Includes notes for physics, Study notes of Physics

Download Includes notes for physics and more Study notes Physics in PDF only on Docsity!

Machines is a Division B and Division C event for the 2026 season. It consists of both a build and test portion involving the fundamental concepts of simple and compound machines, including the types of simple machines, their uses, input and output forces, mechanical advantage, and more. Event Overview Machines is an event in which competitors take a written test and use a homemade lever/lever system to determine the ratios of unknown masses. The included simple machines are levers, pulleys, wheels and axles, inclined planes, wedges, and screws. A simple machine is a mechanical device for applying force. They are useful because they can make physical jobs easier, by changing the magnitude or direction of the force, or the distance that the force is applied over. Compound machines are made of two or more simple machines. A compound machine can allow more complex machines and more complex outputs and functions. The Written Test The written test will include topics such as IMA, AMA, efficiency, work, torque, power, and history. A free response answer will be marked as wrong if significant figures are not taken into account, although some graders may give partial credit. Units should always be included. Force A force, intuitively a push or a pull, is any action that tends to change the motion of an object. A force has the potential to accelerate any object with mass. The SI unit of force is the newton (N). One newton is equivalent to the force required to accelerate a mass of 1 kilogram by 1 kg-m ) s* Forces are represented by the symbol F’. They are vectors, having both magnitude and direction. The net force on an object is the sum of all the forces acting on the object. An object's acceleration is given by Newton's Second Law F = ma, meter per second every second (NV = Machines Type Physics Category Lab Description Teams will complete a written test on simple and compound machine concepts and construct a lever-based measuring device prior to the tournament to determine the mass ratios between three test masses. Event Information Participants 2 Eye Protection None Impound No Allowed » Notes and resources Resources (unlimited, though in practice frequently compiled in a Binder) = Tools and supplies (non- electronic) * writing utensils ® Two Class III calculators Approx. Time 50 minutes History First 5020 Appearance Latest 2026 Appearance Rotates Yes Forum Threads 2026 (ht 2021 (ht 2020 (ht 2015 (ht 2014 (ht tps://sci tps://sci tps://sci tps://sci to:/Aww oly.org/f oly.org/f oly.org/f oly.org/p w.scioly. orums/vi orums/vi orums/vi hDBB3/v org/php where m is the mass of the object. Work Work is the application of a force over a distance. That is, a force F acting on an object is doing 'work' if the object experiences displacement As under the force. Work represents how much mechanical energy is being transferred from one object to another. The SI unit of work (and energy) is the joule (J), which is equal to the energy required to apply one newton of force applied over a distance of one meter (J = N-m). Work can be negative. For example, if object 2 is transferring mechanical energy to object 1, then the work done by object 1 is negative. Emphasis should be put on the difference between work done on and work done by. The work done on an object refers to the mechanical energy transferred to that object, whereas work done by an object refers to the mechanical energy transferred from that object to another. The amount of work performed by a force can be represented by the formula W=F'-d, in which "W" represents the work applied, "F" represents the amount of force, and "d" represents the distance over which the force is applied. If the angle formed by the force and the displacement is@, then the work that fF does on the object is given by W =F - As = |F|- |As| - cos, where F’,, As are vectors, while work W is a scalar. Energy The energy of an object quantifies its ability to affect its environment. The SI unit of energy is JouleJ = N-m. There are many forms of energy. In this event, we primarily consider an object's kinetic energy (the energy it possess from motion) and potential energy (the energy it posses from its location in a field; in this event, the gravitational field). The total mechanical energy of an object is given by the sum of its kinetic and potential energy. The kinetic energy of an object can be calculated as 1 : KE = zm where: KE is the kinetic energy of the object (Joules) m is the mass of the object (kilograms) v is the velocity of the object (meters/second) ewforu ewforu ewforu iewtopic. BB3/vie m.php?f m.php?f m.php?f php?f=1 wtopic.p =474) =369) =322) 86&t=59 hp?f=16 65) 7&t=497 5) Question Marathon Threads 2021 (ht sot 2015 (ht 2014 (ht tps://sci tps:/sci tp:/ww_ tp:/Aww oly.org/ff w.scioly. w.scioly. ie . oly.org/f ¥ Y orums/vi vuneh org/php org/php ewtopic. *™' BBSivie BB3/vie ewtopic. . . php ?f=2 ho ?