Materials Included In Kit

Additional Materials Required

Prelab Preparation

Experiment 1. Balanced and Unbalanced Forces

1. Obtain the wood inclined plane, pulley, wing nuts, screws and washers.
2. Secure the pulley to the inclined plane as shown in Figure 9.
   {13276_Preparation_Figure_9}
3. Obtain a pencil and a ruler.
4. At the end opposite to the pulley, measure approximately 12 cm from the end of the board and lightly mark this point with a pencil. The mark should be far enough from the end of the inclined plane so that all four wheels of the Hall’s carriage are on the inclined plane when the front of the carriage lines up with this mark.
5. Use a ruler to make a light pencil line through this 12 cm mark so the line is parallel to the end of the board. This line represents the “start line.”
6. At the pulley end, measure approximately 7 cm from the end of the board and lightly mark this with a pencil
7. Repeat step 5 to draw the “finish line.”

Experiment 2. Friction Block

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 Bungee-Jumping Egg

1. Set up a ceiling platform for a site to attach the bungee cord string. Ceiling hooks are provided to connect to ceiling tracks found in many schools (follow the instructions provided on the ceiling hook package). A clamping mechanism suitable for your school ceiling design will be needed if the ceiling hooks cannot be used. A C-clamp connected to an I-beam, or clamping or tying the string to a ventilation duct screen may be one option. Do NOT use sprinkler nozzles that may be in the ceiling as an attachment point. It is best to consult the custodial staff if you are unsure about where to hang the bungee cords. Use caution when working on a ladder or step-stool to setup the ceiling platform.
2. Once the jumping platform is set up, use a tape measure to measure the height of the jumping platform above the ground. This may take two people. Measure from the bottom of the platform (the bottom of the ceiling hook if that is used) where the “mark” on the string will be positioned (see Procedure, step 23). Record the height of the platform to the nearest 0.1 cm and give this measurement to your students when they perform the experiment.
   Height of jumping platform (PH): _____________
3. Cut five (5) 150-cm long pieces of string from the string spool prior to class (or enough for each lab group).

Experiment 4. Rings and Discs

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

1. Slide the wooden support feet onto the ends of the metal V-track according to Figure 10.
   
   {13276_Preparation_Figure_10}
2. Wrap the rubber band around the end of the wooden feet as shown in Figure 10. The rubber band will act as a stopper for the ball bearings.
3. Place the metal track on a flat, level tabletop.

Safety Precautions

The 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 step-stool to set up the bungee jump and release the eggs.

Disposal

The materials from each lab should be saved and stored in their original containers for future use.

Lab Hints

Experiement 1. Balanced and Unbalanced Forces

• Enough materials are provided in this kit for one student group. This laboratory activity can reasonably be completed in one 50-minute class period. All materials are reusable.
• Textbooks can be placed under the support stand in order to raise it high enough to achieve the 45° or higher angles. If a tall support stand is used, textbooks may not be necessary.

Experiement 2. Friction Block

• Enough materials are included for two groups of students. This laboratory activity can reasonably be completed in one 50-minute class period. All materials are reusable.
• Each student group needs to share the set of five hooked masses placed at this lab station.
• Additional Friction Blocks kits (AP4605) can be purchased for each individual lab group.
• If the tabletop is too smooth to obtain good results, use the sandpaper strips included. Peel the backing from the strips, secure them to the tabletop, and use that surface as the “tabletop.”

