Newton's Laws of Motion PDF

SH1685 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 sta...

SH1685 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 Diagram 2: A man falls forward after pushing the car, demonstrating inertia. simply balance. The state of an object’s equilibrium is known as Sources: http://www.tumblr.com (car), hero.wikia.com (Amethyst), steven- universe.wikia.com (Pearl), clipartfest.com (man) its inertia (Latin, inactive). Inertia is best defined as the resistance of an object to change its state of motion. Simply put, In such scenarios, there are two (2) clauses to determine the state if acceleration is absent (i.e. 𝑎 = 0 𝑚/𝑠 2 ), the object is in a state of an object, as seen in the opposite. If forces are balanced, the of rest. object will remain in its current state. Going back to the previous Suppose we have a man pushing a car which has an engine example, since both objects are at rest, then all forces are problem, with two passengers (see below). The car, from its balanced. But, since motion was introduced, there was an initial speed of 0 m/s, revved up to 80 m/s in just 6 seconds. The imbalance between the two. As a result, the man began to fall man, who was struggling to push, was at a state of rest. forward. Oftentimes, there is also a change in state when one object is moving in one direction, but an external force keeps on changing the object’s direction. Object is at rest (v = 0 m/s & a = Stays at rest Forces are 0 𝑚/𝑠 2 ) balanced Object is moving (v ≠ 0 m/s, a = 0 Stays in Motion Diagram 1: A man struggles to push the car, demonstrating inertia. Forces are 𝑚/𝑠 2 ) Sources: http://www.tumblr.com (car), hero.wikia.com (Amethyst), steven- applied Object is at rest universe.wikia.com (Pearl), clipartfest.com (man) (v = 0 m/s, a ≠ 0 Object moves Forces are 𝑚/𝑠 2 ) But, when the car started, he started to fall forward because his unbalanced Object is moving body began to move from zero to 80 m/s, the same moment the (v ≠ 0 m/s, a ≠ 0 Object stops 𝑚/𝑠 2 ) car began to run. See the image at right. Diagram 3: A simple analysis to determine the state of an object. 05 Handout 1 *Property of STI Page 1 of 5  SH1685 Isaac Newton has built the first law upon Galileo’s assumptions. Some objects have more tendency to resist changes. This is In it, Galileo stated that objects eventually stop due to the force where mass comes in. Mass is a scalar quantity that measures called friction, which is defined as the resistance that one the object’s resistance to acceleration when a net force is surface, or object, encounters when moving another. In his applied, with its SI unit being the kilogram (kg). Simply put, the rolling ball experiments, he concluded, upon his observations, heavier the object, the higher its inertia. that the ball will achieve the same height as its original position Force and the Free-Body Diagram if friction was eliminated. Furthermore, if the ball was rolled at Newton’s First Law introduces the concept of force to describe an angle in which the planes were oriented, the final height will its notion. We already know, as we were taught before, that a be almost equal to the initial height. If the ball was rolling down force is either a push or a pull. But, nowadays, it is not always a plane with a reduced slope, then the ball will roll a few the case. So, what is a force, then? distances more in order to achieve the same results. Force is defined as an influence that tends to change an object’s state of motion when left unopposed. It can also be defined as the strength or energy which is the result of physical action or movement. From there, we have two kinds of forces. Contact Forces are forces that two (2) objects exert whenever they are in a perceived, physical contact. Examples of these forces include friction, tension force (force resulting from pulling), 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). Source: http://www.physicsclassroom.com/ Noncontact Forces, on the other hand, are forces that two objects Thus, if the ball were to roll at a plane inclined to a near-zero exert at a distance. Examples are gravitational and degree angle, then the ball will roll almost infinitely to reach its electromagnetic forces, wherein the second force can be divided original height. And if rolling on a completely flat plane, the ball into electrical and magnetic