=2 wtopic.p wtopic.p 97&t=18 ae , Np%=19 hp?t=17 482) 733) 38t=623 3&t=502 6) 3) Additional Resources Image Gallery Link (https//scioly.org/galler y/category.php?c=36) Official Resources Division B www.soinc.org/machines-b Website (https:/Awww.soinc.org/machi nes-b) Division C www.soinc.org/machines-c Website (https:/Awww.soinc.org/machi nes-Cc) Division B Results ist Kennedy Middle School 2nd Beckendorff Junior High School 3rd Jeffrey Trail Middle School Division C Results West Windsor-Plainsboro High School South 2nd Marquette University High School 3rd Troy High School 1st The gravitational potential energy of an object can be calculated with PE = mgh where: PE is the potential energy of an object (Joules) applied. A machine with an IMA less than one will move an object a further distance, at the sacrifice of force. The IMA is equal to the ratio of the distance over which the input force is applied to the distance over which the output force is applied. Each type of simple machine has a formula for determining its IMA, as described later in this article. However, the general formula for determining the ideal mechanical advantage is1MA = rk where "IMA" represents the ideal mechanical advantage of the machine, "d" oO represents the distance over which the input force is applied, and "d," represents the distance over which the output force is applied. Actual Mechanical Advantage Actual Mechanical Advantage (AMA) is experimentally determined mechanical advantage which takes friction and wear of the machine into account. It is always lower than the IMA due to energy losses associated with non-ideal conditions. The AMA is experimentally determined and is equal to the ratio of the output force to the input force. The formula for determining actual mechanical advantage is very similar to the general equation for determining mechanical advantage, and is described as AMA = =, where "AMA" represents the 3 actual mechanical advantage of the machine, "F," represents the output force, and "F;" represents the input force). Efficiency Efficiency describes the effect of friction and wear of the device on the output work. The law of conservation of energy states that the amount of energy in a closed system is constant. However, some work is always converted into other undesired forms of energy, such as heat. Efficiency is the ratio of output work to input work and is normally expressed as a percent. This is WwW. W; represents the output work, and "Wj" represents the input work. Efficiency is always less than 100%. Another way to determine efficiency is the ratio of the actual mechanical advantage to the ideal AMA IMA described by the formula 7 = , in which eta (n) represents the efficiency of the machine, "W," mechanical advantage (7 = ), which amounts to the same thing. Friction Friction is any force acting in the opposite direction of the net force on an object. The force of friction can be calculated using: Fy = 4N where: F’; is the force of friction (N) i is the coefficient of friction (unitless) N is the normal force of an object (N), or the force exerted by the surface on which an object is resting. This is not the weight of the object in all cases, but rather the force that pushes back on the object exerting force on it. There are two major types of friction that may be seen in this event: static friction and kinetic friction. Static friction is the force that opposes an effort force when an object is at rest, and kinetic friction is the force that opposes an effort force when an object is in motion. The coefficient of static friction is greater than the coefficient of kinetic friction, and both will vary significantly across materials. Torque Torque, also known as a moment of force, is the rotation equivalent of force. It is denoted by either tT or M. The SI unit of torque is N-m. aN ad Torque is equal to the force times the perpendicular distance between where = . . as the force is applied and the fulcrum (moment arm). The fulcrum is what the ‘ body rotates about. If the force is expressed in Newtons and the distance is expressed in meters, then the units of torque would appear to be Joules. However, in order to put emphasis on the fact that torque is not work, the Force and the units would actually be Newton-meters. The net torque on a body whose corresponding moment rotational velocity is not changing is 0. In simple machines, it can be calculated = a"™. by the formula T=F-d, where d , Known as a moment arm, is calculated by drawing a perpendicular from the center to the force, as shown in the figure to the right. The rotation equivalent formula for energy and power, used in calculations with motors, is B=r-6, P= -w, where 6 is the angular displacement and a is the angular velocity. Power Power represents how fast energy is being transferred or work is being done from one object to another. It is equal to the amount of energy transferred or the amount of work done over the time it took to transfer that energy or to do the work. The SI unit of power is a Watt, which is equal to one J Joule being transferred per second W = - ). Ww As described previously, the formula for determining power is P = — where P is the power developed W is the amount of work performed or energy transferred t is the time over which the