Experiment 3. The Bungee-Jumping Egg

• Enough materials are provided in this kit for five student groups. Position this lab station near the friction block in order for students to borrow one of the 100-g hooked masses during the spring-constant measurement.
• The plastic eggs may have holes in one or both ends. Cover the holes inside with tape or clay. Check for water leaks.
• This laboratory activity can reasonably be completed in one 50-minute class period. All materials are reusable.
• Have students double check all their calculations before bungee jumping.
• The easiest method to attach the bungee cord string to the ceiling hook is to line up the “mark” on the string with the bottom of the hook, and then wrap the loose end of the string around the hook several times. Four or five wraps around the hook will be enough to secure the string and prevent it from slipping during the bungee jump. For additional security, a clothespin clamp or paper clamp can be clamped over the wrapped string on the hook.
• Make sure the bungee cord does not get tangled up or twisted together before the egg is released. Use one hand to hold the string apart and to the side before the drop. Let go of the string immediately after the egg is released.
• Be careful not to drop the bungee cord and break the egg before it is time to bungee jump!
• Measurement errors frequently occur when the length of string or stretched elastic band extends beyond the length of the meter stick. Students must use very precise techniques in order to accurately measure lengths that are longer than one meter. Inaccurate measuring may lead to a cracked egg or a very short “ride.”
• The plastic egg may not crack open as easily as a real egg will. Connecting the egg pieces as “loosely” as possible will make a weak egg that should crack open from light contact with the floor. It may take some practice to determine just how “loose” they need to be. Tape can be added to one side of the egg pieces to act as a hinge. Then the pieces can be very loosely capped and placed into the sandwich bag.
• If students want to really test the safety of their bungee jump, use raw or hard-boiled eggs in place of the plastic eggs. Do they trust their measurements and calculations?
• The Background section assumes previous knowledge about the conservation of energy and Hooke’s law. Please refer to your physics or physical science textbooks for more information about these topics.
• (Optional) Fill a trough or catch bucket with water to act as the pool or lake and place it below the bungee-jump platform. The splash from an over-exhilarated jump can be very dramatic.

Experiement 4. Rings and Discs

• Do not raise the inclined plane up to a large angle because this may cause the ring and disc to slip down the inclined plane rather than roll, which would skew the “expected” results for the rolling objects.
• A towel or other soft barricade can be placed at the end of the inclined plane to stop the ring and discs once they finish the race.
• The moment of inertia differences (speed of descent differences) can best be observed when using the longest inclined plane is at a shallow angle so it takes time for the objects to roll and separate.
• All materials are reusable.

Experiment 5. Collisions in One Dimension

• This laboratory activity can be completed as an inquiry-based lab, in which students experiment with collisions before they are given any Background information about conservation of energy and momentum. Or this laboratory activity can be completed as a reinforcement tool after the topics have been discussed in class. In this case, the Background information and any textbook information should be provided before the experiment.
• Additional experiments include rolling one ball at one stationary ball, rolling two balls at one stationary ball, rolling one ball at two stationary balls and rolling two balls at two stationary balls. Students may also want to experiment with collisions between two moving ball bearings. Students may experiment with different speeds and compare the speed and direction of each ball after the collision. For each additional experiment, students should create and record their observation in a data table.

Teacher Tips

• Set up each lab station accordingly before class. Students should leave the stations as they find them before they move on to the next lab station.
• All materials are reusable!
• Each lab, except the Bungee-Jumping Egg, should take approximately 20–30 minutes. The Bungee-Jumping Egg can be completed in one 50-minute time period. In order to accomplish the Bungee-Jumping Egg in 20–30 minutes, students must read the lab and background information carefully so they know how to do each calculation before class. Five Bungee-Jumping Egg setups are provided so more than one group can work on this activity at the same time.
• Before class, prepare copies of the student worksheets for each student. The Background information for each experiment can also be copied at the instructor’s discretion. However, the Background information for the Bungee-Jumping Egg should be included in order for students to grasp the Hooke’s law concept and have their calculations prepared before class.

  Experiment 4. Rings and Discs

• This activity introduces the concept of the moment of inertia, and reinforces the elementary principles of mechanics and Newton’s laws of motion.

Sample Data

Experiment 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___ Experiment 2. Friction Block

Data Tabe A Data Tabe B Experiment 3. The Bungee-Jumping Egg Sample Calculations
Spring constant of elastic band:

k = (100 g) x (980 cm/s²)/(94.1 cm – 75.0 cm) = 5130.9 g•cm/s²•cm

Calculated stretch distance of elastic band:

X = [2 x (66.5 g) x (980 cm/s²) x (263.1 cm)/(5130 g•cm/s²•cm)]1/2 = 81.8 cm

String length:

SL = 263.1 cm – 75.0 cm – 10.0 cm – 81.8 cm = 96.3 cm

Observations
Student answers will vary depending on the “success” of the bungee jump.

