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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

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Engineering 1182 Lab Overview Team Design/Build Project

Roller Coaster Design Documentation Building Testing Report Presentation

Details are in your course packet: read them and make sure you understand!

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Overview of LabsLab 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 6 RC Building Session #2

Lab 7 RC Building Session #3

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-1: Energy Conservation

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ENERGY is a conserved property of an object that relates to its ability to do work. Energy can have a number of forms, for example mechanical, electrical, chemical, or nuclear. E Units: Joules or N-m (Newton-meter).

There are different formulas describing different forms of energy.

Physics Concept - Energy

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Law of Conservation of Energy (COE)

Energy can neither be created nor destroyed.

Energy can only be changed from one form to another.

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Forms of Energy in a Rolling Ball

Potential Energy (PE)

Energy of the Ball

Kinetic Energy (KE)

Total Mechanical Energy of the ball = PE + KE

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Kinetic Energy in a Rolling Ball

Translational Kinetic Energy (TKE)

Kinetic Energy (KE)

Rotational Kinetic Energy (RKE)

Kinetic Energy of the ball = TKE + RKEA rolling ball has both forms of Energy!

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Translational Kinetic Energy

An object has Translational Kinetic Energy (TKE) when it is undergoing linear displacement

TKE = ½mv2

m = mass of object v = velocity of object

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Rotational Kinetic Energy (RKE)

An object spinning about an axis is said to have Rotational Kinetic Energy.

RKE = ½Iω2

I: Moment of Inertia ω: Angular Velocity (radians/sec)

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Moment of Inertia (I)

The moment of Inertia (I) of an object Measures the resistance an object

has to rotating about a particular axis, similar to the way that mass is the object’s resistance to changing its velocity.

Depends on its mass, shape and axis of rotation.

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Angular Velocity (ω) vs Linear Velocity (V )

)(

)()(

SecondsTime

MetersntDisplacemeLinearinChangeVVelocityLinear

)(

)()(

SecondsTime

RadiansntDisplacemeAnglularinChangeVelocityAngular

RV

This relationship between linear and angular velocities holds if and only if the ball is not slipping

ω

v

R

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Effective Rolling Radius

R’Rails

• The ball sits down between the tracks making the rolling radius smaller.• The angular velocity is increased.• If the rails are not supported and split

further apart, the ball will sit farther down.

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Energy Transfers

As the ball rolls down the roller coaster track, some energy of the moving ball is: Lost to friction and dissipated as heat Spent in overcoming Air Resistance Lost to Structural Deformation Converted to Sound Energy

Unwanted Energy Losses !

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In general, energy transferred away from the ball will NOT come back, and so the total mechanical energy of the ball will be always decreasing.

In the real world, we cannot avoid losses but can only MINIMIZE and/or ALLOW for them.

Energy Transfers (continued)

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Let’s put it together !

For the ball rolling along the roller coaster track, between any two subsequent points:

+ +

= + + + “Energy Losses”1PE 1TKE 1RKE

2PE 2TKE 2RKE

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Design Considerations You will be estimating the velocity of

the ball at selected points along your roller coaster track using energy calculations to: Make sure the velocity into turns is not

too high (making banking difficult) Make sure that the ball can reach the

top of vertical loops Make sure that the ball will not fly off the

top of bumps

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Assignments and Reminders

Lab Memo (Team)