work was performed or the energy was transferred Another useful formula for determining the power a motor is outputting isP = Tw where T is the torque the motor is exerting w is the angular velocity the motor's shaft. Kinematics Kinematics describes the motion of a body in space, and was permitted in the 2021 rules. Linear Velocity Ax Linear velocity is the rate at which an object is traveling per time. It is expressed as:v = Ae where p is the object's momentum m is the object's mass v is the object's velocity Conservation of Momentum Conservation of momentum refers to the velocity of a system remaining constant. This means that the sum of the momentum of two objects in a system will remain the constant throughout any interactions. It can be mathematically expressed as: Piinitial + Prinitial = Pifinal + P2final Where p is the momentum for the various two objects at various stages. Note that the momentums themselves can change, but the sums must stay constant. One example of this is in a "Newton's Cradle" system, where one ball collides with another and they transfer momentum, resulting in a velocity of the ball on the opposite side of the system equal to that of the initial ball. Impulse Impulse is the product of an exerted force and time of an object, and is measured in Newton seconds (N-s). A force applied over a period of time will create an impulse. Impulse is defined as: J = Faverage At where: J is the impulse Fiverage is the average force applied At is the amount of time over which the force was applied Impulse can also be defined as the change in momentum of an object over which the force was applied. This can be mathematically stated as: J = mvy — mv; where: J is the impulse m is the mass of the object vy is the final velocity of the object v; is the initial velocity of the object History Note: History is not a topic on the rules for the 2020 and 2021 seasons « Archimedes studied the lever, pulley and the screw around 3rd century BC, and discovered the principle of mechanical advantage in the lever. He also invented the Archimedes Screw, a device to transfer water to higher elevations. « Heron of Alexandria listed five devices in his book Mechanics that can "set a load in motion", the simple machines excluding the inclined plane, and with wheel and axle replaced by the windlass. « Galileo Galilei published the book Le Meccaniche (On Mechanics) in 1600, in which he expanded the theory behind simple machines. He was the first scientist to know that simple machines do not create energy, but only transform it. # Sir Isaac Newton stated the Laws of Motion in his book Philosophize Naturalis Principia Mathematica in 1687. « Amontons’ Laws of friction, rediscovered by Amontons after da Vinci and expanded by Coulomb, explained the role of friction in simple machines. Lever Discovered by Archimedes in 3rd century BC along with pulley and screw. Archimedes also discovered the idea of mechanical advantage in a lever. The first use of a lever by people was opening and breaking into shells and fruits to eat the food inside. By around 200 BC, scientists like Archimedes were figuring out why levers worked. Pulley It is not recorded anywhere when or by whom the first pulley was made. However, it is believed that Archimedes was the first person to have a documented block and tackle pulley system, as recorded by Plutarch. Inclined Plane Inclined planes have been used by people since prehistoric times, to lift heavy objects. The inclined plane was the last simple machine to be recognized as a machine. This is because it is motionless and can be found in nature in the form of hills and slopes. The ancient Greek philosophers that stated the other five simple machines never decided that an inclined plane should be a machine. However, the inclined plane was finally recognized during the Renaissance along with other simple machines. The first elementary rules of sliding friction on an inclined plane were discovered by Leonardo da Vinci, written in his notebooks in between the years of 1452 and 1519, but they still remain unpublished. The inclined plane was included as a simple machine after Simon Stevin derived its mechanical advantage in 1586. Wheel and Axle The earliest known wheels have been radiocarbon-dated to approximately 4000 to 3500 BCE. In Mesopotamia, wheels served initially as pottery wheels, but several centuries passed before they were placed on vehicles for transportation. Archaeologists have discovered depictions and fragments of vehicles across Afroeurasia, the oldest of which is associated with the Funnelbeaker culture in modern day Germany and Denmark. It remains an open question in archaeology of whether Mesopotamian influence motivated other cultures to create their own wheeled vehicles, or multiple cultures invented wheeled vehicles independently and contemporaneously. Wedge The origin of the wedge is still unknown today. One of the first examples of a wedge is a hand axe. Significant Figures See Significant Figures for information about significant figures. When performing calculations, answers must contain the appropriate number of significant figures when requested. Types