Experiment 5. Collisions in One Dimension

Answers to Questions

Experiment 1. Balanced and Unbalanced Forces

1. Calculate the average time for each trial. Record this information in the Data Table.
2. Calculate the average carriage speed for each inclined plane angle.
   {13276_Answers_Equation_18}

   60° – Average speed = negative (rolls backward)

3. What forces acted on the carriage? (Optional) Draw a free-body diagram depicting the forces acting on the carriage.

   The force due to gravity, frictional forces, the normal force and the tension in the string are all the forces acting on the carriage.

4. During the timing measurements, did the carriage move with the same speed throughout the entire length of the inclined plane?

   No, the speed changed.

5. If the speed of the carriage changed, what does this say about the forces acting on the carriage?

   The carriage accelerated, meaning there is net force acting on the carriage.

6. What happened when the inclined plane angle was at 45°? What does this say about the forces acting on the carriage?

   The carriage did not move. All the forces were balanced.

7. What happened when the inclined plane angle was at 60°? Explain why this occurred.

   The carriage rolled down the inclined plane instead of up. The force due to gravity pulling down on the carriage and 100-g mass finally overcame the force due to gravity pulling the hanging 100-g mass down.

8. When the forces acting on an object are balanced, can the object be moving? Explain.

   Yes, if all the forces acting on an object are balanced, the object can still be in motion. The object will have a constant velocity and will not be accelerating or changing directions.

Experiment 2. Friction Block

Part A: Frictional forces versus surface areas

1. Does it take more force to start an object sliding over a surface or to keep it sliding at a constant speed?

   The force required to keep the object sliding is less than the force required to initially get it to slide. Sliding friction is less than static friction.

2. How do the frictional forces between the two different experiments compare? What influence does the surface area have on the frictional force? Why?

   The static frictional force and the sliding frictional force were the same for both experiments. The surface area is not a factor affecting frictional force when the other variables are constant (on most surfaces). Only the Normal force and the coefficient of friction (static or sliding) determine the frictional force acting against motion.

Part B: Frictional forces versus Normal force

3. On a separate sheet of graph paper, draw a graph of static frictional force versus Normal force, using the information in Data Table C. Draw a “best fit” line through the data points.
   {13276_Answers_Figure_11}
4. Does the data produce a straight “best fit” line? If yes, what does the slope of the line represent?

   Yes, the slope of the line represents the coefficient of static friction between the block of wood and the tabletop.

5. On the same sheet of graph paper, draw a graph of the sliding frictional force versus Normal force, using the information in Data Table C. Draw a second “best fit” line through this data. A different color pen or pencil can be used to distinguish between the two sets of data.
6. Does this data produce a straight “best fit” line? If yes, what does the slope of this line represent?

   Yes, the slope of the line represents the coefficient of sliding friction between the block of wood and the tabletop.

7. Determine the coefficient of static friction and sliding friction between the wood block and the tabletop from the corresponding graphs. Refer to Equation 1.

   Coefficient of Static Friction equals the slope of the “best fit” line from the first set of data. The Coefficient of Sliding Friction equals the slope of the “best fit” line from the second set of data.
   
   Find the slope by taking the “rise over the run” of the line, or from the sample data:

   {13276_Answers_Equation_19}

Experiment 4. Rings and Discs

1. How did the motion of the 5" diameter disc compare to your prediction?

   The 5" disc traveled as quickly as the 3½" diameter disc. My prediction was that it would roll slower.

2. Which round object(s) rolled down the inclined plane the fastest?

   The two discs rolled down with equal speed. The ring was the slowest object.

3. Was mass an important factor for the speed of the rolling objects down the inclined plane? Explain.

   No, mass was not important. The more massive 5"-diameter disc rolled at the same speed as the lighter 3½" diameter disc.

4. What physical property made the speed of the rolling objects different?

   The position of the mass around the rotation point.

Collisions in One Dimension

1. What type of collision did the ball bearings experience—elastic or inelastic? Explain.

   The ball bearings experience elastic collisions because the balls separate after the collision.

