Phys141 Principles of Physical Science Chapter 4 Work and Energy

1. Phys141 Principles of Physical ScienceChapter 4 Work and Energy Instructor: Li Ma Office: NBC 126 Phone: (713) 313-7028 Email: malx@tsu.edu Webpage: http://itscience.tsu.edu/ma Department of Computer Science & Physics Texas Southern University, Houston Sept. 20, 2004

2. Topics To Be Discussed • Work • Kinetic Energy and Potential Energy • Conservation of Energy • Power

3. About Work & Energy • Common meaning of Work • Work is done to accomplish some task or job • When work is done, energy is expended • Mechanically, Work involves force & motion • Energy is a concept, is abstract, is stored work

4. Work • The work done by a constant force F acting on an object is the product of the magnitude of the force (or component of force) and the parallel distance d through which the object moves while the force is applied W = F·d

5. Work (cont) • If only apply force but no motion, then there is technically no work • Only the component of force in the direction of motion has contribution to work • Example: Fh W = Fh·d F Fv d

6. Work (cont) • Unit of Work • In Metric system: N·m, or joule (J) • In British system: pound·foot (ft·lb) • Newton’s third law force pair • When the force is applied, work is done against this force pair • Moving box forward: do work against friction • Lifting the box: do work against gravity

7. Energy • Common sense: • when work is done, some physical quantity changes: work against gravity, height is changed; work against friction, heat is produced; etc. • With concept of energy: • When work is done, there is a change in energy, and the amount of work done is equal to the change in energy

8. Energy (cont) • Energy is described as a property possessed by an object or system • Energy is ability to do work: • An object or system that possess energy has the ability or capability to do work • Unit of Energy • Same as work

9. Work and Energy • Doing work is the process by which energy is transferred from one object to another: • When work is done by a system, the amount of energy of the system decreases • When work is done on a system, the system gains energy • Both work and energy are scalar quantities

10. Work and Energy (cont) • One scenario: when work is done on an object (at rest initially), the object’s velocity changes d = ½a·t2, v = a·t, F = m·a, W = F·d W = m·a·d = m·a·(½a·t2) = ½ m·(a·t)2 = ½ m·v2 So W = ½ mv2 • This amount of work is now energy of motion, or kinetic energy

11. Work and Energy (cont) • Another scenario: when work is done on an object, the object’s position changes • There is also a change in energy, since the object has potential ability to leave that position and do work • This amount of work is energy of position, or potential energy • Kinetic & Potential energy: two forms of Mechanical energy

12. Kinetic Energy • Kinetic energy is the energy an object possesses because of its motion, or simply stated, it is energy of motion: kinetic energy = ½ x mass x (velocity)2 Ek = ½ mv2

13. Kinetic Energy (cont) • If the work done goes into changing the kinetic energy, then work = change in kinetic energy W = ΔEk = Ek2 – Ek1 So W = ½ mv22 - ½ mv21

14. Potential Energy • An object does not have to be in motion to have energy • Potential energy is the energy an object has because of its position or location, or simply, it is energy of position • Examples: lifted weight, compressed or stretched spring, drawn bowstring

15. Potential Energy (cont) • One scenario: Lift an object at a (slow) constant velocity up to a height h from the ground (or saying sea level) • Work is done against gravity Work = weight x height W = m·g·h (W = F·d)

16. Gravitational Potential Energy • The object has potential ability to do work, it has energy • Gravitational potential energy is equal to the work done against gravity gravitational potential energy = weight x height Ep = m·g·h More generally, Ep = m·g·Δh

17. Conservation of Energy • Understanding of conservation • Energy can be neither created nor destroyed • Energy can change from one form to another, but the amount remains constant • Energy is always conserved • The total energy of an isolated system remains constant

18. Conservation of Mechanical Energy • Ideal systems • Energy is only in two forms: kinetic and potential • Conservation of mechanical energy • The mechanical energy of the ideal system remains constant Initial Energy = Final Energy (Ek + Ep)1 = (Ek + Ep)2 (½ mv2 + mgh)1 = (½ mv2 + mgh)2

19. Conservation of Mechanical Energy (cont) • Want the velocity of a freely falling object when fallen a height of Δh: • velocity and acceleration: Vt = gt, Δh = ½ gt2 (Δh = d) => Vt = (2gΔh) ½ • Conservation of mechanical energy: (½ mv2 + mgh)i = (½ mv2 + mgh)t ½ m(v2t - v2i )= mg(hi - ht) => Vt = (2gΔh) ½

20. Power • Do same thing in different amount of time: the rate at which the work is done is different • Power is the time rate of doing work power = work / time P = W/t = F·d/t • Unit: watt in the SI, 1 W = 1 J/s

21. Power (cont) • The greater the power of an engine or motor, the faster it can do work • Power may be thought of as energy produced or consumed divided by the time taken P = E/t => E = p·t