of Simple Machines There are six types of simple machines; pulleys, inclined planes, wheel and axles, levers, wedges, and screws. Pulleys A pulley is a wheel on an axle that is designed to support movement and change of direction of a cable or belt along its circumference. There are two types of pulleys, fixed pulleys and movable pulleys. A fixed pulley is a Input foree Load stationary pulley that that doesn't move with the load. A movable pulley is a Fixed maveabie pulley that is freely suspended and moves with the load. pulley pulley Both types of pulleys are levers. A fixed pulley is a class 1 lever with the effort A diagram illustrating the arm equal to the load arm; a movable pulley is a class 2 lever with the effort __“l"ference between a arm twice the length of the load arm. ed pulley ane a movable pulley. A belt and pulley system has two or more fixed pulleys connected by a belt. The IMA is given by the Pout ratio , and the direction of rotation is the same between the pulleys, unless the belt is crossed in an Tin X shape, in which case the directions of rotation are opposites. Inclined Planes An inclined plane is a flat surface (a plane) that is on an angle (an incline). Inclined planes are used to raise masses to a higher elevation by extending the distance over which the force used to —— raise the mass is applied. The ideal mechanical advantage of an inclined plane is the ratio of the diagonal length (the length of the inclined surface) to the vertical length of which the surface rises to. 4" inclined plane with an ideal d; mechanical advantage of 4. This is illustrated in the formula IMA = rae in which "IMA" represents the ideal mechanical advantage of the inclined plane, "d;" represents the distance of the inclined surface, and "d," represents the vertical distance to which the inclined surface is raised. For example, in the diagram to the right, the inclined surface (the red line) is 4 units long, and the vertical distance to which that inclined surface is raised to (the green line) is 1 unit long, yielding an ideal mechanical advantage of 4. This means that moving the load up the inclined plane theoretically only requires one-fourth of the force required to lift the load up directly. For example, if a 60 newton load is placed at the bottom of the inclined plane, it would theoretically only require 15 newtons of force to move the load up the inclined plane. However, there would generally be significant amounts of friction, resulting in an actual mechanical advantage much less than the ideal mechanical advantage of 4. When static friction is introduced, the minimum required force can be calculated using a free body diagram, with a frictional force towards the bottom of the plane with magnitude |f| = |Fx|- 4 = mgpcos 8, where p is the coefficient of static friction. Wheel and Axles A wheel and axle consists of two parts, a wheel and an axle, in which both parts rotate with each other as a force is transferred from one to another. A wheel and axle system can be used in many ways, including to transport something, to turn something else on the axle, or to turn another wheel and axle. Examples of a wheel and axle include screwdrivers and driving wheel. The wheel and axle is a lever, where the center of rotation for both the Wheel and axie JIMA = R wheel and the axle is the fulcrum, and the rigid bar is turned into a circle. ’ As depicted in the diagram to the right, the formula for finding the ideal An example of a wheel and ; ; R. , icti mechanical advantage of a wheel and axle system is MA = —, in which ene syste Ge pieuna T formula for finding a wheel "IMA" represents the ideal mechanical advantage of the wheel and axle, _and axle system's ideal "R" represents the radius of the wheel, and "r" represents the radius of the — mechanical advantage axle. Levers A lever is a rigid bar resting on a pivot point, known as the fulcrum. There are three types of levers, characterized by the position of the input force (effort), output force (load/resistance), and fulcrum in relation to each other: =" First Class-|he fulcrum Is in the miaale, the effort Is on one side, and the load is on the other. An example iece Force : Force ae of a first class lever would be a seesaw or a crowbar. Load . : . Load " Second Class-The fulcrum is to one side, the load is Fas ae Fulesum ae in the middle, and the effort is on the other side. An lever attached fo fulcrum example of a second class lever would be a wheelbarrow or a nut cracker. Because the effort force As shown from left to right: 1st class, 2nd class, is always a greater distance from the fulcrum than the and 3rd class levers. resistance force (the force exerted on the load), a second class lever always has an ideal mechanical advantage greater than one (refer to the formula described below). « Third Class-The fulcrum is to one side, the load is on the other side, and the effort is in the middle. An example of a third class lever would be tweezers or an elbow. Because the resistance force is always a greater distance from the fulcrum than the effort force, a third class lever always has an ideal mechanical advantage of less than 1 (refer