2. What happened to the colliding ball bearing(s) after the collision?

   The colliding ball stopped after it collided with the stationary ball bearings. It did not bounce back or recoil after the collision.

3. How did the number of stationary ball bearings affect the collision results?

   The number of stationary ball bearings did not affect the number of balls that were knocked away. Only the number of colliding balls affected the number of balls that were knocked away.

4. How did the speed of the colliding ball affect the speed and number of ball bearings knocked away?

   The speed of the colliding ball bearing only affected how fast the knocked-away ball traveled. A faster moving colliding ball still only knocked away one ball. Two fast-moving balls knocked away two balls from the series.

5. How did the number of colliding ball bearings affect the number of ball bearings knocked away?

   One ball bearing could only knock away one from the series—no matter how fast it traveled. Two ball bearings could only knock away two balls from the series. The speed of the colliding balls affected the speed of the knocked-away balls, but not the number.

6. (Optional) If the colliding ball bearings had more mass than the individual stationary ball bearings, how would this affect the results of the collisions? (Would more ball bearings be knocked away? Fewer? Would the colliding ball bearing stop after the collision? How would the speed of the balls that are knocked away be affected?)

   A more massive colliding ball may knock away more than one ball from the series. The total momentum and kinetic energy must still be conserved however. If one ball bearing is knocked away, it will most likely have a higher velocity than the colliding ball because it will be less massive and, in order to conserve momentum, its speed must be faster.

Introduction

This all-in-one Force and Motion Kit is designed to give students the opportunity to explore the fundamentals of forces, collisions, momentum and rotational motion. Five hands-on lab stations can be arranged so student groups can experiment with different aspects of force and motion.

Concepts

• Force
• Net force
• Acceleration
• Friction
• Hooke’s law
• Conservation of energy
• Acceleration of gravity
• Rotational motion
• Moment of inertia
• Newton’s Laws of Motion
• Potential energy
• Kinetic energy
• Collisions
• Conservation of momentum

Background

Experiment 1. Balanced and Unbalanced Forces

A force is the interaction of an object with its environment—typically described as a push or a pull on an object. A force causes an object’s motion to change by slowing it down, speeding it up or changing its direction. This change in motion is known as acceleration. An object is said to accelerate when the object’s motion increases, and decelerate when its motion decreases.

Often times, more than one force will act on an object. On Earth, there is always a force due to gravity pulling objects downward. Therefore, when an object moves on Earth, it will most likely have at least two forces acting on it. When more than one force acts on an object, the object will respond to the net force. Forces are vector quantities, meaning they are defined with a magnitude and direction. All the force vectors acting on an object will add up to one resultant force, and the object will respond to this single net force. In other words, the object moves as if only one force acts on it. If the net forces add up to zero (i.e., the forces are balanced), then no net force acts on the object and it will continue to have the same constant motion. If the object is at rest, it will remain at rest, and if it is in constant motion, it will stay in constant motion. This is commonly referred to as Newton’s first law of motion, or the law of inertia. In order to change an object’s motion, the net force acting on the object must be greater than zero. And when the net force is greater than zero, the object will be accelerated or decelerated.

An important way to illustrate all the forces acting on the object is to draw a free-body diagram. A free-body 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).

Experiment 2. Friction Block

Friction is created when any two surfaces are in contact with each other. The factors that influence friction include the surface finish (or smoothness), the cohesive and adhesive ability of molecules, and the force holding the surfaces together.

Surface finish is a major contributor to the frictional force. All surfaces, no matter how “smooth,” have irregularities. Even the smoothest object will still have irregularities at the atomic level because atoms and molecules never bond together to form completely flat surfaces. These irregularities cause a grinding action to occur when two surfaces move against each other. As a result, heat is generated (the moving objects lose energy) and particles are worn away from the materials. Smaller irregularities, or smoother surfaces, produce less frictional force to act against the direction of motion than larger irregularities.

