First-Year Engineering Program Lab Safety Policies Don’t stand on lab chairs Don’t sit or stand...

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


Overview of Labs

2

Lab 1 Introduction to Roller Coaster Design

Lab 2 Roller Coaster Energy Losses

Lab 3 Roller Coaster Circuits with Circuit Prototyping

Lab 4 Roller Coaster Speed Sensor Calibration

Lab 5 RC Building Session #1



Lab 8 RC Final Construction - Preliminary Testing of Design

Lab 9 RC Final Testing of Design

Lab 10 RC Oral Presentations


Engineering 1182

Roller Coaster Dynamics 2: Energy Losses

3


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”1PE 1TKE 1RKE

2PE 2TKE 2RKE


Recap of physics reading moduleFriction 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


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

gRv

gRv


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 µR (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


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


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


Additional Energy Losses• 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.

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Additional Energy Losses

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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.


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:

g

hv 22distance

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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.

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Circular Arc Apparatus - Friction

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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


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.

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W = mg

motion

β

Body doesn’t slide

Body just begins to slide

W = mg

βNO MOTION

From β you can calculate ΘC, 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.


Vertical Loop Apparatus – G force

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SP3

SP2

SP1

RUNG 5

RUNG 1

STMP

S1,2,3

Hsp1

Hsp3

Hstmp

Hsp2

For consideration only, you will not be actually using this device in the lab.


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


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


You'll make this support structure

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Experimental Setup

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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


Speed Measurement Accuracy

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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!


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


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

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First-Year Engineering Program Lab Safety Policies Don’t stand on lab chairs Don’t sit or stand...

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