07 Handout 3 PDF - Newton's Laws of Motion

SH1690 Newton’s Laws of Motion I. Law of Inertia Newton’s First Law, the Law of Inertia, states that an object will remain in its current state unless there is a change in its equilibrium caused by an unbalanced, outside force. Context In the given definition, equili...

SH1690 Newton’s Laws of Motion I. Law of Inertia Newton’s First Law, the Law of Inertia, states that an object will remain in its current state unless there is a change in its equilibrium caused by an unbalanced, outside force. Context In the given definition, equilibrium is stated. Equilibrium is balance. The state of an object’s equilibrium is known as its inertia (Latin, Figure 2. A man falls forward after pushing the car, demonstrating inertia. Sources: http://www.tumblr.com (car), hero.wikia.com (Amethyst), steven-universe.wikia.com (Pearl), inactive). Inertia is best defined as the resistance of an object to clipartfest.com (man) change its state of motion. If acceleration is absent (i.e., 𝑎 = 0 𝑚/𝑠 2 ), the object is in a state of rest. the man began to fall forward. Often, there is also a state change when Suppose we have a man pushing a car with an engine problem, with one object moves in one direction, but an external force keeps on two passengers (see below). From its initial speed of 0 m/s, the car changing the object’s direction. revved up to 80 m/s in just 6 seconds. The man, who was struggling Isaac Newton has built the first law upon Galileo’s assumptions. to push, was in a state of rest. Galileo stated that objects eventually stop due to the force called friction, which is defined as the resistance that one surface, or object, encounters when moving another. In his rolling ball experiments, he concluded, upon his observations, that the ball will achieve the same height as its original position if friction was eliminated. Furthermore, if the ball was rolled at an angle in which the planes were oriented, the final height will be almost equal to the initial height. If the ball were Object is at rest (v = 0 m/s & a = Stays at rest Figure 1. A man struggles to push the car, demonstrating inertia. Forces are 0 𝑚/𝑠 2 ) Sources: http://www.tumblr.com (car), hero.wikia.com (Amethyst), steven-universe.wikia.com (Pearl), clipartfest.com (man) balanced Object is moving (v ≠ 0 m/s, a = 0 Stays in Motion Forces are 𝑚/𝑠 2 ) But, when the car started, he started to fall forward because his body applied began to move from zero to 80 m/s, the same moment the car began Object is at rest to run. See the image at right. (v = 0 m/s, a ≠ 0 Object moves Forces are 𝑚/𝑠 2 ) There are two (2) clauses in such scenarios to determine an object’s unbalanced Object is moving state, as seen in the opposite. If forces are balanced, the object will (v ≠ 0 m/s, a ≠ 0 Object stops remain in its current state. Going back to the previous example, since 𝑚/𝑠 2 ) both objects are at rest, all forces are balanced. But, since the motion Figure 3: A simple analysis to determine the state of an object. was introduced, there was an imbalance between the two. As a result, 07 Handout 3 *Property of STI  [email protected] Page 1 of 5  SH1690 rolling down a plane with a reduced slope, the ball would roll a few energy, which results from physical action or movement. From there, distances more to achieve the same results. we have two kinds of forces. Contact Forces are forces that two (2) objects exert whenever they are perceived as physical contact. Examples of these forces include friction, tension force (force resulting from pulling), the normal force (force perpendicular to the surface an object is placed upon), air resistance (force exerted by air), spring force (force resulting from compression), and applied force (force directly applied to objects). Noncontact Forces, on the other hand, are forces that two objects exert at a distance. Source: http://www.physicsclassroom.com/ Examples are gravitational and electromagnetic forces, wherein the Thus, if the ball were to roll at a plane inclined to a near-zero degree second force can be divided into electrical angle, the ball would roll almost infinitely to reach its original height. Figure 4. Two (2) contact forces, gravity and normal force, are and magnetic forces. Gravitational force And if rolling on a completely flat plane, the ball will roll continuously acting on this woman, as illustrated by the Free-Body Diagram. simply weights. and, in theory, will never stop rolling. Source: steven- universe.wikia.comIf another of the same magnitude is Newton