Teacher Notes


Teacher Notes
Publication No. 13276
Force and MotionActivityStations KitMaterials Included In Kit
Experiment 1. Balanced and Unbalanced Forces
Hall’s carriage Nuts, 2 Protractor Pulley for inclined plane Screws, thin, 2 Screws, wide, 2 Support rod, metal Washers, 2 Wing nuts, 2 Wood inclined plane Experiment 2. Friction Block Masses, hooked, 100g, 5 Sandpaper strips, 3" x 12", 2 Wood blocks with eyebolt, 2 Experiment 3. The BungeeJumping Egg Ceiling hooks, 2 Elastic bands with metal barb ends, 5 Mass, hooked, 100g Plastic bags, 5 Plastic eggs, 5 String, one spool Experiment 4. Rings and Discs Disc, solid, 3½" Disc, solid, 5" Inclined plane Ring, 3½" Experiment 5. Collisions in One Dimension Metal Vtrack Rubber bands, 2 Steel ball bearings, ¾" diameter, 5 Wooden feet, 2 Additional Materials Required
Experiment 1. Balanced and Unbalanced Forces
Meter stick Pencil Ruler Scissors Spring scale, 250g/2.5N Stopwatch Support stand Support stand clamp Textbooks, 3–4 (optional) Experiment 2. Friction Block Spring scale, 250g/2.5N Tabletop, smooth and clean Tape (optional) Experiment 3. The BungeeJumping Egg Water, 500 mL Water (optional)* Balance, 0.1g precision Beaker, 600mL Clothespin clamp or paper clamp* Marker, ink Meter stick Paper towels Scissors Stepstool or ladder* Tape measure* Trough or catch bucket (optional) Experiment 4. Rings and Discs Balance, 0.1g precision Ruler or meter stick Stopwatch Textbook Towel Experiment 5. Collisions in One Dimension Ball bearings, large (optional) Ball bearings of different materials (e.g., glass, plastic, wood) (optional) *For making optional jumping platform Prelab PreparationExperiment 1. Balanced and Unbalanced Forces
Place the materials at the lab station. The sandpaper strips have sticky backs which can be used to secure them to the tabletop. Alternately, tape can be used to secure the sandpaper strip to the tabletop. Experiment 3. The BungeeJumping Egg
Place one end of the inclined plane on a textbook to make a slight decline. Place a towel a few centimeters from the bottom end of the inclined plane to stop the rolling objects. Experiment 5. Collisions in One Dimension
Safety PrecautionsThe materials in these five laboratory activities are considered safe. Please follow all normal laboratory safety guidelines. If an egg cracks on the floor, clean up the spill immediately to reduce the risk of a slippery surface. Use caution when standing on a ladder, stepstool or chair when releasing the eggs. Only the teacher should climb on the ladder or stepstool to set up the bungee jump and release the eggs. DisposalThe materials from each lab should be saved and stored in their original containers for future use. Lab HintsExperiement 1. Balanced and Unbalanced Forces
Experiement 2. Friction Block
Experiment 3. The BungeeJumping Egg
Experiement 4. Rings and Discs
Experiment 5. Collisions in One Dimension
Teacher Tips
Sample DataExperiment 1. Balanced and Unbalanced Forces Distance between start line and finish line: ___36.8 cm___ Mass of Hall’s carriage: ___55 g___Hanging mass: ___100 g___ {13276_Data_Table_1}
Experiment 2. Friction BlockData Tabe A {13276_Data_Table_2}
Data Tabe B
{13276_Data_Table_3}
Experiment 3. The BungeeJumping Egg
{13276_Data_Table_2}
Sample CalculationsSpring constant of elastic band: k = (100 g) x (980 cm/s^{2})/(94.1 cm – 75.0 cm) = 5130.9 g•cm/s^{2}•cm Calculated stretch distance of elastic band:X = [2 x (66.5 g) x (980 cm/s^{2}) x (263.1 cm)/(5130 g•cm/s^{2}•cm)]1/2 = 81.8 cm String length:SL = 263.1 cm – 75.0 cm – 10.0 cm – 81.8 cm = 96.3 cm ObservationsStudent answers will vary depending on the “success” of the bungee jump. Experiment 5. Collisions in One Dimension {13276_Data_Table_5}
Answers to QuestionsExperiment 1. Balanced and Unbalanced Forces
