Lab 3: Energy Loss Part 2 - Frictional Loss In Loops and Banks, and Velocity Limits
Introduction .
In this lab, your team will continue its investigation of the underlying physics of the roller coaster you will be building this semester. After this lab you will have all the information you need to fully model the behavior of your roller coaster in either Excel or MATLAB. Todays lab will focus on how loops and banked turns affect energy losses in the coaster. Additionally, you will investigate the velocity limitations involved in loops and bumps, as well as banked turns.
Part A: Building the Test Apparati .
You will construct two apparati today in lab. Your team should split into two groups to build the apparati in parallel.
Task 1: Construct Loop Apparatus
The first apparatus will be a slope with a loop. The slope should be no steeper than 45o, and should use the starting tower as an anchor. The loop should be no more than approximately 8” in diameter. Excessively large or small loops will likely result in more work for your team. As will excessively tall and steep starting hills. The support structure of the apparatus should be sturdy, but minimal, again to limit time and effort spent on production.
Once built, do a number of test runs with the ball until you are convinced of its reliably operation. The ball should travel smoothly and reliably through the loop. Most importantly, it should easily make it around the loop without leaving the track at any point.
Once tested, add a speed sensor to the entry point of the loop, the top of the loop, and the exit of the loop. Note that the entry and exit sensors will probably be VERY near one another. Be careful in placement and if need be, move the tracks apart a bit.
Once built, move on to part B and begin data collection.
Task 2: Construct Bank Apparatus
Using the other start tower available at the table, construct a slope with a banked turn at the bottom. The slope should be no more than 45o, and should use the tower as an anchor. The bank should be 180o, and should be approximately 12” in diameter. Excessively large or small banked turns or excessively tall and steep starting hills will probably create more unnecessary work for your team.
Once built, do a number of test runs with the ball until you are convinced of its reliably operation. The ball should travel smoothly and reliably through the bank.
Once tested, add speed sensors to the entry point of the bank, the midpoint, and the exit.
Once built, move on to part C and begin data collection.
Part B: Loop Data Collection .
Task 1: Determine Minimum Start Height
Choose a point on the starting hill at random and release the ball. If the ball cleanly makes it through the loop, move lower. If the ball fails to pass through the loop, move higher. Repeat this process until you find the lowest release point for which the ball cleanly passes through the loop.
It is suggested that you start with very large adjustments in height at first, until you have a point where the ball fails to traverse the loop, and a point where the ball succeeds in traversing the loop. At this point, choose midpoints to narrow your testing range quickly.
Once determined, record the minimum starting height.
Task 2: Low Start Data Collection
For the low start point, choose a starting point on the track from 1”-2” higher than the minimum start point. Mark this point so it can be reused consistently (a snap-fit works well).
From this point, collect velocity data from 5 trial runs.
Task 3: High Start Data Collection
For the low start point, choose a starting point on the track from 5”-10” higher than the minimum start point. Mark this point so it can be reused consistently.
From this point, collect velocity data from 5 trial runs.
Once tasks A through C are complete, break down your apparati and store your kit. The remainder of the exercise can be done out of the lab if desired.
Part C: Bank Data Collection .
Task 1: Determine Start Height Range
Find at least two different heights to start the ball from that are at minimum 3” different in height. The ball should cleanly pass through the bank from both points.
Record both of these heights. They will be used in the next task.
Task 2: Low & High Start Trials
For both the low and high start point collect velocity data from 5 trial runs. (10 runs in total)
Once tasks A through C are complete, break down your apparati and store your kit. The remainder of the exercise can be done out of the lab if desired.
Part D: Calculation of Speed Requirements .
Task 1: Calculate Minimum Loop Speed
Consider the discussion presented in the lab slides. Derive a formula for the minimum speed needed for the ball to successfully travel through a loop. Additionally, derive a formula for the maximum speed the ball may traverse a hill.
Task 2: Calculate Bank Target Speed
Again considering the discussion presented in the lab slides, derive the target speed for a banked turn. For our simplified model of a bank, the target speed is the speed at which the ball will not move up or down the plane in the cross section.
Task 3: Generate Comparisons
For all trial runs, compare theoretical speeds (including frictional losses for straight lines as well as for loops and banks, as discussed in the slides), to both idealized (no friction) speeds and measured data. Generate plots for these comparisons (4 plots in total, 2 for each task)
Calculate the theoretical speed at the top of the loop if the ball was released from the minimum starting height. Compare this velocity to the result from your derived equation.
Discussion Questions
Comment on any notable discrepancies between theory and measured data.
Provide a better model for the banked turns. This model should be presented graphically and should include equations for the normal force(s) involved.
Report: Lab Memo Format