roller coaster energy losses - spring 2015 · circular arc sections of track are used to find the...

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Roller Coaster Energy Losses Background This lab is designed to collect information and calculate various forms of energy losses in your roller coaster design. Some of the calculations will allow you to determine coefficients which can be used in a spreadsheet that roughly models some of the energy losses and calculates the resultant velocities of the ball as it rolls down the track through the various features. Other calculations will give you a better understanding of losses not included in the spreadsheet model. The lab has two major parts:

• Part 1: Rolling and Static Friction • Part 2: Additional Energy Losses

Student teams will work at their tables on Part 2 during the entire lab time. The instructor will notify individual groups to perform Part 1 one-at-a-time during the course of the lab at a special table at the front of the class. Roller Coaster Energy Analysis Spreadsheet Students will be introduced to the Roller Coaster Energy Analysis Spreadsheet during a classroom lecture. The spreadsheet is shown below. To use this spreadsheet with friction effects, three energy loss coefficients are needed (as indicated below). The three coefficients are:

• dE/ds: Frictional losses on straight track sections • dE/ds/dv: Losses associated with speed (i.e. air resistance) • dE/ds/dNC: Losses associated with “G” forces (centripetal acceleration)

Rev A 01/08/03 ROLLER COASTER ENERGY ANALYSIS Copyright 2004: The Ohio State University

Ball mass 0.0100 kg -dE/ds ? J/mg 9.80 m/s^2 -dE/ds/dv ? J*s/m^2

Ball geometric radius 0.01270 m -dE/ds/dNC ? J/m/gBall rolling radius 0.01016 m

Mass Moment of Inertia, I 6.452E-07 kg*m^2

Pos 1 Pos 2h1 0.455 m h2 0.000 mv1 0.000 m/s v2 2.332 m/ss1 0.000 m s2 1.000 m

For LoopsPE1 0.04459 J Dh 0.00 m PE2 0.00000 J

TKE1 0.00000 J Dv 0.00 m TKE2 0.02719 JRKE1 0.00000 J dN 0.000 g RKE2 0.01699 J

E1 0.04459 J dC 0.000 g E2 0.04419 J

E loss_1_to_2: #VALUE! J >>>>>> >>>>>>>> #VALUE!E 0.04459 J E #VALUE! J

^--------------------------- Same ??? Then OK ----------------------------------^

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NOTE: You will only be calculating the first coefficient (dE/ds) in this lab. The remaining two coefficients will be given to you. You will collect information for the calculation of the coefficient in Part 1 of this lab when instructed to do so by your instructor.

The Roller Coaster Energy Analysis Spreadsheet does not account for all losses. This occurs partly because of:

• energy losses due to deformation of the structure • inadequate snap-fit spacing • horizontal curves

When you complete your roller coaster, you'll be asked to instrument some of the features on your coaster to compare your actual energy losses with this spreadsheet. The objectives of this lab are

• to learn how to calculate one of the three above coefficients based on measured data from the lab

• to understand how to use production speed sensors to calculate energy losses in a coaster feature

• to learn how to measure the energy losses in a horizontal curve as a function of g-forces

• to explore the design limitations that these unaccounted for energy losses create

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PART 1: Static and Rolling Friction You will be directed by your instructor to go to a table at the front of the lab when it is your team’s turn to do Part 1. In the meantime work on Part 2. Method The student teams will use three different apparatuses; two different sized circular arcs to measure rolling friction and a linear ramp to measure static friction. Geometric measurements of each apparatus will be supplied for use in data reduction calculations. For the circular arc apparatus, the ball will be released at different starting points. The length of time and number of oscillations before the ball comes to a stop will be recorded. For the linear ramp, conjoined ball-pairs will be placed on the ramp. The angle of elevation (inclination) of the ramp will be slowly increased and recorded when the pair just begins to slide on the ramp. Lab Guidelines The GUIDELINES that MUST be followed AT ALL TIMES in the lab are: • No student will adjust or otherwise change any apparatus (other than for

changing the ramp elevation or plugging/unplugging the electrical power adaptor). Electrical connections are pre-made by staff. If something is not working or is obviously wrong, immediately notify an instructional staff member.

