1. First-Year Engineering Program Lab Safety Policies Don’t stand on lab chairs Don’t sit or stand on lab tables No dangling jewelry or loose clothes. NO open toed shoes. Be careful with sharp corners. Recall location of phone and first-aid kit. Report ALL injuries 1

2. First-Year Engineering Program Overview of Labs 2 Lab 1Introduction to Roller Coaster Design Lab 2Roller Coaster Energy Losses Lab 3Roller Coaster Circuits with Circuit Prototyping Lab 4Roller Coaster Speed Sensor Calibration Lab 5RC Building Session #1 Lab 6RC Building Session #2 Lab 7RC Building Session #3 Lab 8RC Final Construction - Preliminary Testing of Design Lab 9RC Final Testing of Design Lab 10RC Oral Presentations

3. First-Year Engineering Program Engineering 1182 Roller Coaster Dynamics 2: Energy Losses 3

4. First-Year Engineering Program Recap of previous lab  Law of Conservation of Energy Energy can neither be created nor destroyed Energy can transfer from one form to another  Examples of Energy Losses are the following: Resistive forces, such as friction and air resistance Act on a body in motion and cause energy to be transferred to unwanted forms (i.e. heat).  For the roller coaster ball, 4 + + = + + + “Energy Losses”

5. First-Year Engineering Program Recap of physics reading module  Friction is a process that results in a force that opposes an action. Static Friction (acts to prevent motion) Kinetic Friction (exists between moving surfaces) Sliding Friction (due to sliding action of the object) Rolling Friction (due to rolling action of the object)  Friction causes your ball to lose energy as it traverses along the track. 5

6. First-Year Engineering Program  Slippage results from a steep angle causing the ball to slide rather than roll. Sliding friction is generally greater than rolling friction.  Curved Motion Critical velocities: At the top of a loop: At the top of a bump: Bank angle creates the centripetal force needed to keep the ball on the track. 6 Recap of physics reading module

7. First-Year Engineering Program Lets put it all together!  Initial energy (i.e. potential energy) is imparted to the ball by raising it to a certain height ‘h’ Part of the initial energy will be used: To move the ball from the beginning to the end of the roller coaster through loops, bumps, inclined planes and straight sections To overcome all energy losses along the track (including friction)  How much energy will be lost due to rolling friction? The value of µ R (coefficient of rolling friction) can be calculated This will give you a good estimate as long as the ball is not sliding along the track 7

8. First-Year Engineering Program Agenda Friction (one form of energy loss) Slippage Curved motion (and why it needs to be handled separately) Additional (unaccounted for) energy losses In-Lab activities: Experiments to calculate Static/Rolling friction coefficients Experiments to calculate average G-force 8

9. First-Year Engineering Program Roller Coaster Energy Analysis Spreadsheet You will be using a RC Energy Analysis Spreadsheet to model most, but not all of the energy losses that your coaster will experience. This Excel spreadsheet allows for Vertical loops/curves Bumps Horizontal loops/curves Relatively straight sections of track Energy losses due to friction, G-forces and air resistance are included. 9

10. First-Year Engineering Program Snap-fit spacing - Too wide a spacing can cause excessive energy losses through track deformation. Structural stability (including track) - An unstable structure can cause energy losses through movements within the structure. Bending of the track can also cause energy losses. Differential forces between rails along horizontal curves –The ball will exert a different amount of force on each rail of the track. 10

11. First-Year Engineering Program Additional Energy Losses 11  In today's lab You will gain experience: Using the speed sensors Instrumenting one design feature Compare energy losses in coaster to those expected in the RC Energy Analysis Spreadsheet One reason for differences: G-force related losses in horizontal loops  In your final project report you will use this information to discuss where your coaster is losing more energy than shown by this spreadsheet and why.

12. First-Year Engineering Program A final consideration: projectile motion You need to let your ball fall off the end of your track and land in a box – how far away does the box need to be? If the track at the end of the run is horizontal and at a height h, and the ball is at a speed v, then: 12

13. First-Year Engineering Program Lab Activities (Part 1) Lab Apparatus Circular Arc (Rolling Friction) Ramp (Static Friction) Group Rotation Data will be collected at the front table by each team. Each team will take turns rotating to the table and collect data with one ball on a total of three apparatus. Each group will be notified when it is their turn to rotate to the front table. Each group should record their data on the printed worksheet at the front table and on the computer at the instructor’s station. 13

14. First-Year Engineering Program Circular Arc Apparatus - Friction 14 Ball is released at point A. The type of motion (oscillation, simple harmonic motion) is a way to roll a ball a relatively large distance with a relatively small apparatus. Ball oscillates for some time and eventually comes to rest –Why? A

15. First-Year Engineering Program Ramp Apparatus - Slippage In the lab you will determine the value of angle, β, at which the conjoined balls begin to slide down the ramp. 15 W = mg motion β Body doesn’t slideBody just begins to slide W = mg β NO MOTION  From β you can calculate Θ C, the angle above which you can expect slippage of a single ball on your roller coaster (with increased energy losses). The calculation is in the lab procedures.

16. First-Year Engineering Program Vertical Loop Apparatus – G force 16 For consideration only, you will not be actually using this device in the lab.

17. First-Year Engineering Program Vertical Loop Apparatus If this device were used today, you would do the following: Measure the speed of the ball going into the loop using a speed sensor Measure the speed of the ball leaving the loop with another speed sensor. Calculate the amount of energy lost by the ball while rolling through the loop. Compute the energy coefficients for use in the Roller Coaster Energy Analysis Spreadsheet for losses in curved paths (G – forces). 17

18. First-Year Engineering Program Lab Activities (Part 2)  This activity will be done at your table during the entire lab period.  Locate your sample build kit, speed sensors, Arduino board.  Build the support structure and track.  Take measurements for four cases.  Analyze, graph, and discuss your results. 18

19. First-Year Engineering Program You'll make this support structure 19

20. First-Year Engineering Program Experimental Setup 20 You'll add speed sensors at the beginning and end of the horizontal curve and measure the energy losses for different starting points. Sensor A Sensor B

21. First-Year Engineering Program Speed Measurement Accuracy 21 Tests of production speed sensors show an accuracy of about +/- 2% when using a correction factor of 1.085. This is with the LED and photo-transistor visually aligned. Visually confirm that the glued alignment of the two LEDs is correct. If not aligned, errors of up to 10% can occur!

22. First-Year Engineering Program Let’s put things together! Energy losses on straight track: Frictional forces Air resistance Additional energy losses: Snap-fit spacing Structural stability Differential forces between rails A ball following a curved path: Involves centripetal force. Has different frictional losses than when rolling on straight track. 22

23. First-Year Engineering Program Assignments and Reminders Weekly lab checklists, Memo Grading Guidelines and Lab Participation Agreement must be included with the weekly memos. Lab Memo 2 (team) is due next week Update Project Notebook 23