. If something has an acceleration of 5 ft/s² how fast will it be going after 1 second...2 second...3 seconds? After one second it will be going 5 ft/s; after two seconds 10 ft/s; and after three seconds 15 ft/s. Again, it’s just like v=gt (v is velocity, g is the gravitational constant, t is time) but put the rate of acceleration of the object in place of g to get the formula v=at or velocity equals acceleration times time. Let’s do an experiment to make this more clear. This experiment is reportedly an experiment that Galileo did hundreds of years ago. Experiment 1 Fast, Faster, Fastest (A movie of this is available at http://www.bitesizephysics.com/physicsmovies.html.)
You need: At least 3 feet of fairly smooth board. A slightly sloping drivewayworks well too. Books, wood chunks, something to prop one end of the board up on A hard smooth ball (a golf ball, racket ball, pool ball etc.) A timer Pencil Paper Measuring tape or yard stick
1. Place the board on the books or whatever you use to make the board a slight ramp. You really don’t want it to be slanted very high. Only an inch or less would be fine. If you wish, you can increase the slant later just to play with it. 2. Put a line across the board where you will always start the ball. Some folks call this the “starting line.” 3. Start the timer and let the ball go from the starting line at the same exact time. 4. Now, this is the tricky part. When the timer hits one second, mark where the ball is at that point. Do this several times. It takes a while to get the hang of this. I find it easiest to have another person do the timing while I follow the ball with my finger. When the person says to stop, I stop my finger and mark the board at that point. 5. Do the exact same thing but this time, instead of marking the place where the ball is at one second, mark where it is at the end of two seconds. 6. Do it again but this time mark it at 3 seconds. 7. Continue marking until you run out of board.
Take a look at your marks. See how they get farther and farther apart as the ball continues to accelerate? Your ball was constantly increasing speed and as such, it was constantly accelerating. By the way, would it have mattered what the mass of the ball was that you used? No. Gravity accelerates all things equally. This fact is what Galileo was proving when he did this experiment. The the weight of the ball doesn’t matter but the size of the ball might. If you used a small ball and a large ball you would probably see differences due to friction and rotational inertia. The bigger the ball, the more slowly it begins rolling. The mass of the ball, however, does not matter. Now if you want to whip out your calculators you can find out how fast your ball was accelerating. Take your measuring tape and measure the distance from the starting line to the line you made for the distance the ball traveled in one second. Let’s say for example that my ball went 6 inches in that first second. Dust off those old formulas and lets play with d=1/2gt² where d is distance, g is acceleration due to gravity and t is time. We can’t use g here because the object is not in free fall, so instead of g let’s call it “a” for acceleration. Gravity is the force pulling on our ball but due to the slope, the ball is falling at some acceleration less then 32 ft/s². In this case, d is 6 inches, t is 1 second and a is our unknown.
With a little math we see: 6in=1/2 a 1sec² or 12in/sec²=a
So our acceleration for our ramp is 12in/sec² or we could say 1ft/s². With a little more math we can see how far our ball should have traveled for each time trial that we did. For one second we see that our ball should have traveled d=1/2 12(12) or d= 6 inches (we knew that one already didn’t we). For two seconds we see that d=1/2 12(22) or d=24 inches. For three seconds we see that d=1/2 12(32) or d= 54 inches. You can see why we need a pretty long board for this huh? Do your calculations match your results? Probably not. Our nasty little friend friction has a sneaky way of messing up results. You should definitely see the distance the ball travels get greater with each second however. Acceleration is the rate of change in velocity. In other words, how fast is a change in speed and/or a change in direction happening. Velocity is speed and direction. A formula for acceleration can be a=change in velocity/time
1. What is acceleration? 2. If a car is going 35 mph and comes to a stop at a stop sign. Did it accelerate? 3. Is the moon accelerating?
Use d=1/2 at² for these problems. d is distance, a is acceleration, and t is time. (Feel free to skip these if math is not your thing.) 4. How far will a gerbil go in 4 seconds if it continues to accelerate at a rate of 3 ft/s²? 5. How fast is something accelerating if it has fallen 50 feet in 10 seconds?
Answers 1. Acceleration is the rate at which velocity is changing. In other words, it is the rate speed and/or direction is changing. 2. Yes, it changed speed and you could say it accelerated negatively since it lost speed. (Remember, there’s no such thing as deceleration in physics.) 3. Yup, did I get you with that one? I get most folks. The Moon is not changing speed but it is constantly changing direction. 4. d=1/2 at² d=1/2 3ft/s2(4s)² d= 1.5ft/s2(16s²) d= 24 ft 5. d=1/2 at² 50ft=1/2 a(10s)² 50ft=1/2 a(100s²) 50ft/100s²=1/2 a .5ft/s²=1/2 a 1ft/s²=a | ||