Another contributor to friction is the cohesive and adhesive abilities of the atoms and molecules in the materials. Cohesion is the attraction of like atoms or molecules. When two plates of glass come in contact with each other (with no air pockets), the two pieces nearly “fasten” together. Glass is considered to have a very smooth surface, but it is very difficult to pull or slide the two pieces apart. This is an example of cohesion. Adhesion is the attraction of unlike atoms or molecules. Water droplets clinging to the side of a glass beaker is an example of adhesion. These properties affect frictional force because the attraction between two surfaces at the atomic level requires more force to break in order to move the object and maintain its motion at the macroscopic level.

The perpendicular force (or Normal force) holding two surfaces together is a very important factor influencing the frictional force. The larger the force holding two surfaces together, from gravity or some other outside force, the larger the force of friction. In the case of an object sliding on a horizontal surface, the Normal force equals the weight of the object. A mathematical equation for frictional force is as follows:

F_f = Force of friction
μ = Coefficient of friction (Greek letter mu)
N = Normal force

The coefficient of friction is a unique property used to describe the relationship between the frictional properties of two surfaces in contact with one another and the frictional force. This property is based on the first two factors that contribute to friction—the smoothness of the two surfaces, and their adhesive or cohesive properties.

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 Bungee-Jumping 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 = 1⁄2mv²). 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 = 1⁄2kx²). An instant later, the bungee-jumper is flung upwards as the bungee cord relaxes, thereby converting the spring potential energy back into kinetic energy. An egg will simulate a human bungee-jumper 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). 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).

PH = Platform height above the floor
d = separation distance between the egg and the floor at the bottom of the ride
h = Total height of the jump
SL = String length
UL = Unstretched elastic band length
BL = Egg basket length
X = Stretch distance of the elastic band during the jump

The force produced by a stretched spring is directly proportional to the distance the spring is stretched compared to its unstretched state according to Equation 3. This is better known as Hooke’s law. The negative sign in the equation signifies that the force produced by a spring is a restoring force (i.e., the force wants to bring the spring back to its equilibrium, unstretched, state).

F = force produced by a spring
k = spring constant
x = stretch distance (the difference between the stretched and unstretched length of the spring)

The spring constant for the elastic band can be calculated by rearranging Equation 3: 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).

Where m_u is equal to the mass value, g is the acceleration of gravity constant (980 cm/s²), 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.

To determine the total length of the bungee cord needed for a safe and exhilarating bungee jump, the stretched length of the elastic band at the bottom of the ride must be calculated. Since the initial potential energy of the “jumper” will be converted completely into spring potential energy at the bottom when the elastic band is fully stretched, the initial potential energy will equal the final spring potential energy in the elastic band according to Equation 6.

Rearranging Equation 6 to solve for x: The calculated stretch distance of the elastic band at the bottom of the ride (X) is therefore equal to:

m_e = mass of the egg and basket
g = acceleration of gravity, 980 cm/s²
h = height of the ceiling platform above the floor minus the separation distance (d) at the bottom
k = spring constant of the elastic band

Once X is calculated, use the ceiling platform height, unstretched elastic band length, and basket length to calculate the length of the string necessary to complete the bungee cord, following Equation 2.

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). 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). 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). 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). Substituting Equation 14 into Equation 13: Next, solve Equation 15 for v²: 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 conser-vation 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 ½MV², 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 ½MV², 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 two-ball system would then be equal to ½(2M)(V/2)², or ¼MV². The kinetic energy of the two-ball system is one-fourth 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 Overview

Experiment 1. Balanced and Unbalanced Forces
What is a force? When an object moves, does it always have a net force? What is a net force?

Experiment 2. Friction Block
Friction might slow you down, but without it you would not go anywhere. In this experiment, some properties of friction will be tested and discovered.

Experiment 3. The Bungee-Jumping Egg
Bungee jumping would not be as “safe” as it appears without the understanding of some basic physics principles—the conservation of energy and Hooke’s law for springs. A safe and exhilarating bungee jump is one in which no one is injured, the free fall lasts as long as possible, and the bungee jumper comes as close to the ground as possible without touching it. In this activity, the law of conservation of energy and Hooke’s law will be used to build a safe and exhilarating model bungee jump of an egg!

Experiement 4. Rings and Discs
A ring and a disc begin to roll down an inclined plane at the same time. Which one will win the race? Or, will they reach the bottom at the same time? Let’s find out.

