Newton s Second Law Newton s second law is the toughest of his laws to understand, but it is very powerful. In its mathematical form, it is so simple it s elegant. Mathematically it is F=MA or Force = Mass x Acceleration. An easy way to remember the formula is to think of your mother trying to get you out of bed in the morning. Force equals MA! What is Force Anyway? We ve been talking a lot about force this and force that, but what does that mean? Well, trust the force Luke, I m about to tell you. (Sorry, but I had to get one movie quote in here somewhere. I just couldn t help myself!). Force is generally defined as a push or a pull on something. Forces can come from gravity, magnetism, something mechanical, muscle or from a variety of other places. If you look more carefully, you will discover that most forces we have daily contact with originate with gravity or electromagnetic force. Machines and muscles all get their power through electromagnetic force and pretty much everything that moves down is doing so because of or with the help of gravity. Another way to look at Newton s first law is to say that nothing s going to happen without a force. Things won t start moving, stop moving, or change direction without a force being put upon them. The more mass or speed something has, the more force is needed to change its state of inertia. Newton s Second Law Newton s second law can be understood in a few different ways. Usually we see Newton s second law written in formula form as F=MA. We can understand the formula as a way of saying that the combination of mass and acceleration gives us force. The more mass or acceleration something has, the more force it will put on whatever it hits. For example, a car colliding with something at 30 mph will hit a lot harder than a ping pong ball colliding with something at 30 mph because the Mechanics 57
car is so much heavier. Similarly, if you had two cars of exactly the same weight, but one was traveling at 30 mph and the other at 60 mph, the faster car would would hit something a lot harder than the slower car would. But Jim, you may be thinking, if a car is traveling at 30 mph or 60 mph, wouldn t that be its speed or velocity, not its rate of acceleration? The formula isn t Force =Mass x Speed. Good question. As long as the car is traveling at a constant rate of speed in a given direction, that speed is its velocity, but when it hits something, what happens? It slows down, right?! As we learned in the chapter on acceleration, in physics acceleration is defined as any change in speed or direction whether that is going faster or slower or veering off in a new direction. If something slows down, it is accelerating negatively, but it is accelerating. Newton s second law can also be written as A=F/M. How much an object accelerates is affected both by the amount of force put on it and by its mass. The more mass something has, the more force will be needed to get it to accelerate; in other words it will be a lot harder to push a car 3 feet than it will to push a ping pong ball three feet. Another way of looking at it is, the more force you use, the quicker the acceleration. When a 5 year old hits a baseball, it doesn t get going all that fast, but when Barry Bonds hits it, look out!! Yet another way of using the formula is to define mass as M=F/A. In other words, the amount of mass something has can be figured out by finding out how much force it takes to accelerate it, or by seeing how much force it applies when it is accelerating. The importance of force and acceleration in defining mass is a major difference between mass and weight. Something with great weight on Earth may be almost weightless in space (since there s no gravity) but it will still be difficult to get it to accelerate because of its mass. It can also still do a lot of damage if it hits your space station, even though it s weightless! So force = mass x acceleration. Let s try a couple of experiments and see if we can make all the different ways of looking at F=MA make sense. Mechanics 58
Let s Find Out: Little Red Mass You Need: A wagon Something heavy to put into the wagon: weights, rocks, toys, friends whatever is big and handy You This activity is very similar to the Little Red Inertia activity that we did in the inertia lesson but I want you to pay attention to something else here. 1. Start with an empty wagon, 2. Pull it as fast as you can. In other words, get it to accelerate as quickly as possible. 3. Now add weight. Put something in the wagon that weighs at least 50 lbs or so. 4. Pull it again and get it to accelerate as fast as you can. 5. Add more weight and do it again. 6. Keep adding weight until you have a very difficult time getting it to accelerate. So what happened here? Force equals mass x acceleration. The mass was the wagon and whatever was in it. The force was you pulling. The acceleration was how fast you could get it to speed up. The heavier you made the load in the wagon (the more mass there was), the harder you had to pull (the more force you had to apply) to get the wagon to move (to accelerate). Mechanics 59
