lecture 6 Energy and its conservation

1. lecture 6Energy and its conservation Peter J. Nolan, Fundamentals of college physics, Wm. C. Brown Publishers, 1993

2. Energy Energy can be defined as the ability of a body or system of bodies to perform work. A system is an aggregate of two or more particles that is treated as an individual unit

3. Forms of Energy • Mechanical energy • Heat energy • Electrical energy, • Chemical energy • Atomic energy

4. Work The work W done in displacing the body a distance x along the table is defined as the product of the force acting on the body, in the direction of the displacement, times the displacement x of the body If the force acting on the body is not parallel to the displacement, then the work done is the product of the force in the direction of displacement, times the displacement

5. Work In SI units One joule of work is done when a force of one newton acts on a body, moving it through a distance of one meter James Prescott Joule (1818-1889), a British physicist In BES units One foot-pound is the work done when a force of one pound acts on a body, moving it through a distance of one foot

6. A constant force F can do positive, negative, or zero work depending on the angle between F and the displacement

7. A farmer hitches her tractor to a sled loaded with firewood and pulls it a distance of 20 m along level ground (Fig. a). The total weight of sled and load is 14,700 N. The tractor exerts a constant 5OO0-N force at an angle of 36.9° above the horizontal, as shown in Fig. b. There is a 35OO-N friction force opposing the sled's motion. Find the work done by each force acting on the sled and the total work done by all the forces.

8. That leaves the force FT exerted by the tractor and the friction force f. From Eq. the work WT done by the tractor is W T = F T s cosφ = 5000 * 20 * 0.8 = 80 kj The friction force 1 is opposite to the displacement, so for this force φ = l800 and cosφ = -1. The work Wf done by the friction force is Wf = fs cosφ = 3500 20 (-1) = - 70 kJ W = W T + Wf = 80 + (-70) = 10 kJ We know that the y- component of force is perpendicular to the displacement, so it does no work.

9. Example. Work done keeping a satellite in orbit In general, whenever the applied force is perpendicular to the displacement, no work is done by that applied force

10. Power Power is defined as the time rate of doing work. In SI units James Watt(1736-1819), a Scottish engineer In BES units 1 watt of power is expended when one joule of work is done each second

12. Gravitational potential energy Gravitational potential energy is defined as the energy that a body possesses by virtue of its position Because work must be done on a body to put the body into the position where it has potential energy, the work done is used as the measure of this potential energy. The potential energy of a body is equal to the work done to put the body into the particular position Potential energy (PE) = Work done to put body into position

13. Kinetic energy The kinetic energy is defined as the energy that a body possesses by virtue of its motion The kinetic energy of a moving body is equal to the amount of work that must be done to bring a body from rest into state of motion. Conversely, the amount of work that you must do in order to bring a moving body to rest is equal to the negative of the kinetic energy of the body Kinetic energy (KE) = Work done to put body into motion = - Work done to bring body to a stop

14. The conservation of energy In any closed system, that is, isolated system, the total energy of the system remains a constant. This is the law of conservation of energy

15. The conservation of energy There is no change in the total energy of the ball throughout its entire flight. Or similarly, the total energy of the ball remains the same throughout its entire flight, that is, it is a constant

16. The conservation of energy The amount of kinetic energy of the ball lost between levels 1 and 2 will be equal to the gain in potential energy of the ball between the same two levels. Thus, energy can be transformed between kinetic energy and potential energy but, the total energy will always remain a constant

17. The conservation of energy Pendulum

18. A thin rod whose length is L and whose mass is negligible is pivoted at one end so that it can rotate in a vertical circle. The rod is pulled aside through an angle θ and released, as shown in Fig. How fast is the lead ball at the end of the rod moving at its lowest point?

19. A ball of mass m is attached to the end of a very light rod of length L. The other end of the rod is pivoted so that the ball can move in a vertical circle. The rod is pulled aside to the horizontal and given a downward push as shown in Fig. so that the road swings down and just reaches the vertically upward position. What initial speed was imparted to the ball?

20. Further analysis of the conservation of energy at the bottom of the plane

21. Further analysis of the conservation of energy

22. " If it's not simple, It's wrong." Albert Enishtein.

23. Further analysis of the conservation of energy Systems for which the energy is the same regardless of the path taken to get to that position are called conservative systems. Conservative systems are systems for which the energy is conserved, that is, the energy remains constant throughout the motion

24. Further analysis of the conservation of energy The work done in sliding the block up the plane is total energy at the bottom

25. Example: The great pyramids

26. Example: The great pyramids The inclined plane is called a simple machine

27. Example: The great pyramids Ideal mechanical advantage (IMA)