MECE 102: Engineering Mechanics Lab A First Year Course in Newtonian Mechanics, Experimentation, and Computer Tools Created by the Faculty of the Mechanical Engineering Department in the Kate Gleason College of Engineering at RIT

Week 6 Lecture Work and Energy We will study: the motion of a cart moving through a curvilinear path the tradeoff between Work and Energy that occurs during the motion. We will be using Video capture to help determine elevations, distances travelled, and velocities of the moving cart.

iCLICKER: The week 6 Lab Experiment studies the relationship between Work and Energy transfer. Which one of the following units are typically associated with Energy terms? Select your Answer: Joule [J] Meter [m] Pascal [Pa] Hertz [cycles/sec] Liter [L]

iCLICKER: The week 6 Lab Experiment studies the relationship between Work and Energy transfer. Which one of the following units are typically associated with Energy terms? Select your Answer: Joule [J]  derived SI unit [J] = [N] [m] derived US Customary unit [ft·lbf] Meter [m] Pascal [Pa] Hertz [cycles/sec] Liter [L]

FORMULATE: State the Known Information Determine the speed, kinetic energy and potential energy of a vehicle as it traverses the curvilinear path of a track. Use the difference in total energy between cart positions to estimate the work done by the moving cart upon the track, to overcome the irreversible friction force.

Clearly identify values to be determined in analysis: FORMULATE: Identify Desired Information Clearly identify values to be determined in analysis:

Clearly identify and justify all Assumptions used in analysis: FORMULATE: Identify Assumptions Clearly identify and justify all Assumptions used in analysis:

CHART: Schematic Diagram Figure 6.1: Schematic Diagram of a cart rolling down a curved ramp.

CHART: Free Body Diagrams 𝑘 𝜽 𝑖 𝑛 𝑘 fm 𝑡 𝑖

EXECUTE: Recall the Governing Equations The Conservation of Energy (also known as “The 1st Law of Thermodynamics”) states that “The change in the amount of energy stored within a system during some time interval is equal to the net amount of energy transferred into the system by heat transfer from its surroundings during the time interval, minus the net amount of energy transferred out of the system by work done by the system on its surroundings during the time interval.” Recall the “HIP-to-WIN” sign convention for energy transfers.

Ei references the Total Energy at state i EXECUTE: Simplify the Governing Equations Ei references the Total Energy at state i PEi references the Potential Energy at state i KEi references the Potential Energy at state i SEi references the Spring (Elastic) Energy at state i (assumed to be “0” for this experiment)

EXECUTE: Simplify the Governing Equations

iCLICKER: Which one of the following summarizes the unique position and energy status of the cart as it moves along the track? . Select your Answer: State Table Process Table Dinner Table Water Table None of the above Tables

iCLICKER: Which one of the following summarizes the unique position and energy status of the cart as it moves along the track? . Select your Answer: State Table Process Table Dinner Table Water Table None of the above Tables

iCLICKER: In Mechanical Engineering “the state of a physical system fully describes the energy status of the system at an instant of time, and is dependent on the path taken to arrive at the state.“ Select your Answer: True False

iCLICKER: In Mechanical Engineering “the state of a physical system fully describes the energy status of the system at an instant of time, and is dependent on the path taken to arrive at the state.“ Select your Answer: True False  The state is INDEPENDENT of the path taken to arrive at the state.

CHART: Data Tables Each row in the STATE TABLE corresponds to one unique position and energy status of the cart as it moves along the track. Each State, i, corresponds to a unique elevation and the energy condition of the cart when it is at that particular elevation.

CHART: Data Tables Each row in the PROCESS Table describes the exchange of energy, work and heat, as the system moves between states. A “Process" in Mechanical Engineering fully describes the change between two states of the system over an interval of time, and describes the path taken between states.

iCLICKER: Which one of the following is a Scalar value? Select your Answer: Force applied to the mass of the cart Displacement of the cart Work performed by the cart Velocity of the cart None of the above

iCLICKER: Which one of the following is a Scalar value? Select your Answer: Force applied to the mass of the cart Displacement of the cart Work performed by the cart Velocity of the cart None of the above

WORK as defined in Physics and Mechanical Engineering. WORK is defined mathematically using the Scalar Product, or Dot Product, of two vectors.

EXECUTE: Simplify the Governing Equations Equation 6.21 is referenced as the Work-Energy Theorem. Recall that we assumed that there is no Heat Transfer, Q12, occurring between the cart and the surroundings.

Given the 2 vectors:. 𝑠 1 =5 𝑖 −2 𝑗 + 7 𝑘 and Given the 2 vectors: 𝑠 1 =5 𝑖 −2 𝑗 + 7 𝑘 and 𝑠 2 =1 𝑖 +4 𝑗 − 3 𝑘 Compute the Dot Product: 𝑠 1 ∙ 𝑠 2 (also referred to as the “Scalar Product”)

Lab Set-up Pictures

Homework Prior to LAB tomorrow Read section 6.2 of the textbook Watch LAB Videos Complete the on-line LAB quiz in myCourses Attempt to solve all assigned chapter problems in your logbook before RECITATION. Week 6 Problem Set from Section 6.5:        1, 3, 8, 17, 19, 24

Questions?