Work Power Energy & Momentum

1. WorkPowerEnergy& Momentum

2. Work • What do you think of when you hear the word “work”? • WORK happens when a FORCE moves an object through a DISTANCE. • W = F * d • Work is measured in Newton meters (Nm) or Joules (J) • Work is a scalar quantity

3. Work - continued Force Distance • F and d have to be parallel to each other – if a force is perpendicular to a distance then that force is not the cause of the work done

4. Work - continued • Forces exterted at an angle: • Only the vector component parallel to the distance moved does the work • Since work is (F)(d) and one force we deal with is Fg (force of gravity) and Fg = mg then W could = (mg)d F W = F cosΘ d Fx

5. Work problem 4 m To get the 500 N block to the top takes the same amount of WORK whether you lift straight up or push it up the ramp. 500 N 8 m The FORCE to lift anything is its WEIGHT Fg = mg W = Force x distance Lifting Work = (500 N) (4m) = 2000 Nm or 2000J Slide up ramp work = F x d (up the ramp) 2000 J = F (8m) F = 250 N I doubled the distance so the force is halved

6. Simple machines • An inclined plane is a simple machine. • Simple machines allow us to do the same amount of work with less force (effort) • Simple machines include: • Inclined planes • Levers • Screws • Wedge • Pulley • Wheel & axle

7. Power • Power = rate that work is done • P = work/time (J/s)= Watt (W) • A 100 Watt light bulb puts out 100 J of NRG per sec • 1 horsepower = 746 Watts • 1kW = 1000 W • P = work/time = (Fd)/t or Fv • Force might be Fg which = mg so P = (mgd)/t

8. Energy • Energy is the ability to do work • Forms of energy: • Solar, electrical, mechanical, thermal, chemical, nuclear, hydroelectric, light, sound, wind, potential, kinetic, electromagnetic, etc. • Chemistry – focused on thermal, chemical and nuclear energy • Physics – 1st semester focuses on mechanical, kinetic, and potential energy – 2nd semester will focus on electrical, magnetic, thermal, sound, and light energy

9. Types of energy • Mechanical Energy: • Energy which is possessed by an object due to its motion or its stored energy • ME = KE + PE • As a car rolls down a hill it loses PE and gains KE • Kinetic Energy: • Energy of a moving object • KE = ½ mv2 • KE and mass are directly related • if mass is doubled, KE doubles • KE and v2 are exponentially related • If v2 doubles, KE quadruples • If v2 triples, KE x 9

10. Types of Energy - continued • Potential Energy • energy of position, shape, or form • Position example: an object at the top of a hill or cliff or table that has the potential to fall from a height • Shape example: a spring has (stored) potential energy to snap back into shape • Form example: a rubber band, a snap bracelet, a bow to shoot an arrow

11. Types of Energy - continued • Gravitational Potential Energy (GPE) • potential (stored) energy due to a location relative to a reference level. • Assume reference is found or floor unless otherwise stated. • GPE = Mass x acceleration due to gravity x height above or below reference • GPE = mgh

12. Types of Energy - continued • Elastic Potential Energy (EPE) • Potential energy of an elastic object that is stretched or compressed • The spring or rubber band or bow string has to be able to go back to its original shape and size • EPE = ½ x spring constant (stiffness) x distance stretched (ls - lr)2 • EPE = ½ kd2 (NM or J)

13. Conservation of Energy • Law of Conservation of Energy – energy cannot be created nor destroyed, only changed in form • In other words, numerically, total energy will remain constant. • Mechanical energy = sum of kinetic and potential energies • ME = KE + GPE + EPE • Conservation of energy • Etop (GPE = 75 J, KE =0) = Ebottom(GPE =0, KE = 75 J) • GPEt + KEt = GPEb + KEb

14. Conservation of Energy • Pendulum GPE max KE = 0 GPE max KE = 0 Loses GPE Gains KE HalfwayGPE = KE

15. Conservation of energy • Roller Coaster – starts high so we have lots of PE GPE = mgh GPE = 50J KE = 50J V=0 KE=0 GPEmax = 100J Gaining KE V increasing Losing GPE because h is lower If GPE = 60J Then KE = 40J GPE = 0J KE = 100J

16. Work-Energy Theorem • If you do WORK on an object, you change its (kinetic and potential) energy. • Work = Δ E • If I lift books from the desk • Do I do work? • Was there a force applied in the direction of an object’s movement? • Did I change the GPE (gravitational potential energy) of the book? The KE (kinetic energy)?

17. Work-Energy Theorem Formulas • If work = change in KE • Fd = KEf – KEi • Fd = ½ mv2f – ½ mv2i • If work = change in GPE • Fd = mghf – mghi • Fd = mgΔh • If work = change in EPE • Fd = ½ kd2f– ½ kd2i

18. Momentum and Impulse • MOMENTUM is the product of the mass of an object times its velocity • p = mv • Momentum is a vector quantity – its direction is the same as its velocity • The IMPULSE given to an object is the product of the time and the average of force which acts upon an object. • I = Ft = Δp = Δmv • m1v1 + m2v2 = m1v1’ + m2v2’

19. Newton’s 2nd Law & impulse • In the simple case of constant acceleration from rest and a constant time (tf – ti) • a = F/m • v = a(tf – ti ) = [F (tf – ti)]/m • p = mv = F (tf – ti) • An impulse produces a change in momentum that is equal to the impulse in magnitude and in direction • The standard (SI) unit of momentum is 1 kg·m/s

20. Conservation of momentum • The total momentum (vector sum) of a system of massive objects changes only if an outside force acts on the system • Internal forces between the objects can redistribute the total momentum but cannot change the total • Total momentum is represented with a capital P • Calculation of total momentum: • P = p1 + p2 + … + pN • Pf – Pi = Fext(tf – ti)

21. Collisions • Before, during, and after a collision between two or more massive objects that move free from friction or other external forces, the sum of their momenta is constant. • 2- and 3-dimentional collisions can be analyzed in the same way as 1-dimentional collisions.