forces. Gravitational force is simply will roll continuously, and, in theory, will never stop rolling. weight. Newton built upon Galileo’s thoughts by implying that a force If a force is being countered by another of the same magnitude, is not needed in order for an object to maintain its motion. the result is a state of rest, or equilibrium. To demonstrate such Simply put, there is a force that causes the object to revert to its effects, we use free-body diagrams (FBD) to represent them. resting state. Take note as well that all objects resist changes in Free-body diagrams are simple diagrams that represents all their state of motion. forces acting on an object. With that in mind, force is a derived 05 Handout 1 *Property of STI Page 2 of 5  SH1685 vector quantity. Force is represented by an arrow to denote its In Newton’s Second Law, which represents the aftermath of an direction as to where the force is directed at. For its magnitude, object exposed to unbalanced forces, states that an object is said it is represented by its unit, newtons (N), having a value of 1 N to be moving when it is accelerating. And acceleration, = 1 𝑘𝑔 𝑚⁄𝑠 2 according to this Law, is directly proportional to the prevailing unbalanced force (called net force), and inverse to its mass. For example, we have represented a Mathematically, free-body diagram of a woman 𝐹𝑛𝑒𝑡 standing (see diagram 4). There are 𝑎= 𝑚 two forces acting on her – gravity and the force of the floor resisiting gravity. 𝑤ℎ𝑒𝑟𝑒 𝑎 = 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 Since she is not moving, she is at rest, 𝐹𝑛𝑒𝑡 = 𝑎𝑝𝑝𝑙𝑖𝑒𝑑 𝑓𝑜𝑟𝑐𝑒 making both forces balanced. If the 𝑚 = 𝑚𝑎𝑠𝑠 forces that are acting on the object are Rearranging the given equation, we get 𝐹𝑛𝑒𝑡 = 𝑚𝑎, or more not balanced, then these forces are commonly, 𝐹 = 𝑚𝑎. As stated earlier, the net force is the unbalanced. An example would be a difference between the applied force and the countering force book being pushed at a table. When the acting upon the object. Using the FBD, we can represent the book is being pushed, the book slides Diagram 4: Two (2) contact forces as seen in the opposite page. In forces, gravity and normal across the table, but it does not slide force, are acting on this diagram 5, we have represented four forever. The book will eventually stop woman, as illustrated by the (4) forces: Free-Body Diagram. because there is another force present, Source: steven- which is friction. universe.wikia.com  Weight (𝑭𝑾 ) is the force exerted by gravity on the object, represented by the formula, 𝐹𝑊 = II. Law of Acceleration 𝑚𝑔, with 𝑔 is the acceleration due Definition to gravity (going down). An object is said to be accelerating if an unbalanced net force is  Normal Force (𝑭𝑵 ) is the force applied to it, in which the acceleration of the object is directly acting against weight, which is proportional to the net force, is moving along the direction the always perpendicular to the net force is directed at, and is inversely proportional to the surface the object is resting upon object’s mass Diagram 5: Shown here are the (going up). four (4) forces commonly Context  Frictional Force, or friction (𝑭𝒇 ), illustrated in the Free-Body Diagram. Source: steven- is the resistance of a surface or an universe.wikia.com 05 Handout 1 *Property of STI Page 3 of 5  SH1685 object acting upon another object in contact with it (going 𝐹𝑛𝑒𝑡 = 𝐹𝐴 + 𝐹𝐵 left). 𝐹𝑛𝑒𝑡 = 𝐹𝑎𝑝𝑝 + 𝐹𝑓  Applied Force (𝑭𝒂𝒑𝒑 ) is the force directly applied to an Since friction is a leftward, negative force, we get, object (going right). 𝐹𝑛𝑒𝑡 = 𝐹𝑎𝑝𝑝 − 𝐹𝑓 Determining the net force uses only the basic linear equation, 𝐹𝑛𝑒𝑡 = 4500 − 3,875 𝐹𝑛𝑒𝑡 = 𝐹𝐴 + 𝐹𝐵 𝑭𝒏𝒆𝒕 = 𝟔𝟐𝟓 𝑵 This means that the car will move to the direction the force is Assigning what force is 𝐹𝐵 or 𝐹𝐴 is arbitrary. Just remember that, directed to, but it will take a very long time to do so. In in terms of 𝑔, downward motion is positive. Remember as well determining friction, we use the formula, that force is a vector, and make sure to depict all forces acting 𝐹𝑓 = 𝜇𝐹𝑁 on the object. Let us try an example. Suppose we have the same man pushing the car, seen below. 