built upon Galileo’s thoughts by implying that a force is not countering a force, the result is a state of needed for an object to maintain its motion. Simply put, there is a force rest or equilibrium. To demonstrate such effects, we use free-body that causes the object to revert to its resting state. Take note as well diagrams (FBD) to represent them. Free-body diagrams are simple that all objects resist changes in their state of motion. diagrams that represent all forces acting on an object. With that in Some objects have more tendency to resist changes. This is where mind, force is a derived vector quantity. Force is represented by an mass comes in. Mass is a scalar quantity that measures the object’s arrow to denote its direction as to where the force is directed. For its resistance to acceleration when a net force is applied, with its SI unit magnitude, it is represented by its unit, newtons (N), having a value of being the kilogram (kg). Simply put, the heavier the object, the higher 1 N = 1 kg ∙ m⁄s 2 its inertia. For example, we have represented a free-body diagram of a woman Force and the Free-Body Diagram standing (see diagram 4). Two forces are acting on her – gravity and Newton’s First Law introduces the concept of force to describe its the force of the floor resisting gravity. Since she is not moving, she is notion. As we were taught before, we already know that a force is at rest, making both forces balanced. If the forces that are acting on either a push or a pull. But, nowadays, it is not always the case. So, the object are not balanced, then these forces are unbalanced. An what is a force, then? example would be a book being pushed at a table. When the book is Force is defined as an influence that tends to change an object’s state being pushed, the book slides across the table, but it does not slide of motion when left unopposed. It can also be defined as strength or forever. The book will eventually stop because there is another force present, which is friction. 07 Handout 3 *Property of STI  [email protected] Page 2 of 5  SH1690 II. Law of Acceleration Frictional Force, or friction (𝑭𝒇 ) is the resistance of a surface or Definition an object acting upon another object in contact with it (going left). An object is said to be accelerating if an unbalanced net force is Applied Force (𝑭𝒂𝒑𝒑 ) is the force directly applied to an object applied to it, in which the acceleration of the object is directly (going right). proportional to the net force, is moving along the direction the net force is directed at and is inversely proportional to the object’s mass Determining the net force uses only the basic linear equation, Context 𝐹𝑛𝑒𝑡 = 𝐹𝐴 + 𝐹𝐵 Newton’s Second Law, which represents the aftermath of an object exposed to unbalanced forces, states that an object is said to be Assigning what force is 𝐹𝐵 or 𝐹𝐴 is arbitrary. Just remember that, in moving when it is accelerating. According to this law, acceleration is terms of 𝑔, downward motion is positive. Remember that force is a directly proportional to the prevailing unbalanced force (called net vector, and make sure to depict all forces acting on the object. Let us force) and inverse to its mass. Mathematically, try an example. 𝐹𝑛𝑒𝑡 Suppose we have the same man pushing the car, seen below. 𝑎= 𝑚 𝑤ℎ𝑒𝑟𝑒 𝑎 = 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝐹𝑛𝑒𝑡 = 𝑎𝑝𝑝𝑙𝑖𝑒𝑑 𝑓𝑜𝑟𝑐𝑒 𝑚 = 𝑚𝑎𝑠𝑠 Rearranging the given equation, we get 𝐹𝑛𝑒𝑡 = 𝑚𝑎, or more commonly, 𝐹 = 𝑚𝑎. As stated earlier, the net force is the difference between the applied force and the countering force acting upon the object. Figure 6. An FBD representation of the pushing-car problem. Using the FBD, we can represent the Sources: http://www.tumblr.com (car), hero.wikia.com (Amethyst), steven-universe.wikia.com (Pearl), forces, as seen on the opposite page. In clipartfest.com (man) diagram 5, we have represented four (4) He exerts a force of 4,500 newtons, but the road itself exerts its forces: frictional force of 3,875 newtons. How much net force is the car exerting? Weight (𝑭𝑾 ) is the force exerted by To determine 𝐹𝑛𝑒𝑡 , we need to identify what the forces are present, as gravity on the object, represented by seen from the FBD. the formula, 𝐹𝑊 = 𝑚𝑔, with 𝑔 is the 𝐹𝑓 = 3,875 𝑁 acceleration due to gravity (going 𝐹𝑎𝑝𝑝 = 4,500 𝑁 down). Normal Force (𝑭𝑵 ) is the force acting Figure 5: Shown here are the four From there, write down the equation, (4) forces commonly illustrated in against weight, which is always the Free-Body Diagram. Source: steven- 𝐹𝑛𝑒𝑡 = 𝐹𝐴 + 𝐹𝐵 perpendicular to the surface the object universe.wikia.com is resting upon (going up). 