• No dangling jewelry or loose clothes. • No ‘open’ shoes. Close-toed shoes or boots only. • No climbing or standing on chairs or tables. • Be aware of sharp corners and edges which may exist on tables or on apparatus and

tools. • Always know the location of the phone and of the first-aid kit. • Report to the instructor ALL injuries occurring during lab. Lab Room Logistics

• A table will be placed in the front of the lab room. It will contain two circular arc

apparatus and one linear ramp apparatus. Data will be collected at the table by each team.

• Teams will rotate to the front table and collect data on the three apparatus.

INSTRUCTOR will notify each group when it is their turn to rotate to the front table. Each team will record the data they acquire on an apparatus summary worksheet at each table and on the computer at the instructor’s station. The apparatus worksheet is obtained from and started by the first team that tests a given apparatus; and the sheet stays with the apparatus until the lab is completed! The data sheet is to be left on the table for the instructional staff to collect. The instructional staff will email the summarized data to each student.

• Certain geometric measurements from each apparatus are needed for data

reduction. These necessary geometric measurements will be provided to the students. The values are contained in a table of values on the apparatus itself.

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Lab Equipment On the front table you should find:

1. the three apparatus (two circular arcs with different radii and one linear ramp)

2. a single test ball (for circular arc) and conjoined ball set (for ramp apparatus) 3. a meter stick (for ramp apparatus)

4. a table-of-geometric-values related to the apparatus (on the apparatus itself; not

used for ramp apparatus). Note: All Ohio State-issued materials will remain on the lab tables and in the

lab in general. The teams will experiment with test lab setups and circuit components. The student will immediately notify the staff about any missing, damaged, or non-operating parts or devices.

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CIRCULAR ARC APPARATUS

At Rest

( Hrest )

1 Starting Position

( Hsp )

Arc Lengths ( Ssp )

Figure 1: Circular Arc Apparatus

Circular arc sections of track are used to find the energy loss and related rolling friction of a given ball on the track rails. Reduced data from all the circular arc apparatus in the lab can be compared to see what if any affect the track segment radius and/or average velocity has on the performance of the ball. The main intent is to obtain a single value which represents the energy loss per unit distance traveled if in a 1g (gravitational acceleration only) environment.

Figure 2: Staging the Ball for Release

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Circular Arc Test Procedure

1. Prepare to use the stop watch on the table.

2. Record on Worksheet A1 or A2 the apparatus identifier, the height of the ball at rest (Hrest), the arc radius, the initial starting height (Hsp), the initial arc length (Ssp). (see Figure 1)

3. Stage the ball at the marked starting point R3 (see Figure 2). Use your Buck-

ID or equivalent to hold the ball in starting position. The ‘downhill’ face of a starting point snap-fit is the reference used for all AGT height and arc measurements.

4. Remove the ‘holding’ object in the direction of travel to start the ball rolling,

and start the stopwatch at the same time.

5. Count the number of times the ball returns to the starting side of the apparatus (number of cycles) and continue counting cycles and timing until the ball finishes its last ‘definite’ cycle just before coming to rest.

6. Be sure to stop the timing as the ball finishes that ‘last’ cycle!

7. Record the number of cycles, and total time for those cycles to occur.

8. Repeat steps 4 through 8 to obtain 3 trials (runs) at the same starting position.

9. Make sure all results are recorded on the apparatus worksheet and on the computer at your instructor’s station.

10. When collecting your data please leave the worksheet at the table for the instructional staff to collect!

11. The instructional staff will collect the worksheets and e-mail the summarized data to each student.

12. If lab time remaining is sufficient, read the data reduction and analysis section of this procedure document. Ensure you understand what is required, and ask questions of the instructional staff before leaving the lab. Generally, further data processing will be done outside of lab class after raw data has been appropriately shared amongst teams.

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H1

Lab 2 - Part 1: Worksheet A1 (Circular Arc Apparatus)

Note: Before you proceed to take readings, fill in the shaded cells by referring to the AGT of the respective apparatus

Hrest = Hsp =Arc Radius = Ssp =

NOTE: Units==mm & seconds

Trial # Cycles Time Trial # Cycles Time Trial # Cycles Time1 1 12 2 23 3 3

Avg Avg Avg


Avg Avg Avg


Avg Avg Avg

NOTE: Use the same Hsp and Ssp values as the first group

APPARATUS ID

Group G

Group H

Group I

Group B

Group C

Group D

Group E

Group F

Group A

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Lab 2 - Part 1: Worksheet A2 (Circular Arc Apparatus)

