Lecture 09: Work and Kinetic Energy Energy Overview Conservation of Energy Forms of Energy Work Transfer of Energy Relationship to Kinetic Energy 1

Conservation of Energy Energy is “Conserved” meaning it cannot be created nor destroyed! Energy can change form. Energy can be transferred. Total Energy does not change with time. This is a BIG deal! Maybe do example of conservation (like cookies) and counter example. Force is NOT conserved.

Energy Forms of Energy: Units: Joules (J) = kg-m2/s2 Kinetic Energy (energy of Motion) Potential Energy (Stored energy) Heat (later this semester…) Mass (E=mc2) (in Physics 102) Units: Joules (J) = kg-m2/s2

Work by Constant Force W = F x cos (units: J) F Dx F Dx F Dx Work can be positive: Work can be zero: Work can be negative: F q x Dx F WF > 0 if 0  q < 90 since cosq > 0 Dx F WF = 0 if q = 90 since cosq = 0 Dx F WF < 0 if 90 < q  180 since cosq < 0

Work by Variable Force W = Fx Dx Work is area under F vs. x plot. Work Spring F = k x (a changing force). Area = ½ k x2 = Wspring Force Work Distance Force Distance F=kx Work

Kinetic Energy: Motion Apply constant force along x-direction to a point particle m. W = Fx Dx = m ax Dx = ½ m (v2 – v02) Work changes ½ m v2 Define Kinetic Energy: K = ½ m v2 Thus: W = D K (For Point Particles)

Summary Energy is Conserved Work = transfer of energy using force Can be positive, negative or zero W = F x cos(q) Kinetic Energy (Motion) K = ½ m v2 Work = Change in Kinetic Energy Wnet = DK

Example: Block w/ friction A block is sliding on a surface with an initial speed of 5 m/s. If the block travels 3 m before stopping, what is the coefficient of friction between the block and the surface? We will use: Wnet = K To do this, we need to find expressions for Wnet and K First: K Second: Wnet 5 m/s 3 m

Example: Block w/ friction A block is sliding on a surface with an initial speed of 5 m/s. If the block travels 3 m before stopping, what is the coefficient of friction between the block and the surface? K = Kf - K0 = ½ m vf2 – ½ m v02 = 0 – ½ m v02 = – ½ m v02 K = ½ m v2 vf = 0 m/s

Example: Block w/ friction A block is sliding on a surface with an initial speed of 5 m/s. If the block travels 3 m before stopping, what is the coefficient of friction between the block and the surface? WN = 0 since cos90º = 0 Wg = 0 since cos90º = 0 Wf = Ff x cos = -mgd (since cos180º = -1) Fg FN Ff Wnet = WN + Wf + Wg = 0 + -mgd + 0 = -mgd x y

Example: Block w/ friction A block is sliding on a surface with an initial speed of 5 m/s. If the block travels 3 m before stopping, what is the coefficient of friction between the block and the surface? Wnet = D K -mgd = -½ m v02 gd = ½ v02