Conservation of Energy. Machines.

1. Conservation of Energy.Machines.

2. Conservation of Energy • Energy: the ability to do work. • The Law of Conservation of Energy: Energy cannot be created or destroyed. It can be transformed from one form to another, but the total amount energy never changes. It transforms without net loss or net gain. • Example: Newton’s Cradle. • KEi + PEi + Wext = KEf + Pef(with external force) • KEi + PEi = KEf + PEf (without external force)

3. Conservation of Energy Example • A roller coaster operates on the principle of energy transformation. Work is initially done on a roller coaster car to lift to its initial summit. Once lifted to the top of the summit, the roller coaster car has a large quantity of potential energy and virtually no kinetic energy (the car is almost at rest). If it can be assumed that no external forces are doing work upon the car as it travels from the initial summit to the end of the track (where finally an external braking system is employed), then the total mechanical energy of the roller coaster car is conserved. As the car descends hills and loops, its potential energy is transformed into kinetic energy as the car speeds up. As the car climbs up hills and loops, its kinetic energy is transformed into potential energy as the car slows down. Yet in the absence of external force doing work, the total mechanical energy of the car is conserved.

4. Conservation of Energy Example

5. Machines • Machine: • A mechanical device used to multiply forces or simply to change the direction of forces. • The simples mechanism that can use mechanical advantage (leverage) to multiply a force. • Machine cannot multiply work or energy. Energy is transferred or changes forms. It cannot be created or destroyed.

6. Simple Machines • Simple Machines: levers, fulcrum, pulley, wheel and axel, incline plane, wedge, and screw. • The lever: System consisting of a bar pivoting on a fulcrum to lift a load. The amount of effort required is related to the position of the pivot and the length of the bar. • At the same time we do work on one end of the lever, the other end does work on the load. If we push down, the load is lifted up. If the heat from friction is small enough to neglect, the work input will be equal work output. Winput = Woutput (F * d)input = (F * d)output

7. Simple Machines Fulcrum is the pivot point of the lever. It can be relatively close to the load. Then a small input force exerted through a large distance will produce a large output force over a correspondingly short distance.

8. Types of Levers • Type 1 lever: it has the fulcrum between the force and the load, or between input and output. The directions of input and output forces are opposite. Example: a playground seesaw. • Type 2 lever: the load is between the fulcrum and the input force. To lift a load, you lift the end of the lever. The forces have the same direction. Example: raising a car with a help of a long steel bar. • Type 3 lever: the fulcrum is at one end and the load is at the other. The input force is applied between them. The input and output forces have the same direction. Example: the biceps muscles, fulcrum is an elbow, and the load is in your hand.

9. Levers

10. Pulley • A pulley: Pulley are wheels and axles with a groove around the outside • A pulley needs a rope, chain or belt around the groove to make it do work • A kind of lever that can be used to change the direction of a force. A pulley can multiply forces. • A pulley working like a type 1 lever: the axis of the pulley acts as a fulcrum, and both lever distances are equal. It changes the direction of the applied force. The input distance equals the output distance the load moves. • A pulley working like a type 2 lever: the load is suspended halfway between the fulcrum and the input end of the lever.

11. Pulley Pullet Type 1 Pulley Type 2

12. Wheel and Axle • The axle is stuck rigidly to a large wheel. Fan blades are attached to the wheel. When the axel turns, the fan blades spin.

13. Gear – Wheel and Axle • Each gear in a series reverses the direction of rotation of the previous gear. The smaller gear will always turn faster than the larger gear.

14. An Inclined Plane • An inclined plane is a flat surface that is higher on one end. • Inclined planes make the work of moving things easier. • The mechanical advantage of an inclined plane is equal to the length of the slope divided by the height of the inclined plane. • While the inclined plane produces a mechanical advantage, it does so by increasing the distance through which the force must move.

15. Screw • The mechanical advantage of an screw can be calculated by dividing the circumference by the pitch of the screw. • Pitch equals 1/ number of turns per inch.

16. Wedges • Wedges: Two inclined planes joined back to back. • A wedge is just an object with a slanted (inclined) surface. If you push a wedge forward against an object, it will push the object to the left or right. In other words, the force exerted by a wedge is always perpendicular to the direction in which the wedge is moving. A door stop is a good example of this principle: When you shove it under a door, it applies an upward force on the bottom of the door. A plow is another common wedge -- when you drive it forward, it pushes dirt or snow to the sides. • Wedges are used to split things.

17. Compound Machines. Mechanical Advantage • Compound Machine: combination of two or more simple machines. • Mechanical Advantage (MA): the ratio of output force to input force for a machine. • MA = , where MA –mechanical advantage, Fo –output force, and Fi- input force. • Mechanical advantage can also be determined by the ratio of input distance to output distance. • MA = , where MA – mechanical advantage, di – distance of input arm, and do – distance of output arm. • Mechanical Advantage for incline plane (ramp): • MA ramp = , where MA ramp – mechanical advantage of the ramp, dr– distance of the ramp, and hr – the height of the ramp.

18. Efficiency • Efficiency can be expressed as the ratio of useful work output to total work output. • Efficiency = • Efficiency can also be expressed as the ratio of actual mechanical advantage to theoretical mechanical advantage. • Efficiency = • Efficiency will always be a fraction less then 1.