- there will be midterm extra credit available (described after 2 nd midterm)

Transcription

1 Lecture 13: Energy & Work Today s Announcements: * Midterm # 1 still being graded. Stay tuned - there will be midterm extra credit available (described after 2 nd midterm) * Midterm # 1 solutions being discussed in recitation this week. Attend and you get a freebie quiz score of 100% - important to know solutions for final Week 7 Reading: Chapter 7-- Giancoli Week 7 Assignments: (Due 10/08 {Thursday} by the end of the day) Textbook: HW #6 Chp 7: Q3, Q6, Q13, P2, P6, P11, P22, P42, P57, P80 MasteringPhysics: - Assignment 6 (Due 10/08 {Thursday} by the end of class)

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3 Energy: ENERGY: The ability to do work --- but no unique definition - The ability to make something happen It is important to realize that in physics today, we have no knowledge of what energy is -- Richard Feynman Cash Savings Account Paying Bill/receiving paychecks WORK: The mechanical transfer of energy

4 Kinetic Energy: - Kinetic Energy = the energy associated with movement Kinetic Energy = ½ x mass x velocity 2 - just a number (scalar) - never a negative number - Energy (Work) units: = (N *m) = kg x m 2 /s 2 AKA: Joule HINT: (ABB: J) Another famous energy unit: calorie

5 Potential Energy Kinetic Energy Chp 2: h = v 02 /2g Energy transfer (Work): PE = mgh KE = ½ m v 0 2 v 0 - Kinetic energy seems to disappear then return. - Propose instead that it is still there, it just goes into a different form potential energy The transformation of energy to a different (mechanical) form occurs because a force has been acting on an object that moves in space WORK

6 y Work-Energy Theorem v 2 - v 0 2 = 2 a (y - y 0 ) and you thought you could get away with forgetting kinematics : -) ½ m [v 2 - v 0 2 = 2 a (y - y 0 )] Multiply each side by (½) m ½ mv 2 - ½ mv 0 2 = ma (y - y 0 )] v 0 KE - KE 0 = F Δy Work-Energy Theorem (or Principle): ΔKE = KE - KE initial = [F Δx] all = W all

7 Work: Force dot Displacement WORK: The amount of energy transferred by a force - Work is the force times the displacement projected along the direction of the force (dot product): F - F * Δr = F Δr cosθ - F * Δr = F x Δx + F y Δy θ F cosθ Work has a technical definition in physics, but don t confuse it with its English usage - generalized version of Δx in the previous example Δr - just a number (scalar) - Reminder: Dot product: - a type of vector multiplication - A*B is a scalar (a number) A - A * B = A x B x + A y B y - A * B = A B cos (θ between ) θ x B A cosθ

8 Clicker Question: 1) Which person did more work? a) The person carrying the weight around b) The person lifting the weight up c) The person pushing down on the weight up

9 Clicker Question: 1) Which person did more work? a) The person carrying the weight around b) The person lifting the weight up c) The person pushing down on the weight up

10 Clicker Question: 2) Imagine a world where you got paid according to the amount of work you did in a physics sense. Which of the following jobs might you prefer if you were interested in getting rich? a) A Teacher b) A garbageman c) A Computer Programmer d) A Surgeon e) A Lawyer

11 Clicker Question: 2) Imagine a world where you got paid according to the amount of work you did in a physics sense. Which of the following jobs might you prefer if you were interested in getting rich? a) A Teacher b) A garbageman c) A Computer Programmer d) A Surgeon e) A Lawyer

12 Work: Force dot Displacement WORK: The amount of energy transferred by a force - Work is the force x the displacement projected along the direction of the force (dot product): F - F * Δr = F Δr cosθ - F * Δr = F x Δx + F y Δy θ F cosθ Δr Work has a technical definition in physics, but don t confuse it with its English usage - just a number (scalar) but signed quantity - Calculate work for each force F F Δr =0 Δr - No work done by F if the applied force does not result in movement of the object - No work done by F if the applied force is perpendicular to the movement of the object

13 Potential Energy: - Potential Energy = the (stored) energy associated with (relative) position - Two most common examples: - gravity - springs U ΔU = Potential Energy (gravity) = m g (Δx) = mgh U ΔU = Potential Energy (springs) = 1/2 k (Δx)2 - just a number (scalar) - More on the technical definition later

14 Work: Force dot Displacement WORK: The amount of energy transferred by a force - Work is the force x the displacement projected along the direction of the force (dot product): F - F * Δr = F Δr cosθ - F * Δr = F x Δx + F y Δy θ F cosθ Δr Work has a technical definition in physics, but don t confuse it with its English usage - just a number (scalar) but signed quantity - Calculate work for each force F F Δr =0 Δr - No work done if the applied force does not result in movement of the object - No work done if the applied force is perpendicular to the movement of the object

15 Work: Non-constant Force Case ΔW = F(x) Δx cosθ W total = Σ a bunch of little steps F(x) Δxcosθ Δx { (cosθ = 1 if we take component of Force along path) Some path with a varying force along it - If force is not constant then we can t just take F*x - Visualize the total work done as a summed collection of small constant force pieces times Δx

16 Work: Non-constant Force Case Δx Force along path F(x) total W equals the hashed area F(x a ) x a Position along path (x) -Plotting the component of force along a path vs. its position along the path: ΔW(x a ) = F(x a ) Δx

17 Work: Non-constant Force Case Δx Force along path F(x) total W equals the hashed area F(x a ) Answer becomes exact when we sum infinitely many, infinitely narrow rectangles x a Position along path (x) -Plotting the component of force along a path vs. its position along the path: ΔW(x a ) = F(x a ) Δx - The need to find the area under a curve like in the case of work occurs extremely often: Integral - W = Σ ΔW the area between the curve and the x-axis

18 Non-Constant Forces: - If force is not constant then we can t just take F*x ΔW = F(x) cosθ Δx W total = Σ a bunch of little steps, i F(x) i cosθ Δx i Δx { (cosθ = 1 if we take component of Force along path) Some path with a varying force along it W = F x dx (1-D) -or- W = F r * dr (>1-D) x a x b along the path x b W total = Σ F(x) cosθ Δx x a r a r b