# PSWorks™ Conservation of Energy Tracks

## Student Laboratory Kit

### Materials Included In Kit

Catching Curve
Metal balls, ¾" diameter, 2
PSWorks™ Conservation of Energy Tracks
Support rod, metal

Pencil
PSWorks™ Support Stand, or support stand and clamp
Ruler or meter stick

### Safety Precautions

The materials in this laboratory activity are considered safe. Please follow all normal laboratory safety guidelines.

### Disposal

The materials should be saved and stored for future use.

### Lab Hints

• Enough materials are provided in this kit for one student lab group. This experiment may also be performed as a teacher demonstration, in which all the students record the data as the teacher (or one student group) performs the experiment. This laboratory activity can reasonably be completed in one 50-minute class period.
• The Catching Curve is designed to be slightly lower than the end of the tracks. This allows for a smooth transition between the tracks and the curve. However, on the return trip the ball will likely bounce off the track at the transition point. Be prepared to catch or stop the ball if it bounces off the track.
• Instead of using the Catching Curve, allow the metal ball to roll off the end of a tabletop and mark the location that the ball hits the floor (using carbon paper or white paper at the approximate location of impact to display the point of impact). Then, measure the horizontal distance between the end of the tabletop and the mark on the floor. For each track, the horizontal flight distance of the ball should be nearly equal. The kinetic energy, and therefore speed, of the ball will be nearly the same for each track, so the ball should travel the same horizontal distance in the same amount of flight time.
• The ball will not reach the same initial height due to frictional losses during the transition from the track to the Catching Curve. When the ball bounces, or slips, energy is lost. Also, the longer, curved tracks produce friction on the ball for a longer period of time. Therefore, the short, simple inclined plane track tends to produce a ball with slightly more kinetic energy than the other tracks and the ball tends to travel higher up the Catching Curve. Frictional losses reduce the total energy of the rolling ball.

### Teacher Tips

• The Catching Curve models the principle behind the emergency service ramps along the sides of highways in mountainous areas. Any runaway truck can pull off onto a service ramp and the truck will slow down as it gains potential energy while rising up the incline.
• Equation 6 can be used to determine the theoretical speed of the rolling ball when it reaches the bottom of the track.
{12512_Tips_Equation_6}
The moment of inertia of a solid sphere rotating about its center is equal to (2/5)mR2, where R is equal to the radius of the sphere. Rotational speed, ω, is related to linear speed of the ball, v, and the radius, R, of the object: ω = v/R. Substituting these values into Equation 6:
{12512_Tips_Equation_7}
Solving for v2
{12512_Tips_Equation_8}
Notice that Equation 8 shows that the speed of the ball at the bottom of the inclined plane is independent of the size or the mass of the solid ball. This means that any size solid ball will have the same speed at the bottom of the inclined plane, so long as it is released from the same height.
• The Bungee-Jumping Egg (Catalog No. AP6381), Bowling Ball Pendulum (Catalog No. AP6839), and Ring and Discs (Catalog No. AP4634) are excellent kinetic and potential energy experiments and demonstrations, and are available from Flinn Scientific.

### Science & Engineering Practices

Developing and using models
Using mathematics and computational thinking
Planning and carrying out investigations
Obtaining, evaluation, and communicating information
Constructing explanations and designing solutions

### Disciplinary Core Ideas

MS-PS2.A: Forces and Motion
MS-PS3.A: Definitions of Energy
MS-PS3.B: Conservation of Energy and Energy Transfer
MS-PS3.C: Relationship between Energy and Forces
MS-ETS1.A: Defining and Delimiting Engineering Problems
MS-ETS1.B: Developing Possible Solutions
HS-PS2.A: Forces and Motion
HS-PS3.A: Definitions of Energy
HS-PS3.B: Conservation of Energy and Energy Transfer
HS-PS3.C: Relationship between Energy and Forces

### Crosscutting Concepts

Energy and matter
Cause and effect
Scale, proportion, and quantity
Systems and system models

### Performance Expectations

MS-PS3-1: Construct and interpret graphical displays of data to describe the relationships of kinetic energy to the mass of an object and to the speed of an object.
MS-PS2-2: Plan an investigation to provide evidence that the change in an object’s motion depends on the sum of the forces on the object and the mass of the object
HS-PS3-1: Create a computational model to calculate the change in the energy of one component in a system when the change in energy of the other component(s) and energy flows in and out of the system are known.
HS-PS2-2: Use mathematical representations to support the claim that the total momentum of a system of objects is conserved when there is no net force on the system.
HS-PS2-1: Analyze data to support the claim that Newton’s second law of motion describes the mathematical relationship among the net force on a macroscopic object, its mass, and its acceleration.

### Sample Data

{12512_Data_Table_1}

1. Define the term conservation of energy.

The law of conservation of energy states that energy cannot be created or destroyed—only converted between one form and another.

2. How did the shape of the track or the path that the ball traveled affect the maximum height the ball reached on the Catching Curve?

The path of the ball did not affect the maximum height reached by the ball. All four tracks produced a rolling ball with approximately the same kinetic energy (Note: The “straight” inclined plane trace usually produces a ball with more kinetic energy because it is the shortest track, resulting in less overall frictional resistance compared to the other tracks.)

3. Compare the maximum height reached by the ball or the Catching Curve to the initial height of the track. Could the ball ever travel higher than the original height?

All four tracks produced about the same maximum height on the ramp, but the ball never reached the same height as the original starting height. The ball cannot go above the initial height (if released from rest) because that would require more energy.