Part A: Frictional forces versus surface areas
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Student PagesForce and MotionIntroductionThis allinone Force and Motion Kit is designed to give students the opportunity to explore the fundamentals of forces, collisions, momentum and rotational motion. Five handson lab stations can be arranged so student groups can experiment with different aspects of force and motion. Concepts
BackgroundExperiment 1. Balanced and Unbalanced Forces An important way to illustrate all the forces acting on the object is to draw a freebody diagram. A freebody diagram will show the direction of the various forces acting on the object, and the length of the arrows (representing the forces) will show the relative magnitude of the different forces (see Figure 1). {13276_Background_Figure_1_Freebody diagram}
Experiment 2. Friction Block {13276_Background_Equation_1}
F_{f} = Force of friction There are two different types of friction (and therefore coefficients of friction). Static friction is the frictional force that initially prevents two surfaces from sliding past each other. Sliding (or kinetic) friction is the frictional force between two surfaces in contact that are moving past each other. Static friction is larger than sliding friction because when two surfaces are in contact with each other, and at rest, the tiny irregularities of the two surfaces tend to interlock with each other. Also, the adhesive and/or cohesive properties can take effect. When the surfaces slide past each other, there is less of a tendency for the surface’s tiny grooves to interlock, and the cohesive or adhesive properties are less effective. Instead, the two surfaces just ride along the outer edges of “bumps” and there is less force acting against motion. Static friction is the frictional force up to a certain limit. Once that limit is exceeded (by an applied force), the static friction will be overcome and the object will begin to move and sliding friction will take over. Experiment 3. The BungeeJumping Egg The law of conservation of energy states that energy cannot be created or destroyed, only converted between one form and another. During a bungee jump, the potential energy of the jumper on a tall platform (PE = mgh) is converted into kinetic energy during the fall (KE = 1⁄2mv^{2}). This kinetic energy is converted back into potential energy as the bungee cord stretches. At the bottom of the “ride” when the jumper momentarily stops, all the kinetic energy has been converted into spring potential energy—the energy stored in the stretched bungee cord (PE_{spring} = 1⁄2kx^{2}). An instant later, the bungeejumper is flung upwards as the bungee cord relaxes, thereby converting the spring potential energy back into kinetic energy. An egg will simulate a human bungeejumper in this experiment. In order to determine the length of string necessary to make the bungee cord long enough for a safe and exhilarating ride, five values are needed—(1) the total height of the jump that is desired, (2) the initial length of the unstretched elastic band, (3) the spring constant of the elastic band, (4) the mass of egg and basket and (5) the length of the basket (see Figure 2). {13276_Background_Figure_2}
The total height of the jump (h) is the height above the ground at which the jump begins (PH) minus the separation distance (d) between the egg and the ground at the bottom of the ride (Equation 2).
{13276_Background_Equation_2}
PH = Platform height above the floor {13276_Background_Equation_3}
F = force produced by a spring {13276_Background_Equation_4}
By hanging a mass with a known value from the end of the elastic band, and measuring the total length of the stretched elastic band, its spring constant can be calculated (Equation 5).
