Part A: A common framework when working with forces is Newton's laws, first published in 1637 by Sir Isaac Newton in his Philosophiae Naturalis Principia Malhemalica. Philosophia: Naturalis Principia Mathematica is a three book series written in Latin that translates as \"Mathematical Principles of Natural Philosphy\". These books form one ofthe most important works in the history of science and represent Newton's attempts to describe the physical world that he observed in an orderly, mathematical fashion. Before we dive into Newton's laws, let's try to answer some questions about the concepts of forces. Exercise Sl. For these questions. imagine a very heavy object like a refrigerator sitting on a rough floor. 1. If you lightly push on the side of the refrigerator; what will happen? 2. If you increase your force somewhat but not enough to move the refrigerator, what happens? Briefly explain your reasoning as it relates to question 1. 3. If you recruit one of your friends and both of you push horizontally on the side of the refrigerator, making the refrigerator start moving across the floor, what happened? Briefly explain your reasoning. 4. If both of you stop pushing, what will happen? Why? Briefly explain your reasoning. If the refrigerator had been full offood and therefore heavier, how would things have changed? Briey explain your reasoning. P" To understand forces and better answer the above questions, we will focus on Newton's second law which can be stated as: the acceleration of an object is proportional to the net force acting on it and inverser proportional to the object's mass. This can be written mathematically as: _.,. FREE : mil. The net forcejust means what we get when add all the forces acting upon the object. We can state that mathematically as: F112: 2 2 F As we saw in the previous lab, when adding vectors we need to be careful and only add like components (X - components with other X - components, Y - components with other Y - components). The same idea is true for Newton's second law because finding the net force means adding up vectors. This means we can write Newton's second law for each component, a way that is very useful in problem solving, as Fnet,x = > Fx = max Equation 5-1 Fnety = Fy = may Equation 5-1 means that if there is a net force in the x-direction, the object will accelerate in that direction. It also means that if an object is not accelerating in a certain direction, then there is no net force in that direction. This does not mean that there are no forces acting in that direction, just that there is no net force. As an example, think of a book sitting on a table. The book has mass so gravity is exerting a force downward on it. It is also sitting on a table meaning the table is exerting a normal force upward. What is the book doing? Nothing! It is just sitting there meaning it is not accelerating so the net force must be zero (otherwise it would start to accelerate and levitate off the table! ) so the normal force must exactly equal the gravitational force. We need to introduce one more concept before we can accurately describe the scenario discussed in Exercise 5-1: the concept of friction. Friction is a force that opposes motion (or attempted motion) and arises primarily between the roughness of the two surfaces. The surfaces may look smooth but a magnified view would show bumps and valleys, a property called rugosity. As the peaks and valleys of one surface try to slide across the peaks and valleys of the other surface, they create a resistance to motion that we call friction. There is also a part of friction that is due to the attractive forces between the molecules of the two surfaces. This is why rubber soled shoes grip a floor better and slide less than leather soled ones. How much friction occurs between surfaces is different depending on properties of each surface. For the refrigerator example, it would depend on what the floor is made of (tile, carpet, cement, etc.) and what the part of the refrigerator that is touching the floor is made of (plastic, stainless steel, aluminum, etc.). The amount of resistance between the two surfaces is measured empirically (in a laboratory) and is represented by a unitless number called the coefficient of friction, M. It is important to realize that the coefficient of friction depends on the two surfaces but does not depend on how heavy the object is.When we talk about friction between two surfaces. we need to consider two different scenarios. static and kinetic friction. Think about the refrigerator sitting on the floor. When we first pushed on it. it didn't move. We then pushed harder and still it didn't move. These are examples of static friction because nothing was in motion. When we pushed harder, the static friction increased (it wasn't moving so it wasn't accelerating so it had no net force. meaning static friction had to balance out our push}. This means that static friction can have a range of values, going from D to a maximum value. We write this mathematically as f: S #5 FM [qurl 5 2 Where FN is the normal force [the force perpendicular to the surface) and ,us is the coefficient of static friction. This equation means that the force of static friction is less than or equal to some maximum amount, fame: : #sFN We can nd the max value by detem'lining hovv.r much force is required to break the refrigerator free and get it moving (and therefore overcome static friction}. This represents the top bound of the above equation. In other words, fsmax is how much force you would have to exert to get the refrigerator in motion. What happens after we have applied enough force and have overcome static friction? The object is now in motion and the friction that we need to consider is kinetic friction. characterized by the coefficient of kinetic friction, ,uk. Kinetic friction is nom'lally less than static friction (the force we need to exert to keep it in motion is normally less than the force to get it in motion) meaning normally pt; 2} #k. We will discuss kinetic friction more in-depth in Part B. We can visualize these forces with a free-body diagram of the refrigerator resting on a level surface while we apply a force to the right. Figure 5-1 frricrion Applied Force +YI .- +X mg If we use Equation 51 and the fact that the object is not moving up or down (so a). = G), we see that the normal force equals the weight of the object or F N = mg. Exercise 52. Let's revisit the answers to some ofthe questions in Exercise 5l by using a computer simulation. Open the page found at lit! 5. hut.colol'ad(Ledu.-"cn.-"5imulatiolis.-"fb1'ccs- id and click the box that says 'Run Cheerp] BrowserCompatible Version\". On the right-hand side select 'Ref'rigerator'. Note the mass of the refrigerator is written beside the word Refrigerator. 1. 0n the left side of the screen there is a box that says Applied Force [it might say Applied F}. Enter 100 and press Go. what happens? Briefly explain what is happening using the ideas of forces and friction presented in the text above. 2. Click Pause and change the Applied Force to 500. What happens? Briefly explain 1what is happening using the ideas of forces and friction presented in the text above. 3. Click Pause and change the Applied Force to 3000. what happens? Briefly.I explain what is happening using the ideas of forces and friction presented in the text above. 4. Apply different values oprplied Force to nd the minimum force required to get the refrigerator in motion. Minimum Force = N 5. Based on the mass of the refrigerator and the minimum force required to overcome friction, estimate the coefficient of static friction, ,us. Equation 52 may prove helpful