Experiement 5. Collisions in One Dimension
Discover some of the basic laws of physics by studying simple one-dimensional collisions. Smash one ball into a series of three or four balls and observe what happens. Predict how colliding two ball bearings at the same time will affect the collision results.

Materials

Prelab Questions

Experiment 2. Friction Block

In this lab activity, static and sliding friction of objects of different sizes and weights will be studied. In order to obtain accurate measurements, practice the following procedures until confident and reproducible results are obtained.

The maximum static frictional force is the force that is measured on the spring scale just before the block begins to slide. This is best measured by slowly and evenly pulling the block horizontally with the spring scale, while closely observing the spring scale needle. Record the maximum force measured by the spring scale immediately before the block begins to move. Once the block begins to move, the force registered by the spring scale will decrease slightly. With a spring scale, practice measuring the maximum static friction between the tabletop and the wood block until confident results are obtained.

Sliding frictional force is measured when the block is moving with constant speed. Use the spring scale to pull the wood block horizontally. As the block slides, adjust the amount of force needed to keep the block moving until the spring scale reading is balanced. When the spring scale is balanced, the block will be moving at a constant speed because the pulling force and the sliding frictional force are balanced (no net force acting on the block means no acceleration). The measurement on the spring scale at this point will be equal to the sliding frictional force. Again, practice this technique until consistent results are obtained. The speed of the object will not influence the sliding frictional force, but it is generally easier to read the moving spring scale when it is traveling slowly. Pulling the block a meter or two along the tabletop may be required in order to adjust the pulling force appropriately to obtain a constant speed (and therefore balanced forces).

During the experiments, several trials or practice runs may need to be performed in order to obtain accurate measurements for each step. So for each measurement step, perform several trials and record only the most reliable measurement. Record the results (in Newtons) in the appropriate table on the Friction Blocks Worksheet.

Safety Precautions

The 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.

Procedure

Experiment 1. Balanced and Unbalanced Forces

1. Obtain a Hall’s carriage, thin string, a support stand, a support stand clamp and the support stand rod.
2. Measure the mass of the carriage to the nearest gram using the spring scale. Record the mass in the data table.
3. Measure and cut approximately 60 to 80 cm of string.
4. Tie one end of the string to the front of the carriage.
5. Tie a loop in the other end of the string (see Figure 3).
   {13276_Procedure_Figure_3_Loop knot}
6. Use a meter stick or ruler to measure the distance between the “start” line and the “finish” line pencil marks on the inclined plane. Record this distance in the data table on the Balanced and Unbalanced Forces Worksheet.
7. Place the inclined plane flat on the tabletop with the end of the pulley hanging over the edge of the table. Remove the wide screw and nut from the inclined plane, if necessary.
8. Place the front wheels of the Hall’s carriage at the starting line. Hang the string over the pulley so that it hangs down.
9. Obtain a stopwatch and two 100-g masses.
10. Add one mass to the compartment in the Hall’s carriage. Add the second 100-g mass to the loop in the string hanging over the pulley. Do not release the mass yet.
11. Check that the string runs over the pulley and that there is not much slack in the string between the carriage and the mass. Also, check that the front wheels are on the starting line. Prepare the stopwatch for timing.
12. With the stopwatch ready, release the mass and begin timing. Stop timing when the front wheels cross the finish line. Catch the 100-g mass before the carriage reaches the pulley and falls off the table. Safety Note: The cart will travel quickly in the first setup. One lab partner must be ready to stop the cart before it runs into the pulley. Record the time in the data table.
13. Repeat steps 11 and 12 two more times for a total of three trials. Record the time measurements in the data table.
14. Set up the support stand, support stand clamp, support rod, inclined plane and carriage as shown in Figure 4.
    {13276_Procedure_Figure_4}
15. Use a protractor and adjust the angle of the inclined plane to 15°.
16. Repeat steps 8–13. Record the time measurements in the data table.
17. Adjust the angle of the inclined plane to 30°.
18. Repeat steps 8–13. Record the time measurements in the data table.
19. Adjust the angle of the inclined plane to 45°.
20. Repeat steps 8–13. Record the time measurements in the data table.
21. Adjust the angle of the inclined plane to 60°.
22. Repeat steps 8–13. What happens to the carriage? Record observations in the data table.

