Newtons First Law of Motion: The Law of Inertia - Lab Report Example

1.0 Newton's First Law of Motion: The Law of Inertia "An object moves with constant velo unless acted upon by a net external force" Newton's First Law is basically about the concept called Inertia which is defined as the tendency of an object to remain at a constant velocity. There are two parts in Newton's First Law and they are: 1) objects at rest ( velocity, v =0) will remain at rest unless acted upon by an unbalanced force and 2) objects moving at constant velocity (v 0) will remain moving with that velocity and direction unless acted upon by a net external force. Newton's First Laws is intuitive and can be seen directly at work in our daily life. For the first case, an example would be a soccer ball which will not be going anywhere unless someone kicks it or carries it. On the second case, consider a ball rolling with a constant velocity. Without friction and other forces including that of gravity, the ball will continue rolling with the same velocity unless it hits something or someone kicks it. Understanding the concept of a net external force is crucial in understanding Newton's first law. To illustrate this, consider a rope being used in a tug of war. There are two opposing forces in the activity but if the two sides pull with the same force then the rope would not move. That is, the two forces cancel each other out resulting to no net force on the rope. Thus, forces may be acting on an object but they are applied in such a manner that they cancel each other's effects. Force is a vector so it is important to take account of the direction. The result is that there will be no change in velocity since Force, F = 0. In calculus, this would be represented as dv/dt = 0 when F = 0 or simply, there is no differential change in velocity when there is no net external force. This is illustrated in the following; Figure 1. A Physics book pulled downward by gravity but the table exerts an upward push. The book does not move because the two forces cancel out. Note that the table is an inanimate object but is exerting force. The occurrence of force applied by the table will be explained further in Newton's Third law. 2.0 Newton's Second Law of Motion: Force and its Representation "The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object." While the first law describes the behaviour of objects where the F = 0, the second law is concerned with the situation where there is an unbalanced force. If F 0, then dv/dt is 0. In simple terms, the object accelerates, a, the rate of which is equal to the force applied divided the mass of the object. The acceleration of an object produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and is inversely proportional to the mass of the object. In equation form: Newton's Second Law is used to account for the acceleration of an object and not the motion itself. This law made it possible to quantify the concept of force. Whereas before it was previously defined as a push or pull, force was now quantified using the unit Newton (N). 1 N is equivalent to the force required to impart a 1 kg mass with acceleration of 1 m/s/s. The vector nature of force is also highlighted in the second law and gave rise to the need for constructing free body diagrams (FBDs). A free body diagram is a simple representation of an object with arrows. These arrows represent the forces together with its direction and intensity. In constructing FBDs, it is essential to take full account of all the forces acting on the object including action-at-a-distance force. An illustration of FBDs and unbalanced forces are shown: Figure 2. The object is acted upon by forces which are unbalanced in all three cases thereby resulting to an acceleration of the body mass. 3.0 Newton's Third Law of Motion: Action- Reaction "For every action, there is an equal and opposite reaction" All forces result from the interaction of two bodies. One body exerts a force on another body. Even at-a-distance force requires a minimum of two bodies interacting. Yet, what do we really mean by force and how is it generated Our experience would indicate that there is that there is in fact a force. When we push a box, our hands and arms certainly feel a force in the opposite direction. Newton's Third Law declares that this force is exactly equal in magnitude and opposite in direction of the force we exert on the body. If body A exerts a force on body B which we denote by FAB, Newton's Third Law, then, states that: FAB = - FBA This law is quite simple and generally more intuitive than the others. It is so apparent that it is able to explain many observed physical facts. For example, if I am in a sailboat, I cannot move the boat simply by pushing on the front. Though I do exert a force on the boat, I also feel a force in the opposite direction exerted by the boat on me. Thus the net force on the system and the boat remains stationary. We need some external force, like wind, to make the boat move. Newton's third law also gives us a more complete definition of a force because we are made to understand that a force results from the mutual interaction between two bodies. That is, whenever two bodies interact in the physical world, a force results. Whether it be two balls bouncing off each other or electrical attraction between a proton and an electron, the interaction of two bodies results in two equal and opposite forces. An example is shown below: Figure 3. The skaters forces on each other are equal in magnitude and in opposite directions. The Importance of Friction Friction is defined to be a force acting against the direction of motion for two objects in contact sliding across one another. While friction is usually regarded in a negative light because