Teacher Notes



Teacher Notes
Publication No. 12633
Investigating GravityStudent Laboratory KitMaterials Included In Kit
Experiment 1. Investigating Pendulums
Clothespin clamps, 3 Fishing line, 1 roll Plumb bob, 2 sizes, small and large, 3 of each Experiment 2. Archimedes’ Principle Fishing line, 1 roll Modeling clay, 2 sticks Paper clips, 1 box Pipets, Beraltype, 10 Plastic cups, 9oz, 6 Spring scales, 250g, 2 Weighing trays, large, 6 Experiment 3. Center of Gravity Dry erase markers, 2* Fishing line, 1 roll Polygon shapes, set of 3* Shooks, 6 Washers, 3 Experiment 4. Atwood’s Machine Atwood’s machine Pulley cord, 9 m *Shared by all lab station groups. Additional Materials Required
Experiment 1. Investigating Pendulums
Meter stick Protractor Scissors Stopwatch Support stand Support stand ring Experiment 2. Archimedes’ Principle Beaker, 100mL Graduated cylinder, 100mL Paper towels Scissors Experiment 3. Center of Gravity Paper towels Ruler, metric Scissors Support stand Support stand clamp Experiment 4. Atwood’s Machine Heavy books Hooked masses, 200g, 2 (or equivalent) Meter stick Ruler, metric Scissors Slotted mass (or equivalent), 20g Slotted masses, 1 to 2g increments, 5–10 Soft towel Stopwatch Support stand Support stand clamp Table or platform, 1.5 m or taller Prelab PreparationExperiment 1. Investigating Pendulums
Safety PrecautionsThe plumb bobs contain lead. Lead is extremely toxic by inhalation (dust form) and ingestion. The clay is considered nontoxic. During the Atwood’s machine experiment, make sure the weights are tightly secured to the pulley cord so they will not come loose during the experiment. If one weight falls off one end of the pulley system, one side will crash down to the ground, while the other side flies up. The quickly falling and/or rising masses could cause injury. The masses may also be damaged if they hit the floor too hard. Students should wear safety glasses during this activity. Remind students to wash their hands with soap and water after completing each laboratory activity. Students should follow all normal laboratory safety guidelines. DisposalPlease consult your current Flinn Scientific Catalog/Reference Manual for general guidelines and specific procedures, and review all federal, state and local regulations that may apply, before proceeding. The materials from each lab should be saved and stored in their original containers for future use. Materials from this lab can be reused many times or disposed of following Flinn Suggested Disposal Methods #26a. Lab HintsInvestigating Pendulums
Experiment 2. Archimedes’ Principle
Experiment 3. Center of Gravity
Experiment 4. Atwood’s Machine
Teacher Tips
Correlation to Next Generation Science Standards (NGSS)^{†}Science & Engineering PracticesAsking questions and defining problemsDeveloping and using models Planning and carrying out investigations Analyzing and interpreting data Using mathematics and computational thinking Disciplinary Core IdeasMSPS2.A: Forces and MotionMSPS2.B: Types of Interactions HSPS2.A: Forces and Motion HSPS2.B: Types of Interactions Crosscutting ConceptsPatternsCause and effect Scale, proportion, and quantity Systems and system models Performance ExpectationsHSPS12: Construct and revise an explanation for the outcome of a simple chemical reaction based on the outermost electron states of atoms, trends in the periodic table, and knowledge of the patterns of chemical properties. Sample DataExperiment 1. Investigating Pendulums {12633_Data_Table_2}
Test 2
{12633_Data_Table_3}
Experiment 2. Archimedes’ Principle
{12633_Data_Table_4}
Experiment 3. Center of Gravity *Notice: For the “inverse” triangle polygon, the center of gravity lies outside the physical shape of the object. {12633_Data_Figure_17}
Experiment 4. Atwood’s Machine Height of the released mass: ___1.665 m___ Friction “mass”: ___10 g___ {12633_Data_Table_5}
Answers to QuestionsExperiment 1. Investigating Pendulums
Recommended Products


Student Pages


Student PagesInvestigating GravityIntroductionThis allinone Investigating Gravity Kit is designed to provide students the opportunity to explore the fundamental principles of the force due to gravity. Four handson lab stations can be arranged so student groups can experiment with pendulums, center of gravity, acceleration due to gravity and buoyancy (antigravity) forces. Students will use a pendulum to learn about simple harmonic motion and the properties that affect a pendulum’s swing period. In the center of gravity experiment, students examine mass distribution and balance. Using Atwood’s machine and a timer, students will indirectly measure the acceleration due to gravity. And finally, students will learn about the antigravity buoyant force that allows boats to float. Concepts
BackgroundExperiment 1. Investigating Pendulums {12633_Background_Equation_1}
See Figure 1 for a diagram of the forces acting on the plumb bob.