Note: Before you proceed to take readings, fill in the shaded cells by referring to the AGT of the respective apparatus

Hrest = Hsp =Arc Radius = Ssp =

NOTE: Units==mm & seconds


Avg Avg Avg


Avg Avg Avg


Avg Avg Avg

NOTE: Use the same Hsp and Ssp values as the first group

APPARATUS ID

Group F Group I

Group A Group D Group G

Group B Group E Group H

Group C

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2. Slowly lift one end of the ramp until the conjoined pair just starts to move, and hold that ramp position. Use the meter stick as a guide to help maintain a steady position.

3. While one team member holds the ramp steady, have another team member make and record measurements to allow later calculation of the elevation angle (incline) of the ramp. Measure H1 from table top to ramp bottom-edge and the length L of the ramp (see Figure 5). Use Worksheet B to note the values.

Figure 5: Measure H1 and L

4. Repeat steps 1 through 3 with the conjoined pair until three ‘runs’ at the same starting point are obtained.

5. Repeat steps 1 through 4 but use a slightly different starting location of the conjoined balls for each sequence. Since ‘straddling’ a snap-fit location was used for the first, try a location on each side of a snap fit location. (see Figure 4 (b) and (c)).

6. Again repeat steps 1 through 4 but use a slightly different starting location of the conjoined balls for each sequence. If you used a location left of the original ‘straddling’ position, now use a position to the right and vice-versa.

7. Make sure all results are recorded on the apparatus worksheet and on the computer at your instructor’s station.

Leave the worksheet at the table!

8. The instructional staff will collect the worksheets and e-mail the

summarized data to each student. . 9. If lab time allows, read the data reduction and analysis section of the procedure

document. The full data reduction and analysis is generally done outside of lab class, but may be started during lab if all raw data has been obtained.

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Lab 2 - Part 1: Worksheet B (Ramp Apparatus)

Apparatus ID:Length (L):

Trial H1 Trial H1 Trial H11 1 12 2 23 3 3

Average Average Average1 1 12 2 23 3 3


Average Average Average

Trial H1 Trial H1 Trial H11 1 12 2 23 3 3



Average Average Average

Trial H1 Trial H1 Trial H11 1 12 2 23 3 3 Straddle H1

Average Average Average Avg All1 1 12 2 23 3 3 Left H1

Average Average Average Avg All1 1 12 2 23 3 3 Right H1

Average Average Average Avg All

Within each team's measurements,L must be a constant!All measurements should be in millimeters

Left Left Left

Right Right Right

GROUP C GROUP F GROUP I

Straddle Straddle Straddle

Left Left Left

Right Right Right

GROUP B GROUP E GROUP H


Left Left Left

Right Right Right

GROUP A GROUP D GROUP G


H1

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PART 2: Additional Energy Losses A. SETUP 1. LOCATE the following PIECES and PARTS in the bin (the numbers in the

parenthesis indicate number of parts required). I. Tower (1)

II. Tee (9) III. Elbow (4) IV. Drop Ear Elbow (5) V. 6 in. pipe (6)

VI. 4 in. pipe (6) VII. 3 in. pipe (4)

VIII. 2 in. pipe (3) IX. 18 in. pipe (2) X. 12 in. pipe (5)

XI. Nylon tubing (2) {to be used as track} XII. Snap Fits (20)

XIII. Bolts and nuts (10) XIV. Nylon straps (10)

2. Construct the ramp and horizontal curve shown in figures 6 and 7 using the

parts exactly as shown. Use duct tape, if necessary, so that the nylon straps fit snugly on the pipes.

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Figure 6: RC Energy Losses - Part 2 support structure

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Figure 7: RC Energy Losses – Part 2 support structure with track

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3. Try to release the ball from Release Point 1 (indicated in Figure 7). See if the ball stays on the track, rolls smoothly, and doesn’t hit any snap-fits. Bank the horizontal curve as needed to make the ball roll smoothly. Release the ball from Release Point 1 a couple of times to verify that the ball travels consistently till the end of the track.

