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Notes: Free Body Diagrams Level 1: The Normal Force In this section, we are going to look at the different types of forces that can act on an object. We are going to learn the most common ones we see in physics. Weight You are already familiar with weight. Recall from the last section that weight (force of gravity) is: πΉπ = ππ Normal Force A normal force occurs when a surface pushes back on an object. For example, you are sitting in your chair, pushing down on the chair. The chair is pushing up the exact same amount. That means if your weight is pressing 500 N down, the chair is pushing up 500 N. For flat surfaces only, the force of gravity must be equal and opposite to the normal force. When an object is resting on a flat table, the total forces acting on it sum up to zero. We get a net force of zero because there are two forces acting on the object- gravity (which pulls the object down) and the normal force, which pushes back up, and these two forces cancel one another. You will see this written as FN or sometimes just N (thought I hate thisβ¦ it is out there). The forces in this situation are balanced, so the box could be doing one of two thingsmoving at a constant velocity or stilling still. It is not accelerating, unless another unbalanced force gets involved. An example of a resting object with weight and normal forces balanced is your book sitting on a table. An example of an object with the force of gravity and the normal force balanced that is moving at a pretty constant velocity is a hockey puck gliding across the ice. Level 2: Other Types of Forces Force of Friction Friction is a force that fights motion. If you push a box forward, friction will fight your motion. It tries to stop the box from moving. Key Idea Friction always acts in the opposite direction of motion. This means that if a ball is rolling forward across a field, friction is pushing backward. If you push a chair to the left, friction is pushing right. If you slide across the floor in your socks to the right, friction is pushing to the left. If you push a box across the floor, it seems like there is only one force acting on the box. Actually, there are four- the force of gravity (weight) pulling down, the normal force of the floor pushing back up, the force you are applying to the box, and the force of friction. The picture below shows the forces acting on the box. Imagine kicking a book across the floor. Newtonβs 1st Law says the book should go forever, but instead it slows to a stop. What stopped the book? Friction. Here is a picture of that happening: The box in this picture is moving to the right, slowing down. The force of gravity and the normal force are balanced, so they cancel out. That leaves the force of friction as the net force. It looks like the box should be moving to the right. Actually it is moving to the left and slowing down. Why is that? Forces donβt just speed objects up-they cause us to accelerate, which can mean slow down, speed up or change direction. In this case, the force dragging down the box, slowing it down. Force to Tension A force of tension is a force caused by a rope, string or cable pulling on it. You will see this written as F T or sometimes just T. If there is a rope- there is probably a force of tension. Air Resistance This is pretty much friction caused by air. You know, like the stuff that makes your dog look funny when he sticks his head out the window. If something is moving and there is air- there is air resistance. Spring Force The force of a spring acting on an object. We use this for anything stretchy or boing-y. When you go bungee jumping, you are relying on this force to keep you from crashing into the ground below. If there is a spring involved, there is probably a spring force. Force Applied We can use this for pretty much all the other forces acting on the object that donβt fit into the above categories. If a hand is pushing on a block, we can say it is an applied force. If you kick a soccer ball, we can say it is the applied force. You can use this for really any other force, until I tell you otherwise. Level 3: Drawing Free Body Diagrams When we are working with forces, we often need to find the net force acting on an object. To do this, we first start by sketching a picture of the forces acting on it. We call this picture a free body diagram. There are a few rules we should follow when drawing a free body diagram. 1. 2. 3. 4. Always draw the forces from the center of the object. The stronger the force is, the longer the arrow is. The arrow should point in the direction for force is acting Label the forces acting with letters/symbols The picture on the right helps you see what this looks like. Here are a few hints when working with free body diagrams: ο· ο· The force of gravity always points straight down. The normal force will always push straight up from a surface. See the examples below. Look carefully at the last two! ο· ο· If an object is moving in one direction, friction is acting in the opposite direction. Think about whether the forces on opposite sides are balanced or not. If they are, the two arrows should be about the same length. For example, on a flat surface, the force of gravity and the normal force should have the same length. Level 4: Using the Free Body Diagram in Calculations Why do we even waste our time drawing this pictures? Because once we do, it is a lot easier to calculate the net force acting on an object. Calculating Force The equation we use to measure force is: πΉπππ‘ = ππ where Fnet is the total force acting on an object, m is the mass of the object and a is the acceleration of the object. We measure force in Newtons (N). Newton ο kg m/s2 F net (F net) is called a lot of different things: the net force, the total force, or the resultant force. They all pretty much mean the same thing- add the forces acting on the object together. Sometimes people show this with a little summation sign, too. πΉπππ‘ = β πΉ Donβt let that symbol scare you. It just means that you need to add up all the forces acting on the object. It basically means Fnet. This is actually used pretty widely in higher level math. It just means βadd upβ. For example, letβs say you were given three paychecks this month- one for $100, one for $150, and another for $100. We could say: β πππ¦πβππππ = 100 + 150 + 100 = $350 Finding the Net Force Review In previous lessons, we learned to add and subtract forces. We also Do you In real often run into situations that look a little complicated. It helps to keep the forces in the x and y directions. Look carefully at example below to see how to do this. saw a lot of forces that canceled on another out (see the examples below. Above them, their net forces are stated. remember how to find these? life, we more organized the 5-5 ππππ,π ππππ,π = ππ΅ ππππ,π ππππ,π 