4. Would using a heavier ball affect the height the ball would reach on the Catching Curve? Explain.

No, a heavier (or larger) ball would reach the same height as a light ball because the mass and size of ball does not affect the speed the ball reaches at the bottom of the track. A heavier, more massive ball would have more potential and kinetic energy, but the relative changes between potential energy and kinetic energy would be the same for the small and large ball.

5. Compared to a ball that rolls down the track a certain vertical distance, would the same ball that drops straight down the same vertical distance have more, less or the same amount of kinetic energy? Explain.

Each ball would have the same kinetic energy at the bottom because they fall from the same height. However, the ball that drops straight down will only have linear kinetic energy whereas the ball that rolls down the track will have both linear and rotational contributions to the total kinetic energy.

6. Would a ball dropped straight down have more, less or the same speed as the rolling ball at the end of the track? Explain.

The ball that drops straight down would have more speed because it will only gain linear kinetic energy. The ball at the end of the track will have rotational and linear kinetic energy so the rotational contribution will take away from the linear energy, and therefore the linear speed (v) will be lower.

# PSWorks™ Conservation of Energy Tracks

### Introduction

Examine the concept of conservation of energy. Show that when an object falls, the path the object takes does not affect its change from potential energy to kinetic energy.

### Concepts

• Potential energy
• Kinetic energy
• Conservation of energy

### Background

The law of conservation of energy states that energy cannot be created or destroyed—only converted between one form and another. In order to raise a ball to the release point at the top of an inclined plane, one must exert energy. Work, another term for energy, is being performed on the ball in order to raise it. Work is defined as a force used through a distance. It requires work to move any object. If a force used on an object does not make the object move, such as pushing on a brick wall, then no work is performed. The energy used to raise an object, such as a ball, to a position higher than a reference height is “stored” in the ball—the ball is said to have potential energy (PE). This potential energy may be used at a later time to do work. The potential energy of the ball is related to its height and weight. In general, potential energy is equal to the weight of an object, which equals the mass (m) times the acceleration due to gravity (g), times the relative height (h) of the object (see Equation 1 and Figure 1).

{12512_Background_Equation_1}
{12512_Background_Figure_1}
As the ball begins to move down the inclined plane, the potential energy is converted into kinetic energy (energy of motion). For a rolling ball, two types of motion are involved—the ball travels in a straight path down the inclined plane and it rotates. Therefore, the ball has both linear kinetic energy and rotational kinetic energy. Linear kinetic energy (KEl) is related to the mass (m) and linear speed (v) of the ball (Equation 2). Rotational kinetic energy (KEr) is related to the moment of inertia (I) of the ball about the rotational axis and the rotational speed (ω; the lower-case Greek letter omega) of the ball (Equation 3). The total kinetic energy (KET) of the ball is equal to the linear kinetic energy plus the rotational kinetic energy (Equation 4).
{12512_Background_Equation_2}
{12512_Background_Equation_3}
{12512_Background_Equation_4}
In this demonstration, the ball will roll down a track without slipping. The point on the ball in contact with the surface of the track will be instantaneously at rest with respect to the track. The frictional force between the surface of the rolling object and the surface of the track acts against, and balances, the force due to gravity pulling the object down. Since no slipping occurs between the two surfaces, energy will not be dissipated or lost as heat and all the potential energy the ball has at the top of the track will be converted into kinetic energy at the bottom (Equation 5).
{12512_Background_Equation_5}
Therefore, the ball will have the same energy at the bottom of the track that it has at the top of the track. It does not matter what path the ball takes, as long as the relative change in height is the same, the kinetic energy at the bottom will equal the potential energy at the top.

### Materials

Catching Curve
Metal ball, ¾" diameter
Pencil
PSWorks™ Conservation of Energy Tracks
PSWorks™ Support Stand, or support stand and clamp
Ruler or meter stick
Support rod, metal

### Safety Precautions

The materials in this laboratory activity are considered safe. Please follow all normal laboratory safety guidelines.

### Procedure

1. Slide the metal support rod through the hole at the top of the Conservation of Energy Tracks. Then, slide the support rod into the fourth hole from the base of the PSWorks™ Support Stand (see Figure 2). Alternatively, a support stand and clamp may be used to support the track. Adjust the height of the track so that a ball will just begin to roll down the tracks when placed at the top. If the tracks are positioned at too great an angle, the ball may “hop” as it travels down the curved tracks.
{12512_Procedure_Figure_2}
2. Place the Catching Curve at the base of the track that the metal ball will roll down.
3. Place the metal ball at the top of the appropriate track.
4. Release the ball (without providing any “extra push”). Note: Be prepared to catch the ball if it misses the Catching Curve or if it hops off the track on its return. If necessary, adjust the position of the Catching Curve to properly “catch” the ball and repeat step 4.
5. Observe the change in speed of the ball and the height the ball travels up the ball-catcher ramp. Use a pencil to make a light mark on the ball-catcher ramp at the maximum height achieved by the ball. Note: Mark lightly with only a pencil.
6. Repeat steps 3–5 two more times for the same track.
7. Use a ruler to measure the average height the ball traveled up the Catching Curve.
8. Record the value of the average height, and any additional observations concerning the motion of the ball, in the data table on the Conservation of Energy Worksheet.
9. Erase the pencil marks from the ball-catcher ramp.
10. Repeat steps 2–9 for the three remaining tracks. Release the ball from the same height for each trial and for each track. Make a small mark on the ball-catcher ramp to indicate the maximum height for each trial, and erase the marks before moving on to the next track.
11. Consult your instructor for appropriate storage procedures.

### Student Worksheet PDF

12512_Student1.pdf

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