4. Measure the radius of the horizontal curve, RH and record in Lab 2 - Part 2:

Data Sheet. Radius of the horizontal curve (RH): _____________ m. 5. Attach sensors to the beginning and end of the horizontal curve respectively,

as shown in Figure 7. 6. Insert one end of the telephone cable to the telephone jack of a sensor and

the other end to the telephone jack of the Arduino board. Repeat for the other sensor. The telephone jacks on the Arduino board are labeled from 1-8. Use the first two telephone jacks. The piano pins on the side of the Arduino board should be pushed down to activate the sensors which are connected to Arduino. Only push down the pins of the corresponding telephone jacks being used.

7. Connect the 9V power supply to the Arduino board. 8. Once the Arduino is connected the alignment of red LED and photo

transistor on the sensors must be verified and the sensors must be checked. Press reset to see this menu:

Figure 8: Arudino Display Press B1 to align the sensors. A value of 0.4 volts or less is acceptable to continue. If greater than 0.4, manually align the sensors and realign. Press B2 to test the sensors. The Arduino will display “Brk Me” until the beam is interrupted and will display “Good”. Verify that all the sensors are functioning properly. Once these checks have been completed press B3 to record velocities.

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The Arduino will record the velocity in meters per second and the time the coaster ball takes to pass through the speed sensor beam in milliseconds. The time the ball takes to pass through the sensor is measured by recording the leading edge (LE) and trailing edge (TE) times. B. DATA COLLECTION 1. Use the spreadsheet called Lab 2 – Part 2: Data Sheet below to record the

velocities measured in this lab.

2. The next step has to be performed fairly quickly or you will receive a timeout error message. Read the next step carefully before you proceed.

3. Have one member of your team press B3 to “Get Velocities”. A second

member needs to release the ball from Release Point 1 a total number of three times. This should generate six velocities and six sensor leading edge and trailing edge times. Record the velocities and pulse times.

4. Repeat steps 2-6 for release points 2, 3 and 4respectively.

****You will have to change the bank angles for the track between release points to ensure that the ball travels as smoothly as possible to the end of the track. This means the ball does not bounce or hit snap-fits and runs very smoothly during its journey to the end of the track.

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No. Sensor 1 Velocity Sensor 2 Velocity No. Sensor 1 Velocity Sensor 2 Velocity(m/s) (m/s) (m/s) (m/s)

1 12 23 3

Average Average

No. Sensor 1 Velocity Sensor 2 Velocity No. Sensor 1 Velocity Sensor 2 Velocity(m/s) (m/s) (m/s) (m/s)

1 12 23 3

Average Average

Release Point 4Release Point 3

Lab 2 - Part 2: Data Sheet

Release Point 1 Release Point 2

Radius of the horizontal curve (RH) =

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POST-LAB DATA ANALYSIS PART 1: Static and Rolling Friction (use all groups’ data)

Make sure that you receive the excel file containing the group data from your Instructor.

In the excel file, below the group data, you will see a calculation worksheet

template. You will use the group data and the appropriate formulae (discussed below) to populate the calculation template. Use the data from all groups.

Make use of cell referencing feature in excel for accurate and efficient

calculations.

You need to email an electronic copy of the completed calculation worksheet template to the instructor within 2 days of the completion of the lab. Make sure to name the file as Eng1182_Lab2_Group *.xls where * represents your group letter A, B, C ... The instructor will then provide feedback.

Pay special attention to the units used in the calculations.

BALL PARAMETERS Use the following parameters for the ball wherever applicable: Geometric radius of the ball, r = 0.01272 m Effective rolling radius of the ball on the track, r’ = 0.01018 m Mass of the ball, m = 0.0097 Kg Weight of the ball, W = 0.0951 N UNITS TO BE USED IN DATA ANALYSIS Use SI units to be consistent throughout the data analysis. Specifically, use the units as mentioned below for the following quantities: Length: meters Speed: m/s Acceleration: m/s2 If the collected data appears to be in units other than the above mentioned, make sure to convert them to appropriate units before you proceed to analyze your data. CIRCULAR ARC APPARATUS The calculation steps given below will result in “energy loss per meter of travel”, Es which will be used to calculate the coefficient “dE/ds”

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dE/ds=overall average value of Es from all apparatuses and starting points. Circular Arc Apparatus Data Reduction

Reducing data from the circular arc apparatus generally requires some knowledge of simple harmonic motion. To make this data reduction reasonable, an assumption has been made which results in a simple expression for the distance the ball travels. The expression is:

24 spNS

S =

where: S is the total distance traveled (length units), N is the number of cycles the ball experienced and,

Ssp is the initial arc distance from starting point to resting point (length units).