Experiment 2. Friction Block

Part A. Frictional forces versus surface area

1. Place the wood block flat on a tabletop.
2. Attach a spring scale to the eyebolt.
3. Measure the static friction between the block and the tabletop. Record the results in Data Table A on the Friction Blocks Worksheet.
4. Measure the sliding friction between the block and the tabletop. Record the results in Data Table A.
5. Now, place the same wood block on its edge (thin side) and again attach a spring scale to the eyebolt.
6. Measure the static friction between the block on its edge and the tabletop. Record the results in Data Table A.
7. Measure the sliding friction between the block on its edge and the tabletop. Record the results in Data Table A.

Part B. Frictional forces versus Normal force

8. Obtain 5 manufactured masses at 100-gram increments.
9. Place the wood block on the tabletop and attach a spring scale to the eyebolt.
10. Measure the static and sliding friction between the wood block and the tabletop. Record the results in Data Table B.
11. Place one 100-gram mass on the wood block. Enter the weight of the mass in Newtons in Data Table B. (Multiply the mass in grams by 0.0098 to obtain the weight in Newtons.)
12. Again, measure the static and sliding friction between the wood block, with the additional mass, and the tabletop. Record the results in Data Table B.
13. Repeat steps 11–12 using 200-, 300-, 400- and 500-g masses. Record the total weight used for each trial, and the corresponding frictional force results in Data Table B.

Experiment 3. The Bungee-Jumping Egg

1. Obtain the elastic band, 150 cm of string, scissors and a meter stick.
2. Measure the unstretched length of the elastic band with a meter stick. Record the unstretched length to the nearest 0.1 centimeter in the data table on the Bungee Jump Worksheet.
3. With scissors, cut a 15-cm length of string from the 150-cm piece. Save the remaining 135-cm string for step 20.
4. Securely tie one end of the 15-cm string to one end of the elastic band as close to the metal barb as possible. (The metal barb will prevent the knot from slipping off the elastic band.)
5. Tie a loop knot at the other end of the string. Refer to Figure 5.
   {13276_Procedure_Figure_5_Loop knot}
6. Add a 100-g hooked mass (m_u) to the loop at the end of the string.
7. Hold the other end of the elastic band by the metal barb and allow the elastic band to hang vertically as the mass stretches it.
8. With the meter stick, measure the length of the stretched elastic band. Note: Measure between the metal barbs only. Record the stretched length to the nearest 0.1 centimeter in the data table.
9. Calculate the spring constant, k, for the elastic band using Equation 5. Record the spring constant, k, in the data table. What are the units for the spring constant?
10. Fill a 600-mL beaker ¾-full with water.
11. Fill a plastic egg with water by submerging the two pieces of the egg in the water in the beaker. Note: The plastic eggs may have small holes in each end. Cover the holes inside with tape or clay. Connect the two egg pieces together while they are submerged and full of water. To obtain a “weak” egg, it may be necessary to connect the two pieces loosely. It may take practice to determine the minimum tightness the two egg pieces need to be so that they stay together in the egg basket, but still crack open when the egg hits a rigid surface.
12. Place the water-filled plastic egg into a plastic bag. Dry off the outside of the plastic bag if necessary.
13. With a balance, weigh the water-filled plastic egg and bag. Record the mass of the egg and bag basket to the nearest 0.1 g in the data table.
14. Attach the egg basket to the end of the string tied to the elastic band by using a “looping” knot. Refer to Figure 6.
    {13276_Procedure_Figure_6_“Looping” knot}
15. With a meter stick, measure the length of the egg basket from the elastic band’s metal barb to the bottom of the bag. It is best to do this when the basket is hanging. Record this length to the nearest 0.1 centimeter.
16. Record the height of the ceiling “jumping platform” as measured by your instructor.
17. Calculate the total height of the jump. Choose a separation distance (d) less than 5 cm, depending on how exhilarating the bungee jump will be.
18. Calculate the stretch distance of the elastic band (X) according to Equation 8.
19. Calculate the length of additional string that is necessary to successfully complete the jump (Equation 2).
20. Obtain the long, 135-cm piece of string that was saved after step 3.
21. Measure this string to the necessary string length (SL) with a meter stick. Use scissors to cut the string about 15 cm beyond the necessary length so that excess string can be used to tie and clamp the string to the elastic band and jumping platform.
22. Tie one end of the string to the free end of the elastic band as close to the metal barb as possible.
23. From the knot at the tied end, measure the string to the calculated string length (SL) again, and use a marker to mark the correct length on the string. This mark will be the connecting point of the string to the jumping platform. Your instructor will use a ceiling hook, C-clamp or other hooking mechanism to secure the free end of the string to the jumping platform. Make sure the ink mark on the string is clear so that your instructor can match this point up with the very bottom of the platform.
24. Once the bungee cord is secured to the platform, double check the total length of the bungee cord and egg basket. Make sure to lift the egg basket slightly until the elastic band begins to slack in order to reestablish the unstretched length of the bungee cord.
25. Raise the egg to the correct bungee-jump starting position.
26. Release the egg!
27. Did the egg survive the bungee jump? Was it the most exhilarating ride possible? If not, what are some possible errors that need to be accounted for and corrected?