it causes wear and tear and a larger force to be exerted, it does play an important role in the physical world. The fact is that we would not be able to go anywhere without friction. The importance of friction can be best understood by taking Newton's First Law which states that an object remains moving if there is no net external force applied on it. As an example, consider a moving car. If there is no friction generated between the tires and the road, then the car will continue moving even if the brakes are applied. A FBD of the moving car will indicate that there is a downward pull of gravity counteracted by the upward push of the ground but there is the presence of a horizontal velocity which could only be dissipated by a force acting against the motion which is frictional force. Indeed, one can say that there are other bodies which can exert a force on the car to stop it moving but this would mean that we would be crashing on something just to be able to stop. How would it even be possible for a body to locate itself in a position to exert a force on the car if he just continues sliding. Without friction, we could not even be able to place a book on the table because it will just slide. We will not be able to walk because there is no friction between our shoes and the ground. We cannot even write because pencils and pens would just slide out of our hand when we grasp it. Erasing would not even be possible because the eraser would just slide over the printed material. Cars would not even move as the tires would just keep spinning without the friction on the ground. In other words, much of the activities that we do today could not have been possible without the molecular irregularities and the resulting friction of two objects in contact sliding with each other. The Disadvantage of Friction Friction is always directed against the direction of the motion of the object. Thus, it tends to slow and eventually stop the object from moving or even it from moving at all. That means that one needs to overcome the frictional force first before being able to move the object. The problem is further compounded by the fact that friction exists while trying to move the object (static friction) and is still there when an object moves (kinetic friction). This means that one needs to exert an extra force just to overcome friction. This extra effort translates to an increase in the use of energy which could mean more gasoline or electricity consumed. Furthermore, the Law of Conservation of Energy states that the amount of energy remains constant. Thus, the energy that "lost" to friction in moving an object is really turned to heat energy. The friction of parts rubbing together creates heat. This in turn causes wear and tear on the object. It may even melt the object so that it would be rendered useless which implies that it needs replacement. To illustrate, we can take a car as an example. When the road is well-paved, every driver would be able to notice that there is less consumption of gasoline per unit distance as compared to driving into a rugged terrain with the same distance. This is because well paved highways offer less friction because the irregularities which causes friction has been 'minimized' as compared to rugged terrains where the car needs to overcome mud, rocks and depressions which presents such huge amounts of friction. Cars that do use well paved highways are known to live longer than their counterparts because the wear and tear on the tires is less than that which is generate on rough roads. This is partly because of the generated heat between the tire and the ground due to friction and partly because of the shearing of material when they slide against each other. Computation for Lorry in Ice: Note : Friction, f = N where N is the normal force exerted by the iced ground on the lorry. In this case, N = Wcos For the lorry not to slide: f = Wsin But Wcos = Wsin Simplifying: = tan When tan is greater than 1 then the Wsin is greater than Wcos which means that the force exerted by the weight of the lorry parallel to the surface is greater than the frictional force. Exclusive OR Logic Gate A logic gate is an elementary building block of digital circuits. At any given moment, every terminal is in one of the two binary conditions low (0) or high (1) represented by different voltage levels. The logic state of a terminal change often as the circuit processes data. The XOR (exclusive-OR) gate acts in the same way as the logical "either/or." The output is "true" if either, but not both of the inputs are "true" while the output is "false" if both inputs are "false" or if both inputs are "true". The Exclusive-OR gate has both a symbol and a truth table pattern that is unique and is shown below: In the following diagram, we have an Exclusive-OR function built from a combination of AND, OR and NOT gates: The top rung (NC contact A in series with NO contact B) is equivalent to the top NOT/AND gate combination. The bottom rung (NO contact A in series with NC contact B) is equivalent to the bottom NOT/AND gate combination. The parallel connection between the two rungs at wire number 2 forms the equivalent of the OR gate in allowing rung 1 or rung 2 to energize the lamp. To make the Exclusive-OR function, it is needed to use two contacts per input: one for direct input and the other for the "inverted" input. The two "A" and two "B" contacts are physically actuated by the same mechanism. The common association between contacts is denoted by the label of the contact. There is no limit to how many contacts per switch can be represented in a ladder diagram as each new contact on any switch or relay (either normally-open or normally-closed) used in the diagram is marked with the same label. Read More