{This expression is only a crude approximation to the actual distance traveled, but is sufficient for the comparison purposes of this lab. It assumes a linear decay in the amplitude of oscillation. This assumption is simplifying for our case, but would not be a good assumption for real-world engineering. The use of the above expression results in estimates of distance traveled that are as much as 20% too large}.

1. Calculate the total distance, S, traveled by the ball

Spreadsheet tip: a. It should be noticed that once all the cells in the “Circular Arc Worksheet” are

populated, then the corresponding Circular arc apparatus (in grey and red) in the “Class Data & Calc. Temp” worksheet should also be populated.

b. Use the value of Ssp for one of the circular arcs and its computed average value of N.

2. Calculate the average speed, Vavg of the ball.

tSVavg =

where: Vavg is the average speed (m/s), S is total distance traveled (m), t is the time the ball was in motion (s). Do not forget that the total distance travelled (i.e. S) in the spreadsheet is measured in millimeters and time is in seconds. The calculated velocity should be in m/s.

3. Calculate the average rolling friction coefficient, μr,:

SHrestHspμ r

−=

where: Hsp is the height of the ball at the starting point (m). Hrest is the height of the ball at its resting position (m).

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4. Calculate the centripetal acceleration, ac:

R

Va avg

c

2

=

where: R is the effective radius of the arc segment (m). Remember that the radius is measured in mm in the spreadsheet whereas acceleration should be in m/s2 5. Calculate the normalized centripetal acceleration, n:

gan c+= 1

where: g is the gravitational constant (9.81 m/s2) 6. Adjust the rolling friction coefficient for normalized acceleration by:

nμμ r

cr =

7. Calculate the energy loss per meter of travel, Es. WμE crs = where: W is the weight of the ball (force units). (Note that Es has units of force). 8. Repeat steps 1 through 7 for the other circular arc apparatus. Be aware of units

on values! 9. At this point, you should have final data values for both circular arc

apparatus.

10. Calculate a single overall average value of Es from both apparatus. Use this single value as the dE/ds coefficient in the Roller Coaster Energy Analysis spreadsheet.

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LINEAR RAMP APPARATUS The calculation steps given below will result in “maximum angle for a no-ball-slippage condition”, (θc). Slippage will occur when the inclined track sections of the roller coaster have inclination angles greater than θc. More energy is lost when the ball slips instead of rolling ‘cleanly’. Slippage can also cause unrepeatable results. Ramp Apparatus Data Reduction

Using the averaged class data at each starting position: 1. Use geometry to calculate the incline angle (β) at which the conjoined ball-set just

started to move. Spreadsheet tip: For calculating β use the trigonometric identity sin-1 = (H1/L)

2. Calculate the static friction coefficient (μ0) and the maximum angle for a no-ball- slippage condition (θc) :

)tan(0 βμ = ,

3. where β is the average incline angle

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛+= −

2

01 '

251tan

rrμθc ,

where, θc is the angle in radians (i.e., track slope) below which the ball will

not slip as it rolls. r is the geometric radius of the ball (see BALL PARAMETERS).

r’ is the effective rolling radius of the ball on the track (see BALL PARAMETERS).

This calculated θc that is in radians. It needs to be converted to

degrees by multiplying by the appropriate conversion factor

L

β

H1

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4. Average all θc angle data to obtain one final angle in degrees. Refer to this value as you design incline sections of your roller coaster.

Slippage will occur when the translational acceleration of the ball is greater than the rotational acceleration of the ball. Remember the value of θc as you design inclined track sections. More energy is lost when the ball slips instead of rolling ‘cleanly’. Slippage can also cause unrepeatable results.

RANGE OF VALUES FOR ENERGY LOSS COEFFICIENTS

For reference purposes, the following table is provided to give an idea of the range of values of the three coefficients.

Coefficients Range(dE/ds) 0.00045 – 0.00075

(dE/ds/dv) 0.001 – 0.002

(dE/ds/dNC) 0.010 – 0.0130

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PART 2: Additional Energy Losses (use your own group’s data) 1. Calculation of energy losses

You obtained average inlet and exit speeds of the roller coaster ball with the help of the sensors for different release points and configurations.