𝑤ℎ𝑒𝑟𝑒 𝜇 = 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛 𝐹𝑁 = 𝑛𝑜𝑟𝑚𝑎𝑙 𝑓𝑜𝑟𝑐𝑒 Using the same example, let us determine the friction coefficient if the car has a weight of 15,778 newtons. Identifying the given, we get that weight 𝐹𝑊 = 15,778 𝑁. Knowing that 𝐹𝑁 = 𝐹𝑊 , we also get that 𝐹𝑁 = 15,778 𝑁. Since that 𝐹𝑓 = 3,875 𝑁, we can write down the formula as, 3,875 𝑁 = 𝜇(15,778 𝑁) Diagram 6: An FBD representation of the pushing-car problem. Transposing the values we get that, Sources: http://www.tumblr.com (car), hero.wikia.com (Amethyst), steven- −𝐹𝑓 universe.wikia.com (Pearl), clipartfest.com (man) 𝜇= 𝐹𝑁 He exerts a force of 4,500 newtons, but the road itself exerts its frictional force of 3,875 newtons. How much net force is the car 3,875 𝑁 exerting? 𝜇= 15,778 𝑁 To determine 𝐹𝑛𝑒𝑡 , we need to identify what the forces are present, as seen from the FBD. 𝝁 = 𝟎. 𝟐𝟒𝟓𝟔 𝐹𝑓 = 3,875 𝑁 There are two (2) kinds of friction to be considered. First is static 𝐹𝑎𝑝𝑝 = 4,500 𝑁 friction, the friction in which an object needs to overcome in From there, write down the equation, 05 Handout 1 *Property of STI Page 4 of 5  SH1685 order to move. Kinetic friction, on the other hand, is the friction between friction, applied force, weight, and normal force when experienced by moving surfaces interacting on each other. it comes to walking. In conclusion, Newton’s Second Law provides the explanation As seen in diagram 7 (opposite page), the woman shifts her for the behavior of objects, in the case that the forces applied to weight from one foot to the other, while at the same time it do not balance. Also, forces do not simply cause motion – providing enough weight to support her by means of the normal forces cause accelerations, which cause motion. force provided by the ground. As she takes a step, friction keeps her foot from slipping as she directly uses applied force to push herself forward. This, in turn, creates a cycle, shifting between III. Law of Interaction the two force-pairs, allowing her for a smooth, continuous Definition motion. For every force, there is always an equal – and opposite – reaction to it. References: Context Bauer, W., & Westfall, G. D. (2016). General physics 1 (2nd ed.). Columbus, OH: McGraw-Hill Education. The premise of this Law is simple: there is always an equal – Bauer, W., & Westfall, G. D. (2016). General physics 1 (2nd ed.). Quezon City: Abiva Publishing House, Inc. and opposing – amount of force counteracting against another Bautista, D.C. (2013). Science impact: Integrated science (3rd ed.). Antipolo City: Academe force. In context, the Third Law explains Publishing House, Inc. Belleza, R.V., Gadong, E.S.A., …, Sharma, M. PhD (2016). General Physics 1. Quezon City, the First and Second Laws. An example of Vibal Publishing House, Inc. this would be Normal force (𝐹𝑁 ). In it, the CHED (2017). Newton's first law of motion. Retrieved 2017, March 10 from Teach Together: CHED K-12 Curriculum Sharing Site: normal force is always paired with weight http://teachtogether.chedk12.com/teaching_guides/view/87 (𝐹𝑊 ), which is normal force’s polar CHED (2017). Newton's second and third laws of motion. Retrieved 2017, March 10 from Teach Together: CHED K-12 Curriculum Sharing Site: opposite. The two force, when paired http://teachtogether.chedk12.com/teaching_guides/view/90 together, are called interaction force-pairs. Freedman, R. A., Ford, A. L., & Young, H. D. (2011). Sears and zemansky's university physics (with Modern physics) (13th ed.). Addison-Wesley. Other force pairs are applied force and Nave, C. R. (2016). Mechanics: Motion. Retrieved from the Georgia State friction, weight and air resistance, applied University’s HyperPhysics: http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html#mechcon force and tension, and so much more. The The Physics Classroom (2016). Newton’s laws. Retrieved 2017, March 13 Law of Interaction explains how things get from The Physics Classroom website: http://www.physicsclassroom.com/Physics-Tutorial/Newton-s- to move. Say, a fish uses its tail to push Laws away the water. But, as explained by the Santiago, K. S., & Silverio, A. A. (2016). Exploring life through science: Senior high school physical science. Quezon City: Phoenix Publishing House, Inc. other Laws, this propulsion of water Somara, S. (2016). Newton’s laws: Crash course physics #5. Retrieved from YouTube: allows the fish to move forward. Diagram 7: Shown here are https://www.youtube.com/watch?v=kKKM8Y-u7ds Another example is the interaction the force-pairs in action. Source: steven- universe.wikia.com 05 Handout 1 *Property of STI Page 5 of 5