Chapter 5 Work and Energy September 11 Work 5.1 Work Done by a Constant Force

1. Chapter 5 Work and Energy September 11 Work 5.1 Work Done by a Constant Force Work: The work done by a constant force acting on an object is equal to the product of the magnitudes of the displacement and the component of the force parallel to that displacement. A constant force F acting in the same directionas the displacement d does work If the force acts at an angle q to the displacement of the object, then the component of the force parallel to the displacement is . A more general equation for work done by a constant force is

2. More about work: If there is no displacement, no work is done. If the force is perpendicular to the displacement, no work is done. The sign of work: Work done can be positive (when ) or negative (when ). Work is a scalar. The SI unit of work is newton·meter (N ·m), 1 N · m =1 joule (J). Example 5.1: Applied Psychology: Mechanical Work Total work: The total work, or the net work, is defined as the work done by all the forces acting on an object, which is the sum of the work done by each force. Example 5.3: Total or Net Work

3. 5.2 Work Done by a Variable Force Spring force (restoring force): When stretched or compressed, the spring exerts a force that opposes the deformation of the spring. Hooke’s law: The spring force (Fs) is proportional to the change in length of the spring from its unstretchedposition. Here k is the spring constant, with the unit N/m, measuring the stiffness of the spring. Work done on a spring: Work done in stretching or compressing a spring can be evaluated from the F-vs-x graph, which is

4. Example5.4: Determining the Spring Constant

5. Read: Ch5: 1-2 Homework: Ch5: E2,3,17,25 Due: September 20

6. September 13 Kinetic energy and potential energy 5.3 The Work–Energy Theorem: Kinetic Energy Energy: Energy is possessed by an object, which measures the capacity of the object to do work. Energy is one of the most important concepts in science. Work done by a constant force parallel to the direction of motion of an object: Kinetic energy is the energy contained in the motion of an object, which is defined as: It has a unit of J. It is a scalar.

7. The work–energy theorem: The net work done on an object by all the forces acting on it is equal to the change in the kinetic energy of the object. • Relations between work and energy: • Energy is the capacity to do work. • Work is the mechanical means of transferring energy. • Example 5.5: A Game of Shuffleboard: The Work–Energy TheoremExample 5.6: Kinetic Energy: Mass versus Speed

8. Potential energy is the energy stored in a certain structure of a system. This energy may be released when the structure of the system changes. • Examples of potential energies: A lifted rock, a compressed spring, a firework, a pancake • More on potential energies: • Potential energy is associated with the position of each object within a system. It is a property of the system, rather than a particular object. • Potential energy may be thought of as stored work: • Change in potential energy of a system = work done by external force to change the position or structure of the system (without increasing its kinetic energy) • There are many kinds of potential energy, and each need to be treated separately, which makes the world wonderful. Gravitational potential energy: Work done in lifting an object Gravitational potential energy Potential energy of a spring (elastic potential energy): Work done in stretching a spring: Potential energy of a spring

9. Reference point and change in potential energy: Potential energy is an energy of position. The potential energy at a particular position (U) is meaningful only when referred to the potential energy at some other position (U0). the difference in potential energy associated with two positions is the same regardless of the zero reference point (where U = 0). The zero reference point may be chosen for our convenience. Example5.9: A Thrown Ball: Kinetic Energy and Gravitational Potential Energy

10. Read: Ch5: 3-4 Homework: Ch5: E30,31,37,41 Due: September 20

11. September 16,17 Conservation of energy 5.5 Conservation of Energy A physical quantity is conservedif it does not change in time. Anisolated system is a system where the particles have no interaction with anything outside of the system. Law of conservation of total energy: The total energy of an isolated system is always conserved. • Conservative and nonconserevative forces: • Conservative force: A force is said to be conservative if the work done by it in moving an object is independent of the path of the object. Example: gravitational force, spring force. • The work done by a conservative force depends only on the initial and final positions of an object. • The concept of potential energy is associated only with conservative forces. A change in potential energy is defined in terms of the work done by a conservative force. • Equivalently a force is conservative if the work done by it in moving an object through a round trip is zero. • Nonconservative force: A force is said to be nonconservative if the work done by it in moving an object depends on the path of the object. Example: frictional force.

12. Total mechanical energy is the sum of the kinetic and potential energies of all the objects in a system. Total mechanical energy = Kinetic energy + Potential energy Conservative system is a system in which only conservative forces do work. Law of the conservation of mechanical energy: In a conservative system, the sum of all types of kinetic energy and potential energy is constant and equals the total mechanical energy of the system at any time. Example5.11: Look Out Below! Conservation of Mechanical Energy Example5.12: A Matter of Direction? Speed and Conservation of Energy Example5.13: Conservative Forces: Mechanical Energy of a Spring

13. Work done by the nonconservative forces: From the work–energy theorem and the definition of potential energy, The work done by the nonconservative forces acting on a system is equal to the change in mechanical energy of the system. Example5.14: Nonconservative Force: Downhill Racer

14. Read: Ch5: 5 Homework: Ch5: E45,49,56 Due: September 27

15. September 18 Power 5.6 Power Power is time rate of doing work. The average power is the work done divided by the time it takes to do the work: The SI unit of power is 1 J/s = 1 watt, or W. A conventional unit of power is the horsepower, 1 horsepower (hp) = 746 W. The power done by a constant force F on an object moving a parallel displacement d is If the force and displacement are not in the same direction, then Example5.16: A Crane Hoist: Work and Power Example5.17: Cleaning Up: Work and Time

16. Mechanical efficiency is a measure of the useful work output compared with the energy input. It is given as a percentage, It can also be written in terms of power, Efficiency has no unit. The efficiency of any real system is always less than 100%. Example5.18: Home Improvement: Mechanical Efficiency and Work Output

17. Read: Ch5: 6 Homework: Ch5: E64,69 Due: September 27