PHYS 1020 Lecture 18 Work Energy

PHYS 1020 Lecture 18 Work Energy

Work done by a constant force Since -1 cosθ 1, W can be positive or negative.

See lecture posted online for corrected version. You can calculate the work done on an object by individual forces and by the net force. ex: A person pulls a block (mass 10 kg) up an inclined plane at constant speed. The block moves 1 m along the plane and the tension force acting on the block is parallel to the plane. Find the work done on the block by (a) the tension force (b) gravity (c) the normal force (d) the kinetic friction force (e) the net force Use µ k = 0.20.

The Work-energy theorem and kinetic energy An external force acts on an object. The object is displaced a distance s, in the same direction as the net force: F s W = ( F)s = ( ma)s

Constant forces: use kinematics equations for constant a in 1-d. v 2 = v 2 0 + 2a( x x 0 ) s ( as) = 1 ( 2 v2 2 v ) 0 W = m( as) = 1 2 mv2 1 2 mv 2 0 Kinetic energy KE = 1 2 mv2

The Work-Energy Theorem When a net external force does work on an object, the KE of the object changes according to W net = KE f KE 0 = 1 2 mv 2 f 1 2 mv 2 0 Image reprinted with permission of John Wiley and Sons, Inc.

i>clicker C&J conceptual question 5 A 3.00-kg model airplane has velocity components of 5.00 m/s due east and 8.00 m/s due north. What is the plane s kinetic energy? a) 134 J b) 96 J c) 38 J d) 254 J

C&J 6.20 A 16-kg sled is being pulled along the horizontal snow-covered ground by a horizontal force of 24 N. Starting from rest, the sled attains a speed of 2.0 m/s in 8.0 m. Find the coefficient of kinetic friction between the runners of the sled and the snow.

i>clicker

Conservative forces and potential energy Conservative force: work done by the force when an object moves from point A to point B doesn t depend on the path. Examples of conservative forces: gravity, electric, spring force. Friction is a non-conservative force!

Gravity is a co ervative force. Move block from A to B by: (a) Lift to height 2h then move horizontally x, or (b) carrying the block up the stairs to point B. Calculate the work done by gravity.

Gravitational potential energy (PE) W = ( F cosθ)s W g = mg( h f h ) 0 W g = mgh f ( mgh 0 ) W g = mgh 0 mgh f W g = PE 0 PE f = ΔPE PE = mgh Image reprinted with permission of John Wiley and Sons, Inc.

Gravitational PE is the energy that an object of mass m has due to its position relative to the surface of the earth, measured by the height h of the object relative to an arbitrary zero level: PE = mgh

Also Example: Gymnast on Trampoline in C+J (P. 152-3 10 th edition)

Potential energy Potential energy is stored in the configuration of (Consider the situation when W_g is balanced by W_T.) a system. e.g. Earth and object, not just the object. Only defined for conservative forces e.g. Work done by gravity W c = ΔPE Examples of conservative forces: gravity, springs, electromagnetic forces m m m m mg mg mg mg W = mgh W = mgh W = mg cos 90º = 0 W = mgh + 0 + mgh + 0 = 0

More on conservative and nonconservative forces Conservative force does no work on an object moving around a closed path, starting and ending at the same point. Image reprinted with permission of John Wiley and Sons, Inc. Friction always points in direction opposite to motion. W = F cosθ ( )s = f k cos180 s = f k s Work done by friction is always negative friction is a non-conservative force and no PE defined for it. Another example of a dissipative force is air resistance.

i>clicker C&J conceptual question 12 Air resistance is a nonconservative force. It always opposes the motion of an object. An airplane flies from New York to Atlanta and then returns to its point of departure. The net work done by air resistance during this round trip. a) is zero b) is positive c) is negative d) is negative for slow speeds and positive for high speeds. e) is positive for slow speeds and negative for high speeds.

Work-energy theorem New statement of theorem when both conservative and nonconservative forces are present. W net = ΔKE W c +W nc = ΔKE ΔPE +W nc = ΔKE W nc = ΔKE + ΔPE Work-energy theorem

Two statements of the work-energy theorem 1) Work done by the net force W net = ΔKE 2) Work done by nonconservative forces W nc = ΔKE + ΔPE The change in both the KE and PE is always the final value minus the intial value.

Conservation of mechanical energy Total mechanical energy Work-energy theorem E = KE + PE W nc = ΔPE + ΔKE = ΔE If the work done on an object by nonconservative forces is zero then the total mechanical energy is constant (conserved). E f =E 0

THE PRINCIPLE OF CONSERVATION OF MECHANICAL ENERGY The total mechanical energy (E = KE + PE) of an object remains constant as the object moves, provided that the net work done by external nonconservative forces is zero.

C+J 6.37A gymnast is swinging on a high bar. The distance between his waist and the bar is 1.1 m, as the drawing shows. At the top of the swing his speed is momentarily zero. Ignoring friction and treating the gymnast as if all of his mass is located at his waist, find his speed at the bottom of the swing. (Where is the max and min KE? The max and min PE?)

Work and energy so far W = Fs cosθ W net = ΔKE = 1 2 m ( v 2 2 f v ) 0 W cons = ΔPE PE = mgh Constant force, straight path Work done by net force Work done by conservative force Gravitational potential energy W nc = ΔPE + ΔKE Work done by nonconservative forces

Homework Read All of Chapter 6. Last section is Power. Office Hours: Allen 514 Tuesday 2:30-4:30 pm Midterm: Preparation session with Dr. Basnet Tuesday, October 25, 12:00 2:00 in room 224 Education Building (next page)

Midterm: Please continually check the course website http://www.physics.umanitoba.ca/undergraduate/ phys1020/exams.htm There will be a formula sheet http://www.physics.umanitoba.ca/undergraduate/ phys1020/wa_files/ Phys1020_20formula_20sheet_20midterm_202016.pdf Prohibited calculators are described at http://www.act.org/content/act/en/products-and-services/ the-act/help.html

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