Acceleration, Terminal Velocity and Newton s Second Law In this next activity, we are going to combine acceleration and terminal velocity to explore Newton s second law a little further. I accidentally discovered this activity with my daughter s toy car and my driveway. Are you ready? Here we go. Let s Find Out: It s All Downhill A movie of this experiment is available at www.bitesizephysics.com. Click on Bite-Size Movies and go to the Mechanics section. You need: Something slightly slanted, a slanted driveway works great, a long board with one end propped up a little works well too. Something to move down the slant. A toy car, a tennis ball, a skate board. Stopwatch Pen and Paper I m going to assume you re using the toy car and a driveway. Feel free to modify my wording for whatever you are using. 1. Take the toy car to the top of the driveway. 2. Let it go. 3. Watch it carefully as it rolls. 4. Time the car and mark how far it goes every second like we did in Fast, Faster Fastest in the chapter on acceleration. 5. Measure the distances your car went each second and write them down. What you should see here is that the car accelerates from zero to a certain velocity but then stays at that velocity as it continues down the driveway. In other words, it reaches its terminal velocity. If you timed Mechanics 60
and marked the distances, you should have seen that the car went the same distance each second if it did indeed reach its terminal velocity. If the object you are using to roll down the slant, continues to accelerate down the entire ramp, see if you can find a ramp or rolling object that has some more friction to it or a ramp that is less slanted. Don t Forget Friction! Ok, so what s going on? F=MA right? Acceleration can t happen without force. What force is moving the car? (Imagine the Jeopardy theme song here). If you said gravity, give yourself a handshake. But wait a minute! When the car is going at a constant velocity, is it accelerating? Nope, acceleration is a change in speed or direction. But Jim, you just said that gravity is the force that causes acceleration on my car and yet my car is not always accelerating even though gravity is always pulling on it. Why not? Well, there s one little thing I haven t mentioned yet, which is why we did this activity. Another force is affecting the speed of your little car and that would be...friction! When terminal velocity is reached, the force of gravity pulling the car down the slant and the force of friction slowing the car down is equal. Remember, we learned before that terminal velocity is reached when the force of gravity pulling down is equal to the force of friction resisting the pull of gravity. In the case of our car, there will be friction from the surface it is rolling down and air friction. When our car was traveling the same distance each second, the net force on the car was zero. The pulling force of gravity was equal to the holding force of friction so there was zero force on the car. Force is measured in newtons (name sounds familiar right?) so imagine that there are 3 newtons of force pulling on the car due to gravity and 3 newtons of force holding the car in place due to friction. 3-3 = 0. Zero force equals zero acceleration because you need force to have acceleration. By the way, 1 newton is about the same amount of force that it takes to lift an apple. The video Net Force may help illustrate this concept as well. It is available at www.bitesizephysics.com. Click on Bite-Size Movies and go to the Mechanics section. Mechanics 61
Conclusion To finish things off, here is just one more amazing example of Newton s second law: Let s Find Out: Newton s Amazing Bike Wheel A movie of this experiment is available at www.bitesizephysics.com. Click on Bite-Size Movies and go to the Mechanics section. You need: A bicycle wheel (it needs to be detached from a bicycle. The front wheel is pretty easy to detach.) A post to run through the center of the wheel to use as an axle A hook to attach to your axle on one side String 1. Carefully hold the bicycle wheel by the axle and give it a spin. Try to get it to spin as fast as you can but be VERY careful to hold onto it tightly and don t get your fingers caught in the spokes. It works well if someone else can spin it for you. 2. While it s spinning try to move it around. You ll find that the wheel does not want to be moved around and tries to do its own thing when you move it. 3. Take a string and loop it around the hook on your axle. Make sure that the hook is attached well to the axle and the string is strong enough to hold the weight of the wheel and then some. Spin the wheel fast and let go of the wheel while holding onto the string, keep- Mechanics 62