{12633_Background_Figure_1}
T = period of oscillation Archimedes was born about 287 B.C. in Sicily and was killed by a Roman soldier about 211 B.C. He is generally regarded as the greatest mathematician and scientist of antiquity and one of the three greatest mathematicians of all time, along with Isaac Newton (1643–1727) and Carl Friedrich Gauss (1777–1855). Archimedes was very involved in a wide range of scientific and mathematical studies. The famous “gold crown story” stemmed from the fact that the king was suspicious about the purity of the gold in his crown and asked Archimedes to find a way to determine if it was the real thing. Solving the problem seemed to be nearly impossible because little was known about chemical analysis in Archimedes’ day. The story goes that one day Archimedes was thinking about the problem while he was taking a bath. As he lay floating in a pool, he thought about how his body felt “weightless.” Suddenly he realized that all bodies “lose” a little weight when placed in water, and the bigger their volume, the more weight they lose. He realized that the density of a metal could be found from its weight and its weight loss in water. The weight of the king’s crown and its apparent loss of weight in water could tell him if the crown was made of pure gold. According to the story, when Archimedes realized this experimental design, he ran into the street yelling “Eureka! I have found it.” Density is a characteristic property of a material and pure elements or compounds may be identified by their density. Density is defined as the mass of a substance per unit of volume (Density = mass/volume). Density is commonly expressed as g/cm^{3} or g/mL. The density of pure water is 1.00 g/cm^{3} at 20 °C. Objects with a density greater than 1.00 g/cm^{3} will sink in pure water. Objects with a density less than 1.00 g/cm^{3} will float in pure water. Buoyant forces cause objects to “lose” weight when they are submerged in a liquid or fluid. This “antigravity” is generated by any fluid, including air. The buoyant force on a submerged object is equal to the weight of the liquid, or fluid, displaced by the object. The amount of fluid displaced by the object is equal to the volume of the object. Therefore, the density of the object can be determined by dividing the mass of the object by the volume of liquid it displaces. The weight of this displaced fluid is equal to the buoyancy force. The weight of the displaced liquid can be determined using the density of the liquid and the volume displaced. Experiment 3. Center of Gravity Gravity is the attractive force between all objects. The most familiar gravitational force is that of the Earth, which pulls all objects toward the ground and is more commonly referred to as an object’s weight. The more massive two objects are, the greater the gravitational force that exists between them. According to Isaac Newton’s (1643–1727) laws of gravitation, the Earth attracts every tiny particle of mass of every object and pulls them toward the center of the Earth. For any specific object (composed of many tiny particles), the center of gravity of the object is the location where all the individual gravitational forces acting on the individual particles add up and result in one net downward force. Consequently, the center of gravity is the point where we can assume all of the mass of the object is concentrated, and therefore is also referred to as the center of mass. The location of the center of gravity, especially for irregularly shaped objects, is critical for the overall stability and balance of an object on the Earth’s surface. An object is most stable on the Earth’s surface when the object’s center of gravity is at its lowest point, and is centered about the object’s supporting base. In general, when a force acts on an object, it can be assumed that the force acts on the center of mass of the object. If a force is specifically applied to an object at a position other than the center of mass (i.e., to the left, right, up or down from the center of mass), then this force will cause the object to rotate about its center of mass. When an object hangs from one corner, its center of mass will be located directly below the suspended point. This occurs because the object is most stable when its center of mass is at its lowest possible point. By drawing a vertical line through the