Lab 2: Energy Conversion & Energy Loss Part 1 - Frictional Loss in a Straight Line

Introduction .

In this lab, your team will focus on the underlying physics of the roller coaster system, that you will be building this semester. After this lab and the following roller coaster physics lab, you will have all the information you need to fully model the behavior of your roller coaster in either Excel or MATLAB. Today’s lab will focus on energy conversion and the basics of energy loss associated with the roller coaster project. Specifically, the following topics will be covered:

1. Potential (PE) and Kinetic (KE) energy are introduced2. The components of kinetic energy, Translational (tKE) and Rotational (rKE) kinetic energy are

explored.3. Conversion of energy equations to convert PE to KE and vice versa4. Frictional loss, including both rolling and sliding friction

Part A: Energy Conversion .

In this part of the lab you will be given several energy equations, build a test apparatus, and make predictions of energies at points along the apparatus. Finally, your group will run trials and calculate actual energy values from velocities given by the speed sensors mounted on the apparatus.

Background - More detail from slides For the roller coaster project, there are two primary energies we need to consider: potential energy and kinetic energy. The total energy of the ball, at any point along the track is given as the sum of the ball’s kinetic and potential energies. In theory, if the track is frictionless (implying no energy loss), this total should remain constant.

Gravitational Potential Energy (PE), is the energy stored in a body due to its height (h). The height is always measured relative to some reference level. Additionally, it should be measured from the bottom of the body. In the case of this lab, a good choice of a reference would be the table top. In other words, any time PE needs to be calculated, the height of the ball should be measured from the table top to the bottom of the ball. The equation for PE is given in (1), where m is the mass of the ball in kilograms, g is the gravitational acceleration (9.81 m/s^2), and h is the height (in meters). The nylon balls used in class have a weight (on average) of 97 grams.

P .E .=mgh (1)

Kinetic Energy of the ball is energy stored in the ball as motion. When the ball rolls down from the start point of the coaster, potential energy is being converted into kinetic energy. Two forms of kinetic energy exist and need to be calculated: translational kinetic energy (tKE) and rotational kinetic energy (rKE). The sum of these two energies is the total kinetic energy (KE). In theory, the sum of the total kinetic energy and the potential energy should remain constant throughout the run of the coaster.

Translational kinetic energy (tKE) is energy the object has as a result of displacement in space. The formula for tKE is given at (2), where m is the mass of the object (kg), and v is the linear velocity of the object (m/s^2). For this project, velocities will either be theoretical (that is, calculated from energy equations) or measured with the provided speed sensors.

t . K .E .=12mv2

(2)

Rotational kinetic energy (rKE), is energy an object possesses as a result of spinning around an axis. The formula for rKE is given at (3), where I is the moment of inertia, and ω is the angular velocity of the object. The formula for both I and ω is given in equations (4) and (5) respectively.

r . K . E .=12l ω2

(3)

The moment of inertia for a solid sphere (kg*m^2) is given by equation (4), where m is the mass of the sphere and r is the radius of the sphere.

I=2mr2

5(4)

Finally, the angular velocity of the ball,ω , can be found by it’s linear velocity, v (assuming there is no slippage occurring. More on this later). To convert the linear velocity to the angular velocity use equation (5), below. ωis in units of radians/second.

ω= vr

(5)

Together these equations can be used to make predictions about the behavior of the ball at various points along the coaster. Since the sum of PE and KE should be constant (again, ignoring loss), if one is found, the other can be predicted. Further, if part of the KE (either tKE or rKE) is known, the other can be found.

For example, if we find the PE at both the top of a hill, and the bottom of the hill, and we start the ball rolling at the top of the hill (KE = 0), we can make a direct prediction as to the KE at the bottom of the hill using the following equation:

PETOP+KETOP=PEBOTTOM+KEBOTTOM (6)

PETOP+KETOP−PEBOTTOM=KEBOTTOM (7)

In this manner, various energy levels can be found at all key points along the coaster moving from the starting point to the next point, solving for all energies at that point, then moving on to the next point from there, and so on.

Task 1: Construction of Testing Apparatus

i) Building the Frame and TrackBefore your group can take any measurements or perform any experimentation, you will need to construct a test apparatus. For today, that apparatus will be two sections of straight track at approximately 165 o to each other. On section will be level with the table, the other a slight upward hill. The specific dimensions for this apparatus are not strictly important, however it is recommended that you follow the following guidelines:

1. Use smaller pieces of PVC pipe (3” and 4”) rather than larger2. Use snap-fits evenly spaced along a ‘ladder’ of PVC built out of short lengths and T-connectors3. Spend a good deal of time making sure that both sections of the track are as straight, even and

level as possible. Look down the length of the track and adjust snap-fits to do this4. Do not use an overly steep or tall hill, as this will likely yield worse experimental results

See the picture below for an example apparatus. Notice that by using different length pipes, the angles between the two track sections can be adjusted to each other.

