Work & Energy

1. Work & Energy WORK Force x Distance WORK Force x Distance Energy Kinetic + (Potential)

2. Work and Energy • Chapter 6 Roadmap • Method Differences • Work and energy • Crate example • 2 important points about work

3. Work and Energy • Combination of Force, Distance, and how they’re working together creates scalar WORK. • WORK either increases or decrease scalar KINETIC ENERGY – involves velocity magnitude. • Some types of WORK are always difference of 2 endpoints, and can be treated as difference in scalar POTENTIAL ENERGY. • LOSS OF PE often equals GAIN OF KE (or vice-versa). Thus POTENTIAL + KINETIC (scalar) is CONSERVED • Great shortcut – Solve complicated paths looking only at endpoints!

4. Method Differences • Chapter 3 • Position, velocity, acceleration vectors. • X and y components. • Chapter 4 • Force and acceleration vectors. • ΣF = ma is vector equation. • Solve F=ma in x and y directions. • Chapter 5 • Force and acceleration vectors. • Solve F=ma in radial and other directions. • Chapter 6 • Work and energy scalars. • Forget direction, throw everything in “big mixing pot”.

5. Review Chapter 3 • From chapter 3 (solve for time) (plug time in here) • Combined to give • Required multiplication of vectors! • Defined “scalar product” • Magnitude of each times “how much they’re inline” (Boldface = vector)

6. Modifying 3rd Equation • Modified 3rd Equation • Consider several cases • Product of a and Δx, and how they’re working together, either increases/decreases/keeps-constant v2 • Note v2 is scalar, no direction!

7. Work and Energy • Modified 3rd Equation • Multiply by ½ m • ma = Force • Work equals change in Kinetic Energy • All scalars, use only magnitudes! • Units N-m, or kg m2/s2 Joules (J)

8. Conclusions • Product of force, distance, and how they’re working together increases or decreases the magnitudeof v. • How force and distance work together is very important. • If f and d inline, magnitude of v increases. • If f and d partially inline, magnitude of v increases a little. • If f and d perpendicular, magnitude of v remains constant. • If f and d partially opposed, magnitude of v decreases a little. • If f and d opposed, magnitude of v decreases. • If f but no d v remains constant.

9. Work Definition • Definition F . x .cos(θ) • Cos(θ) extracts F and x working together • +1 when together • -1 when opposed • -1 to +1 when in between • 0 when perpendicular • Work is a scalar quantity F x

10. Work done by Crate • Example 6.1 • 50 kg crate, pulled 40 m • FP = 100 N, Ffric = 50 N • Method 1 • Solve for net force • 100 N cos(37) – 50 N = 30 N • Multiply by 40 m = 1200 J • Method 2 • Find individual works • Wmg = 0, WFn = 0, WFP = 3200, WFfric = -2000 • 0J + 0 J + 3200 J – 2000 J = 1200 J • Work of sum = sum of works

11. Problem 8 Man lowering piano • Forces • Fg = 3234 N • Ffric= μ mg cosθ = 1142 N • FP = mg sinθ - μ mg cosθ = 376 N • Works • Wfr = 1142 N x 3.6 m (-1) = -4111 J • WP = 376 N x 3.6 m (-1) = -1353 J • Wg = 3234 N x (3.6 sin28) = +5465 J • Wnormal = 0 (perpendicular) • Total work is 0 • Work of gravity was Fg times height • Had it accelerated work would not be 0

12. Problem 8 – Work done by gravity • Work done by gravity • Force component along incline times total incline distance. • or • Distance component along vertical times total vertical force. • 2nd is just weight times height (mgh) 3234 sin28 3234 3.6 sin28 3.6

13. Two important things • Total Work is • The work of the sum of all forcesΣFi x distance • or • The sum of the individual works of all forces. Σ(Fi x distancei) • Individual Work is • Force component in direction of displacement. • or • Displacement component in direction of force.

14. Work and Energy Fxcosϴ = ½ mv2 - ½ mvo2 Work = ΔEnergy Work equals change in energy

15. Examples of Work and Energy • Example 6.5 – Work to increase car speed • Problem 18 – Work to stop car • Problem 23 - Air resistance on baseball • Example 6.8 – Falling baseball • Use 2nd law • Use work • Example 6-9 - Roller coaster • Use work • Couldn’t do easily by 2nd law! • Vertical circle example (use work) • Note how you “mix up” dimensions!

16. Outta here October Potter County hiking / camping