{13276_Background_Equation_5}
Where m_{u} is equal to the mass value, g is the acceleration of gravity constant (980 cm/s^{2}), and x_{u} is the stretch distance of the elastic band as a result of the hanging mass, m_{u}. Remember that the stretch distance of the elastic band is the stretched length minus the unstretched length. {13276_Background_Equation_6}
Rearranging Equation 6 to solve for x:
{13276_Background_Equation_7}
The calculated stretch distance of the elastic band at the bottom of the ride (X) is therefore equal to:
{13276_Background_Equation_8}
m_{e} = mass of the egg and basket Experiment 4. Rings and Discs Why does a solid disc roll down an inclined plane faster than a ring? All mass has the property of resisting a change in motion, or inertia. An object in motion wants to stay in motion, and an object at rest wants to stay at rest. For rotational motion (spinning motion), the motion “resistance” is a property based on the mass and the spatial distribution of the mass around a point of rotation (or axis of rotation). This specialized case of inertia is called moment of inertia. The distribution of the mass affects the moment of inertia in such a way that the further the bulk of the mass is distributed from the point of rotation, the larger the moment of inertia will be, and therefore, the harder it will be to change the object’s motion. In this activity, the 3½" ring and the 3½" solid disc have similar mass, but the 3½" ring has a larger moment of inertia than the 3½" solid disc because all the mass is distributed at the edge, far away from the center of the ring (the axis of rotation for the rolling ring). The mass in the solid disc is spread out evenly throughout the entire disc and therefore the “bulk” of the mass is located closer to center of the disc, so the moment of inertia is lower. The object with the lower moment of inertia will move faster down the inclined plane, as a result of the force due to gravity, and win. An interesting property of rolling objects is seen when the 3½" and 5" solid discs travel down the inclined plane in the same amount of time. The solid discs have the same mass distribution (density) and shape and therefore have the same “resistance to mass” ratio. This means that all objects of similar density and shape resist a change in motion equally, regardless of their mass or their size. The actual moment of inertia will be larger for a larger, more massive solid disc compared to the smaller solid disc, but the “resistance” relative to the mass will be the same for both solid discs. The “resistance to mass” ratio is larger for a ring than for a solid disc, and therefore the ring will always lose the race down the inclined plane to the solid disc. A more advanced approach to describe this activity incorporates kinetic and potential energy. When an object is at the top of the inclined plane, it has potential energy (stored energy). Potential energy (PE) is equal to the weight of the object, which equals the mass (m) times the acceleration from gravity (g), times the relative height (h) of the object (Equation 9). {13276_Background_Equation_9}
As the object begins to move down the inclined plane, the potential energy is converted into kinetic energy (energy of motion). For a rolling object, the motion is both linear (straight down the inclined plane) and rotational (the object rolls about its central axis), so two forms of kinetic energy are involved. Linear kinetic energy (KE_{l}) is related to the mass (m) and linear speed (v) of the object (Equation 10). Rotational kinetic energy (KE_{r}) is related to the moment of inertia (I) of the rolling object about the rotational axis and the rotational speed (ω; the Greek letter omega) of the rolling object (Equation 11). So, the total kinetic energy (KE_{T}) of a rolling object is equal to the linear kinetic energy plus the rotational kinetic energy (Equation 12).
{13276_Background_Equation_10}
{13276_Background_Equation_11}
{13276_Background_Equation_12}
All the potential energy the objects have when they are at the top of the inclined plane will be converted into kinetic energy at the bottom (Equation 13).
{13276_Background_Equation_13}
Equation 13 can now be used to determine the speed of rolling objects as they reach the bottom of the inclined plane. For rotational motion, the rotational speed is related to the linear speed by the radius (R) of the object (Equation 14).