Figure 1: An example apparatus

ii) Adding Sensors (‘Instrumentation’)After assembling the apparatus, your group will next need to instrument it. Instrumentation means to add sensors to an apparatus to collect data. In this case, your coaster kit includes a number of C-shaped sensors designed to snap in place on parallel pieces of track. Attach three of these sensors to the track, one half way down the hill, one at the transition from the hill to the flat, and one at the end of the flat. Be sure that the back of the sensor (the side with no components attached to it) is the side the ball will approach from. In this way, should the ball leave the track, it won’t hit and damage components on the sensor.

Figure 2: A Speed Sensor

iii) Connecting Sensors Once the sensors are in place, locate your tables assigned speed sensor reader (see figure 3 below). Connect the sensors using the cables provided in your groups speed sensor kit. It is critical that these sensors be attached to the reader in the order the ball will travel through them. Sensor one should be attached to port 1, sensor 2, to port 2, and so on. Figure ## shows the port numbers on the speed sensor reader.

Figure 3: The Speed Sensor Reader

Finally, once the sensors are attached, ensure that only the ports in use on the reader are activated. See figure 4 below. Locate the bank of switches shown in the figure, and set only the first 3 to ‘ON’.

Figure 4: Switches with only switch 1 ‘on’

Task 2: Calculate Initial and Predicted Energies

i) Calculating PEsDetermine a starting point for the ball on the top of the hill. Using a spare snap-fit, your BuckID, or some other object, obstruct the path of the ball. This defines the starting point of your test apparatus, and all ball drops should start from precisely this position. With the ball sitting at this position, measure the distance from the bottom of the ball to the table, and record on an excel sheet.

At every speed sensor, have one team member hold the ball in place, centered within the sensor, while another member measures the height of the ball. Record all three of these heights in the same column as the first measured height.

Use the equations and explanation presented above and in the slides to fill data into a spreadsheet similar to the one on the lab page on EEIC.

Task 3: Trial Runs and Data Collection Locate the 9v power supply in your lab tables equipment box. Plug it into the power strip and the speed sensor reader.

Once the reader has booted, you will be given the following menu:

Press the first button to enter calibration mode. Gently adjust the position of the LEDs and photo sensors on the speed sensor boards until all three sensor readings are below 0.25. Ask for assistance if you need help!

Once all three sensors are calibrated, reset the board with the right-most switch. Once booted, you will select the third option to run trials. Note that once selected, the third option will only remain active for 30 seconds.

Start the ball at the chosen starting position, and run 5 trials. Record the velocities of these trials on the excel spreadsheet, and use excel to calculate the average velocity at each sensor throughout the trials.

Task 4: Calculate Actual Potential and Kinetic Energies By using the table constructed in Task 2 and the velocities found in task three, complete a full table of values to compare to your predicted results. These are your experimental results. Consider the difference between your predicted and experimental results.

Part B: Frictional Loss in a Straight Line .

In part A, your groups theoretical results should have differed significantly from your experimental results. Specifically, the total energy in the system should have been found to be decreasing over time. This indicates that there is some path for energy to leave the system. In fact, there are numerous ways in

which energy can leave the coaster system including, but not limited to, friction, air resistance, structural loss, and sound. In this part of the lab your group will derive the amount of energy lost by the ball as is travels in a straight line.

Task 1: Distance Between Sensors Carefully measure the distance between the two sensors along the straight portion of the track. Be sure to measure from the same point on each sensor.

Task 2: Find the Energy Lost Compare the total energy in the system at both sensors. Find the amount of energy lost during travel between the two sensors.

Task 3: Find Energy Lost Per Meter Normalize the energy lost over the distance measured to energy lost per meter. Record this value for future reference, you will need to refer to it during future labs as well as during the coaster construction process.

Task 4: Repeat with Glass Marble (optional) Recollect the data from Part A for the provided Glass Marble. Repeat the calculations for Part A and Part B, and record the data

Discussion QuestionsWhat issues did your encounter while assembling structures with the kit? How might these issues be alleviated?

What other sources of energy loss might come into play? How significant do you think these issues will be? What physical factors influence these energy losses?

The energy that leaves the system is not destroyed, but rather converted. What is the energy converted into in this case? Include thoughts on ALL energy loss, not just frictional loss.

Given that your coaster will use 25’ of track, how significant is the energy-loss- per-meter that you found? How high must the ball start to just overcome this loss?

Report: Lab Memo Format