− Calculate the energy loss experienced by the ball when it travels between sensor 1 and sensor 2 of the horizontal curve for each release point and configuration. Summarize the results in a tabular format (Table 1). (The two sensors are located at the same vertical height, so the energy loss can be estimated by calculating the difference in the kinetic energies at the two sensor locations.)

For the specific case at hand (spherical ball rolling on a pair of cylindrical rails) the total mechanical energy of the ball can be written as:

⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛++= 2

22

'51

21

rrVgHmE

where r is the geometric radius of the ball = 0.01272 m, r’ is the effective rolling radius of the ball on the track = 0.01018 m m is the mass of the ball = 0.0097 kg

Since the two sensors are at the same height, the change in mechanical energy (energy losses) is given by

⎟⎟⎠

⎞⎜⎜⎝

⎛′

+−= 2

22

22

1_ 51

21)(

rrVVmE actualLoss ,

where V1 is the average inlet speed (Sensor 1) V2 is the average exit speed (Sensor 2) 2. Plot ELoss_actual versus Inlet Velocity V1 for each release point and call it Plot 1. Your

vertical axis will be “energy loss”. Your horizontal axis will be “inlet velocity”. − (Use “scatter with data points connected by smoothed lines” option in Excel to plot

data). Label the axes and legend appropriately.

3. G-forces: G-forces in a given location of a horizontal loop are estimated by

gRv

mgR

mv

H

H2

2

=⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

where m is the mass of the ball, RH is the radius of the horizontal curve, v is the velocity of the ball at that given location and g is the acceleration due to gravity.

− Estimate the average G-force in the horizontal partial loop by taking the average of the G-forces at the inlet and exit of the horizontal curve for all release points

− Average G force = [(Vin + Vout) /2]2 /(RH ×g)

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− Summarize the results in the form of Table 1 as shown below. Use the energy loss values ELoss_actual calculated in step 1.

Table 1

− Plot values of ELoss_actual versus average G force in Excel for plotting. This is Plot 2.

4. Comparison with respect to Excel Spreadsheet calculations: Recall that you used an Energy Analysis spreadsheet for your initial roller coaster design calculations. The design spreadsheet also gives an estimate of energy losses as indicated by Figure 9. Use the design spreadsheet to calculate the energy losses in the horizontal partial loop of the lab 2 setup for all the release points and configurations. (Use the sensor 1 speed for ‘v1’ in the spreadsheet. You can approximate the horizontal curve as a semi circle and use it’s

circumference for ‘s2’. ‘h1’ and ‘h2’ will both be equal to 0.19m).

Figure 9: Energy loss prediction by spreadsheet

− Subtract the energy loss (ELoss_calc) you obtain from the Energy Analysis spreadsheet from the corresponding energy loss (ELoss_actual) obtained in Table 1.

− Call the subtracted value “ELoss_actual - ELoss_calc” (actual “minus” calc).

Release point Number Average G force ELoss actual (Joules)

1 2 3 4

Ball mass 0.0100 kg -dE/ds 0.0000 J/mg 9.80 m/s^2 -dE/ds/dv 0.0000 J*s/m^2

Ball geometric radius 0.01270 m -dE/ds/dNC 0.0000 J/m/gBall rolling radius 0.01016 m

ss Moment of Inertia, I 6.452E-07 kg*m^2

Pos 1 Pos 2h1 0.455 m h2 0.000v1 0.000 m/s v2 2.332s1 0.000 m s2 1.000

For LoopsPE1 0.04459 J Dh 0.00 m PE2 0.00000

TKE1 0.00000 J Dv 0.00 m TKE2 0.02719RKE1 0.00000 J dN 0.000 g RKE2 0.01699

E1 0.04459 J dC 0.000 g E2 0.04419

E loss_1_to_2: J >>>>>>>>>>E 0.04459 J E 0.04419

^--------------------------- Same ??? Then OK ----------------------------------^

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− Summarize the results in the form of Table 2 as shown below. (Average G forces will remain the same as calculated in step 3 above.

− Insert one sample Energy loss spreadsheet (properly filled out) for one release point/configuration. Then show a sample calculation ELoss_actual - ELoss_calc for this release point/configuration.

− Plot values of “ELoss_actual - ELoss_calc” versus average G-force obtained for each configuration (in the same graph). This is Plot 3.