Experiement 4. Rings and Discs

1. Obtain the inclined plane.
2. Elevate one end of the inclined plane using the textbook (see Figure 7).
   {13276_Procedure_Figure_7}
3. Use a pencil and a straightedge to make a lengthwise mark approximately 10 cm from one end of the inclined plane. (This will be the “starting line.”)
4. Obtain the smaller (3½" diameter) disc and measure its mass using a balance. Record the mass in the data table on the Ring and Discs Worksheet.
5. Position the disc at the starting line, aligning it so that it rolls straight down the inclined plane.
6. Release the disc and observe its motion down the incline plane. If it did not travel straight down the inclined plane, adjust your release method, or adjust the inclined plane so that it is as level as possible using paper shims, if necessary. Once the disc travels straight down the inclined plane, move on to step 7.
7. Using a stopwatch, measure the time it takes the disc to travel from the starting line to the end of the very end of the inclined plane (just after it rolls off the end of the inclined plane). Make sure the disc rolls straight down the inclined plane. Record the time measurement in the data table.
8. Perform step 7 two more times for a total of three time trials. Record the time in Data Table 1.
9. Repeat steps 5–8 using the ring.
10.  Obtain the larger (5" diameter) disc and measure its mass using a balance. Record the mass in the data table.
11. Make a prediction: Will the larger disc roll faster or slower than the small disc? Will the larger disc roll faster or slower than the ring? Record the prediction in the data table.
12. After making the prediction, repeat steps 5–8 using the larger disk.

Collisions in One Dimension

1. Place three steel ball bearings in the middle of the V-track. The three ball bearings must be in contact with each other (see Figure 8).
   {13276_Procedure_Figure_8}
2. Roll one ball bearing into the three-ball bearing system from the left. Record the results of the collision in the data table on the Collision in One Dimension Worksheet. (Did the colliding ball stop or recoil? How many ball bearings were knocked away from the stationary ball-bearing series? How did the speed of the knocked-away ball compare to the initial speed of the colliding ball?)
3. Repeat steps 1 and 2. For step 2, however, roll the colliding ball with more speed at the stationary ball bearings. Record the results of the collision in the data table.
4. Repeat step 1.
5. Roll a system of two, nearly touching ball bearings into the three-ball system. To ensure that the ball bearings stay in contact as they roll, push on the ball bearing of the two-ball series that is farthest away from the series of stationary ball bearings. This way both ball bearings will roll with the same speed and remain close together. Also, release the ball bearings a short distance away from the stationary ball bearings. Record the results of the collision in the data table.
6. Repeat steps 4 and 5. For step 5, increase the speed of the two colliding ball bearings. Make sure the two rolling ball bearings are nearly touching as they make contact with the stationary ball bearings. Record the results of the collision in the data table.

Student Worksheet PDF

13276_Student1.pdf