to the formula described below). To find the IMA of a lever, divide the distance between i ‘ tage the fulcrum and the effort by the distance between the | ——— A | , fulcrum and the load. This can be represented by the st “ IMA= = d; i il i ‘ —_ = : formula IMA = in which "IMA" represents the ideal ¢ A 0, effort he 2nd class ' = arm mechanical advantage of the lever, "dj represents the ‘“" a 5 "d= load distance from the input force to the fulcrum (known as i ; arm the input or effort arm), and "d, represents the distance = 3rd class - from the output force to the fulcrum (known as the load, The locations of the load and effort arms of all output, or resistance arm). These two distances are three classes of levers. depicted in each of the three classes of levers in the diagram to the right. _ , 6 ee me igh One way to remember the different classes of levers is with the mnemonic ee ra "FRE 123", in which "FRE" stands for fulcrum, resistance, and effort, p u i 9 a respectively. These correspond in order to the class of lever (the "123" in the mnemonic). Depending on which component of a lever (fulcrum, The "FRE 123" mnemonic resistance force, or effort force) is in between the other two, the class of lever can be determined by matching that letter with its corresponding number. For example, knowing that the effort force is in the middle between the fulcrum and resistance force in a pair of tweezers, it can be determined that tweezers are a 3rd class lever (because 3 corresponds the "E" in "FRE"; "E" representing the effort force, which is in the middle for tweezers). The lever is balanced if it is at rest or rotating at a constant rate. When a lever is balanced, the net torque is zero, so the effort torque is equal to the load torque, FP; di, = out Donut » IMA= nm din out Wedges A wedge is a triangularly shaped compound inclined plane. A wedge converts a force applied to its blunt end (the side opposite of where the two inclined surfaces meet) to forces perpendicular to the inclined surfaces. Uses of a wedge include separating two objects, splitting an object, lifting an object, Therefore, the differential pulley has mechanical advantage _ As 1_z R the radius of the two axles become closer, the mechanical advantage becomes much bigger. The mechanical advantage of a differential windlass can be calculated similarly, with the long handle providing even more mechanical advantage by acting like a wheel and axle. The Device Diagram for a differential pulley In the Device testing portion of the event, teams use a class 1 lever to _ and differential windlass. determine the ratios between three unknown masses. The goal is to determine the ratios as quickly and accurately as possible. The mass of the unknown masses can vary between parameters specified in the rules. The maximum allowable ratios defined in the rules vary by level of competition. Material Metal is the strongest material to use for building the lever. However, it is more difficult to work with than wood without experience, may produce a wobbling effect, and is also more expensive. Wood is probably the easiest to work with, but it may bend if the wood is too light, and often causes more friction than the other materials. PVC pipe will bend and may break with higher masses. However, the material can be used to create a sliding fulcrum design. Designing the device Almost all designs involve a stand supporting the lever. However, there are many designs to connect the lever to the stand: 1. Put the center of mass of the lever on an object which acts as the fulcrum. This is the simplest design, but is hard to work with because the lever may slide and get unbalanced. The masses will also be placed on top of the lever, so it may be difficult to read the distance from the mass to the fulcrum. 2. Build a stand and then hang the lever off of it. This design has minimal friction and thus is accurate. However, because of its minimal friction, balancing the lever would be time consuming, with a lot of fine tuning. 3. Build a stand and put a bar on top. Drill a hole through the lever and slide the bar through that hole. The design is similar to Design 1, but it is easier to work with and is higher off the ground. The device has more friction than Design 2, and therefore is faster but less accurate. (not proper description) 4. Build a stand and hang a ring from it that the lever can slide through. This design is the fastest for measuring the ratios. However, moving the fulcrum would cause the weight of the lever to also generate torque and produce error in the measurement. This error can be minimized by building the lever with light wood or PVC piping, or by incorporating the weight of wood in the calculation. Tips » The lever is very close to balanced when it is not rotating, even if it is not perfectly level. « Practice: Make sure the lever can measure the ratio for all possible masses and all possible mass ratio. For example, consider the size parameters for the mass « Devices such as the Steelyard Balance (https://en.wikipedia.org/wiki/Steelyard_balance), although not suitable for the event parameter, may provide inspiration for the design.