𝐹𝑛𝑒𝑡 = 𝐹𝑎𝑝𝑝 + 𝐹𝑓 07 Handout 3 *Property of STI  [email protected] Page 3 of 5  SH1690 Since friction is a leftward, negative force, we get, For every force, there is always an equal – and opposite – reaction to it. 𝐹𝑛𝑒𝑡 = 𝐹𝑎𝑝𝑝 − 𝐹𝑓 𝐹𝑛𝑒𝑡 = 4500 − 3,875 Context 𝑭𝒏𝒆𝒕 = 𝟔𝟐𝟓 𝐍 This law’s premise is simple: there is always an equal – and opposing This means that the car will move in the direction the force is directed – the amount of force counteracting against another force. In context, to, but it will take a very long time to do so. In determining friction, we the Third Law explains the First and Second Laws. An example of this use the formula, would be Normal force (𝐹𝑁 ). In it, the normal 𝐹𝑓 = 𝜇𝐹𝑁 force is always paired with weight (𝐹𝑊 ), which is the normal force’s polar opposite. The two 𝑤ℎ𝑒𝑟𝑒 𝜇 = 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛 forces, when paired together, are called 𝐹𝑁 = 𝑛𝑜𝑟𝑚𝑎𝑙 𝑓𝑜𝑟𝑐𝑒 interaction force-pairs. Other force pairs are Using the same example, let us determine the friction coefficient if the applied force and friction, weight and air car weighs 15,778 newtons. Identifying the given, we get that weight resistance, applied force and tension, and so 𝐹𝑊 = 15,778 𝑁. Knowing that 𝐹𝑁 = 𝐹𝑊 , we also get that 𝐹𝑁 = 15,778 𝑁. much more. The Law of Interaction explains how things get to move. Say, a fish uses its tail Since that 𝐹𝑓 = 3,875 𝑁, we can write down the formula as, to push away the water. But, as explained by the other Laws, water propulsion allows the 3,875 𝑁 = 𝜇(15,778 𝑁) fish to move forward. Another example is the Transposing the values, we get that, interaction between friction, applied force, weight, and normal force when walking. −𝐹𝑓 𝜇= As seen in diagram 7 (opposite page), the 𝐹𝑁 3,875 𝑁 woman shifts her weight from one foot to the = other while at the same time providing enough weight to support her 15,778 𝑁 = 𝟎. 𝟐𝟒𝟓𝟔. employing the normal force provided by the ground. As she takes a step, friction keeps her Figure 7. Shown here are the force-pairs in action. There are two (2) kinds of friction to be considered. First is static foot from slipping as she directly uses applied Source: steven- universe.wikia.com friction, the friction in which an object needs to overcome to move. On force to push herself forward. This, in turn, the other hand, Kinetic friction is the friction experienced by moving creates a cycle, shifting between the two force- surfaces interacting with each other. pairs, allowing her for a smooth, continuous motion. In conclusion, Newton’s Second Law explains the behavior of objects References: if the forces applied to it do not balance. Also, forces do not simply Bauer, W., & Westfall, G. D. (2016). General physics 1 (2nd ed.). cause motion – forces cause accelerations, which cause motion. Columbus, OH: McGraw-Hill Education. Bauer, W., & Westfall, G. D. (2016). General physics 1 (2nd ed.). Quezon City: Abiva Publishing House, Inc. Bautista, D.C. (2013). Science impact: Integrated science (3rd ed.). III. Law of Interaction Antipolo City: Academe Publishing House, Inc. Definition 07 Handout 3 *Property of STI  [email protected] Page 4 of 5  SH1690 Belleza, R.V., Gadong, E.S.A., …, Sharma, M. PhD (2016). General Physics 1. Quezon City, Vibal Publishing House, Inc. CHED (2017). Newton’s first law of motion. Retrieved 2017, March 10 from Teach Together: CHED K-12 Curriculum Sharing Site: http://teachtogether.chedk12.com/teaching_guides/view/87 CHED (2017). Newton’s second and third laws of motion. Retrieved 2017, March 10 from Teach Together: CHED K-12 Curriculum Sharing Site: http://teachtogether.chedk12.com/teaching_guides/view/90 Freedman, R. A., Ford, A. L., & Young, H. D. (2011). Sears and zemansky’s university physics (with Modern physics) (13th ed.). Addison-Wesley. Nave, C. R. (2016). Mechanics: Motion. Retrieved from the Georgia State University’s HyperPhysics: http://hyperphysics.phy- astr.gsu.edu/hbase/hph.html#mechcon The Physics Classroom (2016). Newton’s laws. Retrieved 2017, March 13 from The Physics Classroom website: http://www.physicsclassroom.com/Physics-Tutorial/Newton- s- Laws Santiago, K. S., & Silverio, A. A. (2016). Exploring life through science: Senior high school physical science. Quezon City: Phoenix Publishing House, Inc. Somara, S. (2016). Newton’s laws: Crash course physics #5. Retrieved from YouTube: https://www.youtube.com/watch?v=kKKM8Y-u7ds 07 Handout 3 *Property of STI  [email protected] Page 5 of 5