ing the wheel out and away from your body. The wheel will continue spinning and defy gravity by staying straight up and down. Really! Try it, it s very cool! The bike wheel activity we just did demonstrates the power of Newton s second law: Force equals mass times acceleration. The mass is the mass of the wheel, in particular the mass of the tire. The acceleration is the spinning wheel. Remember, acceleration is not just change in speed but also change in direction. Every point on the spinning wheel is constantly changing direction so the wheel is constantly accelerating. Since acceleration times mass has to equal force, (math says so) the spinning wheel has a force. This force is strong enough to defy gravity and is what you feel when you hold the axles of the wheel and try to move it. This same force is what keeps a top spinning, why footballs are thrown with a spiral, why satellites spin and so on. It s pretty incredible to think that a force can be created by nothing more than accelerating mass. Mechanics 63
In a Nutshell Force is a push or a pull on something. Acceleration is a change in velocity. In other words, a change in speed and/or a change in direction. Newton s second law is F=MA or force equals mass x acceleration. In other words, the more mass something has and/or the faster it s accelerating, the more force it will put on whatever it hits. Another aspect of Newton s second law is, the more mass something has, the more force that s needed to get it to accelerate. A=F/M Yet another aspect of Newton s second law is, the more force or acceleration that is required to get something to move, stop moving or change direction, the greater its mass must be. M=A/F Mechanics 64
Did You Get it? 1. What is force? 2. Does something with a lot of mass need a lot or a little force to get it going? 3. Newton s second law is...? 4. Newton s first law is...? 5. What makes an object change its motion? 6. What happens if something is moving downhill and the force of gravity is 4 newtons but the force of friction is 3 newtons? 7. If you are riding your bike and stop pedaling, why do you slow down? 8. If you are riding your bike on a level surface and air friction combined with the friction from the bike is a total of 10 newtons, how much force do you need to exert to keep moving forward at a constant speed? Use F=MA for these problems. F is force, M is Mass and A is Acceleration. 9. A 20 kg wagon is pulled with a force of 10 N. How fast does it accelerate? 10.A 40 kg sled experiences a friction force of 20N. What is its negative acceleration? 11.What force is being applied to a 30 kg bike that is slowing at 5 m/s 2? Mechanics 65
Answers 1. A force is a push or a pull on something. 2. A lot of force is needed to get an object with a lot of mass moving. 3. Force = mass x acceleration. 4. An object at rest tends to stay at rest, an object in motion tends to stay in motion unless an outside force acts upon it. 5. Force causes acceleration which is a change in motion (slowing down, speeding up or changing directions). 6. It speeds up. That something is accelerating because there is a net positive force of 1 newton. The force of gravity is greater than the force of friction. 7. The force of friction is acting on your bike, slowing you down. 8. 10 newtons. Any less and you slow down, any more and you speed up. If the net force equals zero, acceleration is zero, so there is no change in speed. 9. For this problem, F=10N or 10kg/m/s 2 (a newton is the amount of force it takes to move something 1kg per second per second), M=20kg and A is what we are trying to figure out. 10kg/m/s 2 =20kg(A) (10kg/m/s 2 )/20kg =A.5m/s 2 =A 10.Remember friction always slows us down and that negative acceleration simply refers to the fact that something is slowing down rather than speeding up. So we are really just solving for A (acceleration) in our trusty old formula. F=MA, our F is 20N (kg/m/s 2 ) and our M is 40kg. Let s figure out what A is. 20N=40kg(A) 20N/40kg=A.5m/s 2 =A 11.Here we know that our M is 30kg and A is 5m/s 2. Let s figure out what F is. F=MA Mechanics 66
F=30kg(5m/s 2 ) F=150 N Mechanics 67