hanging location, the line will also go through the center of mass. To pinpoint the center of mass, the object can be hung from another location and another vertical line may be drawn. The intersection of the two lines is the center of mass of the object. Hanging the object from a third location and drawing a third line will help verify the location of the center of mass of the object. Experiment 4. Atwood’s Machine The Atwood’s machine was developed by George Atwood (1745–1807) in the late 18th century to indirectly measure the acceleration of gravity. When two unequal masses are tied to the ends of a length of string and hung over a pulley, the larger mass will accelerate down, while the smaller mass accelerates up at the same rate. If the pulleys are assumed to be massless and frictionless, the acceleration depends on the acceleration due to gravity, the total mass of the system and the difference in mass between the two hanging masses. This follows Newton’s second law of motion—force equals mass times acceleration (F = ma). In the laboratory however, pulleys always have mass and are slowed by friction. Because real pulleys have mass, when they rotate their rotational energy takes away from the total energy that would otherwise be used to move the masses (in the ideal situation). The pulley sheave axles also produce a frictional force that acts against the rotation and decreases the total energy of the system. The frictional force is not constant, but increases as more weight is placed on the axles. In order to obtain realworld results that are closer to the accepted value of gravitational acceleration, the Atwood equation needs to include both the mass of the pulley as well as a term to account for the friction in the pulleys (see Figure 2). {12633_Background_Figure_2}
Refer to Figure 2 and the following equations for the derivation of the Atwood’s machine equation.
{12633_Background_Equation_2}
{12633_Background_Equation_3}
{12633_Background_Equation_4}
T_{1} = tension in string 1 {12633_Background_Equation_5}
Equation 5 reduces to
{12633_Background_Equation_6}
Substitute for T_{1} and T_{2} from Equations 1 and 2:
{12633_Background_Equation_7}
Rearrange to solve for g:
{12633_Background_Equation_8}
The pulley sheave’s mass is a constant. For the Atwood’s machine in this experiment the mass of the pulley sheave is 5.3 ±0.1 grams. The frictional “mass” can be inferred from the static friction of the pulley system and is dependent on the total mass hanging from the pulleys.
Experiment OverviewExperiment 1. Investigating Pendulums Materials
Experiment 1. Investigating Pendulums
Clothespin clamp Fishing line, 75 cm Meter stick Plumb bob, 2 sizes, small and large Protractor Scissors Stopwatch or watch with second hand Support stand and ring Experiment 2. Archimedes’ Principle Water Beaker, 100mL Fishing line, 30 cm Graduated cylinder, 100mL Modeling clay, 30g piece Paper clip Paper towels Pencil Pipet, Beraltype Plastic cup, 9oz Scissors Spring scale, 250g Weighing tray, large Experiment 3. Center of Gravity Dryerase marker Fishing line, 30 cm Paper towel Polygon shapes, set of 3 Ruler, metric Scissors Shooks, 2 Support stand Support stand clamp Washer Experiment 4. Atwood’s Machine Atwood’s machine Heavy books Hooked masses, 200g, 2 (or equivalent) Meter sticks, 2, or tape measure Pulley cord Slotted mass (or equivalent), 20g Slotted masses, 1 to 2g increments, 5–10 Soft towel Stopwatch Support stand Support stand clamp Table or platform, 1.5 m or taller Safety PrecautionsThe plumb bobs contain lead. Make sure the weights are tightly secured to the pulley cord so they will not come loose during the experiment. If one weight falls off one end of the pulley system, one side will crash down to the ground, while the other side flies up. The quickly falling and/or rising masses could cause injury. The masses may also be damaged if they hit the floor too hard. Wear safety glasses. Wash your hands with soap and water after completing this laboratory activity. Please follow all normal laboratory safety guidelines. ProcedureExperiment 1. Investigating Pendulums
Test 2. The period of the pendulum versus the length of the pendulum
Experiment 2. Archimedes’ Principle
Experiment 3. Center of Gravity
Experiment 4. Atwood’s Machine
B. Measure the friction “mass” of the pulley system
C. Measuring acceleration
Student Worksheet PDF 