{13276_Background_Equation_14}
Substituting Equation 14 into Equation 13:
{13276_Background_Equation_15}
Next, solve Equation 15 for v^{2}:
{13276_Background_Equation_16}
{13276_Background_Equation_17}
Equation 17 represents the speed of a rolling object at the bottom of the inclined plane. The object that will have the highest speed at the bottom of the inclined plane will be the first to reach the bottom. The denominator [m + I (1/R)^{2}] represents the “resistance” (total inertia) of the object. Experiment 5. Collisions in One Dimension When an object is set in motion, the object has a property known as momentum. Momentum is calculated by multiplying the mass of the object by its velocity. A fundamental principle of physics is that the momentum of a system of objects always remains constant. This principle is known as the conservation of momentum. If objects within a system collide, the momentum of the individual objects before and after a collision may change, but the total momentum of the system will remain constant. There are two types of collisions—elastic and inelastic. An elastic collision occurs when the objects that collide separate after the collision. An example of an elastic collision is the collision between a baseball and a bat. An inelastic collision occurs when the objects that collide stick together and move as one object after the collision. An example of an inelastic collision is when the baseball hits the catcher’s mitt and stops. In every collision, elastic or inelastic, momentum is always conserved. The main difference between the two types of collisions is that for an elastic collision, the kinetic energy of the system also remains the same. The conservation of energy principle does not apply to an inelastic collision because in an inelastic collision much of the energy is lost as heat and sound due to frictional forces that arise when the objects deform and “stick” together. In this activity, elastic collisions occur because the ball bearings separate and one set continues to move after the collision. Since these are elastic collisions, both the conservation of momentum and the conservation of kinetic energy principles apply. The conservation of energy principle limits the number of ball bearings that can be knocked away from the stationary series. No matter how fast a single colliding ball bearing hits the stationary series of ball bearings only one ball bearing will be knocked away (provided they are the same mass). If two ball bearings collide with the stationary ball bearings, two ball bearings will be knocked away. Example: A moving ball with mass (M) and velocity (V) collides into a stationary series of three ball bearings, each with the same mass as the colliding ball. The momentum and kinetic energy of the colliding ball is MV and ½MV^{2}, respectively. The colliding ball comes to a complete stop after the collision and its momentum and kinetic energy are transferred to the ball bearing at the end of the series. Momentum is conserved during every collision so the ball bearing is knocked away with velocity V (momentum equal to MV). The kinetic energy of the ball bearing is equal to ½MV^{2}, clearly showing that energy has also been conserved. Assume instead that two ball bearings were knocked away by the one colliding ball bearing. In order to conserve momentum, the two ball bearings (2M) would be knocked away from the series with half the velocity of the colliding ball [MV = 2M(½)V]. However, the kinetic energy of this twoball system would then be equal to ½(2M)(V/2)^{2}, or ¼MV^{2}. The kinetic energy of the twoball system is onefourth the original kinetic energy and is clearly not conserved as it should be during an elastic collision. Therefore, this result is not possible. One colliding ball will knock away only one ball (provided the masses are equal). One ball cannot knock away two or more balls no matter how fast it is traveling. Experiment OverviewExperiment 1. Balanced and Unbalanced Forces Materials
Experiement 1. Balanced and Unbalanced Forces
Hall’s carriage Inclined plane setup (assembled) Masses, hooked, 100g, 2 Meter stick Pencil Protractor Ruler Scissors Spring scale, 250g/2.5 N Stopwatch or watch with a secondhand String, thin Textbooks, 3–4 (optional) Experiment 2. Friction Block Masses, hooked, 100g, 5 Spring scale, 250g/2.5N Tabletop, smooth and clean Tape Wood block with eyebolt Experiement 3. The BungeeJumping Egg Water Balance, 0.1g precision Beaker, 600mL Ceiling hook or rod support platform Egg, plastic Elastic band with metal barb ends Marker, ink Mass, hooked, 100g Meter stick Paper towels Plastic bag Scissors String, thin, 150 cm Tape, transparent (optional) Experiement 4. Rings and Discs Balance, 0.1g precision Disc, solid, 3½" diameter Disc, solid, 5" diameter Inclined plane Ring, 3½" diameter Ruler or meter stick Stopwatch Textbook Experiement 5. Collisions in One Dimension Metal Vtrack Rubber bands, 2 Steel ball bearings, ¾" diameter, equal mass, 5 Wooden feet, 2 Prelab QuestionsExperiment 2. Friction Block Safety PrecautionsThe materials in these labs are considered safe. Do not allow the mass to drop to the floor. If an egg cracks on the floor, clean up the spill immediately to reduce the risk of a slippery surface. Please follow all other laboratory safety guidelines. ProcedureExperiment 1. Balanced and Unbalanced Forces
Part A. Frictional forces versus surface area
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