Table 2 Release

Point ELoss_calc (J) Average G Force ELoss_actual - ELoss_calc (J) 1 2 3 4

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DISCUSSION QUESTIONS 1. In your own words, briefly describe what is meant by the conservation of energy principle.

2. Communicate in your own words, your understanding of static friction and rolling friction.

3. Make observation about the static friction test. How much did results vary in regards to different teams doing the same measurements? Why is static friction important to your roller coaster design? What is the maximum track angle of inclination you should consider if you wish to minimize energy loss due to slippage of the ball?

4. Explain with educated reasoning how each of the concepts learned in this lab exercise might help you estimate the ball speed at a given point along the roller coaster track your team designs.

5. What is the effect of velocity and G-forces on the energy losses in a horizontal curve?

6. How do the losses you observed compare with the energy loss predictions of the excel spreadsheet as a function of release point?

7. Comment on what impact the additional energy losses create for your design.

Notes:

• Refer to Memo grading guidelines for exact organization of the report and points breakdown.

Due: At the beginning of next Lab

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Roller Coaster Energy Losses Lab Memo Grading Guidelines

Content Points Worth

Point Value

Header Information 5 pts

Introduction 10 pts 1. Brief Introduction of objectives/ goals of the labs. 8 2. Introduction to contents of the report. 2 Rolling and Static Friction 50 pts

1. Show samples hand calculations for: (Use values from your group data) (Total - 10) a. Circular arc apparatus: S , Vavg, μr, ac, n, μrc, Es

b. Linear Ramp: β, μ0, θc

( 1 point for each calculation)

This includes every calculation and all formulas you used to complete your calculation worksheet template. Refer the reader to the page number where the respective raw data worksheet is placed.

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2. Circular arc apparatus observations & conclusions (Total – 20)

− There were 2 circular arc apparatus, each with a different radius. Using the values from the calculation Worksheet, create a table (Table 1) summarizing the resultant average rolling friction coefficients (μrc) values and the average energy loss values (Es) along with the corresponding effective radii for the 2 arc apparatus. Plot (Figure 1) the average rolling friction coefficient, μrc (vertical axis) versus the effective arc radius, R (horizontal axis).

− Similarly construct a table (Table 2) to summarize the rolling friction, μrc and average Vavg values for each the two arc apparatus. Construct a graph (Figure 2) by plotting μrc versus Vavg for the 2 different apparatus radii (in other words, plot μrc versus Vavg for all the different arc radii in the same graph).

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3. Discussion Question 1 5 4. Discussion Question 2 5 5. Discussion Question 3 5 6. Discussion Question 4 5

Supplementary Documents 20 pts

o Email your INSTRUCTOR an electronic copy of the Completed Calculation Worksheet Template that you used for data analysis. Make sure to name the file as Eng1182_Lab2_Group *.xls where * represents you group letter A,B,C ...Also, make sure to enter the correct formulae in the excel cells while completing the spreadsheets.

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Additional Energy Losses 100 pts 1. Completed Part 2 data sheet 20 2. Table 3: Create a table listing inlet velocity, exit velocity, and energy loss for each release

point (step 1, data analysis). Show sample calculations for energy losses for a combination of release points

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3. Figure 3: ELoss_actual vs. Input Velocity for each release point. 5

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4. Table 4: Create a table listing average G-Force and energy loss for each release point (step 3, data analysis). Show sample calculations for avg G-force for a combination of release points. Average G force = [(Vin + Vout) /2]2 /(RH ×g)

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5. Figure 4: ELoss_actual vs. average G force for each release point. 5 6. Table 5: Create a table listing energy loss calculation (ELoss_calc) from excel spreadsheet,

Average G-forces, and ELoss_actual - ELoss_calc for each release point (step 4, data analysis). Insert one sample Energy loss spreadsheet (properly filled out) for one release point (Figure 5). Then show a sample calculation ELoss_actual - ELoss_calc for this release point.

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7. Discussion Question 5 8 8. Discussion Question 6 8 9. Discussion Question 7 8 Conclusions 10 pts

o Briefly state the goals achieved by undertaking this lab activity. 8 o Briefly mention any difficulties that you came across during this lab. 2

Weekly Checklist & Lab Participation Agreement 5 pts **Sample Calculations- Show correct formulae and substitute appropriate values to calculate the final result.