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WORK

WORK. The quantity obtained when force is multiplied by displacement Connected to concept of energy Some has energy when it has the capacity to due work, that is, apply force over some distance Conversely, work changes the energy status of a system. Work  W = F x Scalar

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WORK

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  1. WORK • The quantity obtained when force is multiplied by displacement • Connected to concept of energy • Some has energy when it has the capacity to due work, that is, apply force over some distance • Conversely, work changes the energy status of a system

  2. Work  W = F x • Scalar • Unit: N m = joule, J • The force & a component of displacement must coincide • Positive Work = Force is applied in same direction as motion

  3. A component of force must be applied in direction of displacement • F ┴ x = no work done • Pushing on wall = no work • Can be positive -  energy status, negative -  energy status, or zero

  4. Multiple forces acting on object, the total work = work done by each force separately  Wtotal = W1 + W2 + … = Σ W • Can also be found by determining vector sum of forces: Ftotal  Wtotal = Ftotal x

  5. KINETIC ENERGY & THE WORK – KINETIC ENERGY THEOREM • Positive work  energy status • Causes objects to move faster • Negative work = slower

  6. Consider an apple falling through air • As apple falls through distance y, a kinematic describes its motion

  7. The quantity measuring the change in motion = kinetic energy, K  K = ½ m v2 Unit: kg (m/s)2 = J • Scalar quantity, but never negative

  8. Connection between work & energy = work-energy theorem  Wnet = Δ K • V is not linear with respect to K • Doubling v ≠ 2 K • V is squared  4 K

  9. CONSERVATIVE & NONCONSERVATIVE FORCES • The work done is stored in the form of energy that can be released later • Consider gravity • Lifting a box at constant speed does work  W = F x = w y = mgy • Releasing the box, gravity does the same work equal to the same amount of K

  10. Contrast to friction • Work is done sliding a box around on the floor  W = μ m g x • But, when released, the box does not move  no K • A nonconservative force – work is converted into other energy forms

  11. Conservative forces are path independent • Only depends on initial & final positions • Route taken does not effect results • Any closed path, total work = zero

  12. POTENTIAL ENERGY • Work done lifting an object higher position changes energy status • W did not  K, it is stored energy by virtue of its position • It gained potential energy, U • It has potential to do work • Gravitational Potential Energy, Ug  Ug = m g y Unit: J

  13. The location of zero potential is problem dependent • Usually a convenient location • Often the lowest point of problem

  14. POTENTIAL ENERGY OF SPRINGS • Springs are another conservative force • Springs can store energy like gravity can • Experiments show a linear relationship between force applied and amount of stretch  F α x • Constant that creates an equality = k – spring constant F = - k x Hooke’s Law

  15. Negative indicates F is a restoring force  F is in opposite direction as x • Unit for k = N / m • How stiff the spring is • Large k = stiff spring

  16. Since force is not constant, we cannot use W = F x • Consider the graphical representation of F vs. x • If we were to stretch spring from x = 0 to x, the area under curve represents work

  17. Area = ½ (base)(height) = ½ (x)(kx)  W = ½ k x2 • Work done stretching/compressing = the energy stored  Us = ½ k x2

  18. CONSERVATION OF MECHANICAL ENERGY • Mechanical energy, E = U + K • Regardless of what happens in systems with conservative forces, E is always conserved  E = constant • Energy can be converted in form, but the sum remains constant

  19. Makes many problems a simple matter of bookkeeping  Initial energy = final energy • For conservative forces only

  20. WORK DONE BY NONCONSERVATIVE FORCES • Nonconservative forces change the amount of mechanical energy in a system • Typically a decrease due to conversion of thermal energy K0 + U0 ≠ K + U Einitial > Efinal

  21. To balance equation, an additional factor must be added to right • Call it Wnc K0 + U0 = K + U + Wnc

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