5, left 3-3 ππππ,π = ππ΅, ππππ πΉπππ‘,π¦ = ππ΅ ππππ,π 3-3 πΉπππ‘,π¦ = ππ΅ Finding the Acceleration Once we know the Fnet in each direction, we can learn a lot about how an object is moving. We do this by using the equation I already forced you already learned πΉπππ‘ = ππ. These can actually be pretty fun. They are usually little puzzles. You figure out whatever you can and keep working at it until youβve solved the whole thing. They are close cousins of Sudoku puzzles. You should try them next time you are out on a relaxing date. Let me model one for you. Letβs say someone gave me the free body diagram below and asked me to find its net force, mass, and its acceleration. Well, first, I would kick back, put on some slippers, maybe make some calming tea, and settle into my favorite chair at home for a comfy evening puzzle solving. Example Find Fnet, mass and acceleration in the situation below. First, I would figure out the net force, because that looks pretty easy. There are no forces in the x direction, so I would have to write: πΉπππ‘,π₯ = 0 Then Iβd total up the forces in the y direction. πΉπππ‘,π¦ = 40 β 25 = 15 π π’π Notice I included the direction there. That is necessary. That was easy enough. Now, they asked me to find the mass. Hmmmβ¦ at first this seems impossible because I donβt have the acceleration. But then I realize they gave me the force of gravity (look up at the free body diagram). Woot woot! I can use the weight equation for find mass. πΉππππ£ = ππ β25 = π(β9.8) π = 2.6 ππ Alright! Now we are rolling. At this point, I would probably reward myself with a tasty oatmeal cookie. Now, we are really close. Just a little furtherβ¦. we have to find the acceleration. To do this, I would use what I learned above. πΉπππ‘ = ππ 15 = (2.6)π π = 5.8 π/π 2 Andβ¦ done! Now I would congratulate by telling myself that Iβm smart and having a celebratory cookie. Constant Velocity and Acceleration You should always check the problem for the words βconstant velocityβ and βat restβ. These words should reach out and slap you in the face. If you see these words, it means the forces need to be balanced. The net force will have to add up to zero. If you donβt see these words, you can assume the object is accelerating. Words βat restβ or βconstant velocityβ What They Mean No acceleration The forces shouldβ¦ Be balanced Cancel one another out Fnet=0 βacceleratingβ βspeeding upβ βslowing downβ Accelerating Unbalanced Some of the forces cancel out, but not all of them Fnet=ma Example Problem A toy car glides along a floor with a constant velocity. Its motor pushes it forward with a force of 20 N. What is the force of friction acting on it? Solution The force of friction acting on the toy car is 20 N. We know this because the car is moving at a constant velocity. This means it has balanced forces acting on it. The two 25 N force are already balanced. That means the 20 N force must be canceled out by another 20 N force. Level 5: Friction So far, weβve covered how to solve for how to find the net force, missing forces and the acceleration. In some of those problems, we even found friction. In many of them, I gave you the force of friction. Where did that number come from? How can we calculate force? In this section, we explore how to do that. Types of Force Static Friction: This is the type of force that fights us when we want to get something to start moving. If I push against a refrigerator, and I push and push and it just wonβt budge, I am fighting static friction. The harder I push, the more the object pushes back. All the way up until the last second, when it starts to move then, it isβ¦ Kinetic Friction: Kinetic friction is the type of friction that fights your motion when you are already moving. This is the type you are used to. If my car is rolling down the highway, friction is trying to slow it down. When a book slides across a tabletop, friction is what brings it to a stop. The Coefficient of Friction The coefficient of friction is a number that tells us how much two surfaces rub against another. If the coefficient of friction is a small number, there wonβt be a lot of friction. If the coefficient of friction is a high number, there will be a lot of force. Here are some common coefficients of friction: Notice there is a coefficient of friction for static friction (in the left column) and one for kinetic friction (in the right column). These are not always the same. Some object are very smooth and wonβt rub against one another very much. They have a small coefficient of friction (such as Teflon and steel, whose µK = 0.04). Sometimes two surfaces really rub against one another and cause a lot of friction (like steel on steel, µ K = 0.57) Notice there arenβt any units on the coefficient of friction. This is kind of nice- we actually donβt have any. Itβs one of the few values in physics that doesnβt have a unit. If the object is at rest, you will use ππ , the coefficient of static friction. If the object is moving, you will use ππ , the coefficient of kinetic friction. Calculating Friction Weβve cover this equation in the past, so it might be familiar to you: πΉππ = ππΉπ πΉππ ο force of friction (Newtons) π ο coefficient of friction. Like that symbol? It is called mu. Ask me and Iβll show you a stupid way to remember it. This guy has no units. πΉπ ο normal force (Newtons) Letβs practice an easy calculation. Example Problem A rubber tire with a normal force of 100 N is moving across dry concrete. a) What is the coefficent of friction between the two surfaces? b) What is the force of friction on the tire? Use the chart above to help you. Solution a) Looking at the chart, I see rubber and dry concrete is listed. Which one should I choose? Well, the tire is moving, so I need to choose the coefficient of kinetic friction. The chart tells me ππ ,= 0.8 b) πΉππ = ππΉπ πΉππ = (0.8)(100) πΉππ = 80 π Example Problem A sled made of waxed wood has a mass of 10 kg. A girl (mass=25 kg) sliding to a stop on wet snow. How much friction is acting on her? Use the coefficient chart to help you out. Solution Draw a free body diagram of the situation. We donβt actually know the value of any of these forces yet, so we will have to calculate them. We have the masses, so finding the force of gravity should be pretty easy. πΉπ = ππ We have use the mass of the kid and the sled together. πΉπ = (35)(9.8) πΉπ = ππ πΉπ = 343 π I added this to my free body diagram (right). If that is the force of gravity, what is our normal force? It should have the same magnitude, but the normal force pushes up, not down. Now, all we need to find is the force of friction. At first, it looks hopeless. Then, we remember the friction equation. πΉππ = ππΉπ We already know the normal force (343 N). We use the chart to look up the coefficient of kinetic friction between wood and snow. ππ ,= 0.1 πΉππ = (0.1)(343) πΉππ = 34.4 π