Total Mechanical Energy

state that something is conserved remain constant under certain conditions examples: TME, mass, electric charge, energy Conservation Laws

Air resistance A falling object exerts force on the air; the air exerts a force back on the falling object. This is true of all objects moving through air. TME is not conserved:

Air resistance Air resistance increases with increased velocity. For a falling object, eventually air resistance balances the force of gravity. TME is not conserved:

Air resistance When air resistance and gravity, the only two forces on a falling object, are balanced, a = 0; the velocity no longer increases. TME is not conserved:

Air resistance This is called terminal velocity. Kinetic energy remains constant, but potential energy decreases. What happens to it? TME is not conserved:

Air resistance The potential energy becomes thermal energy, raising the temperature of the falling object and the air around it. TME is not conserved:

Air resistance Thermal energy is not mechanical energy. TME is not conserved:

Friction Friction changes mechanical energy to thermal energy, acoustic energy, or other forms. Brakes are a good example of this. TME is not conserved:

Friction Lubrication reduces friction and the change of mechanical energy to thermal and acoustic energy. TME is not conserved:

Friction Springs have internal frictional forces. Ideal springs, by definition, have no significant internal friction. TME is not conserved:

TME is conserved when only conservative forces are at work. All conservative forces are central forces. Example: gravity TME is conserved:

Path-independence: Work done against gravity is the same regardless of the path taken. TME is conserved:

p. 221 example: W = F g Δh This formula holds regardless of the starting and ending points. Path-independence is validated. TME is conserved:

Example 10-1: Since TME is conserved, both kinetic and potential energy are equal at points B and D. TME is conserved:

the minimum speed that an object of mass m requires to leave a larger object of mass M so that mass m cannot return due to gravitational attraction alone Escape Speed

to calculate: Escape Speed v R =2G r M assumes the speed of the object at an extreme distance is zero

Simple Machines

A machine is a device that changes the magnitude or direction (or both) of an applied force. Machines can be simple or complex. Machines

definition of ideal mechanical advantage (IMA): Mechanical Advantage...in the absence of friction IMA = F out F in

other results of IMA: Mechanical Advantage...in the absence of friction W in = W out F out F in d in d out = IMA

actual mechanical advantage (AMA): Mechanical Advantage...as actually measured in real life AMA = F out F in

ramps wedges screws Inclined Planes

defined: a metal shaft surrounded by a helically coiled wedge The pitch of a screw is the distance between two successive threads. Screws

defined: a rigid bar that turns around a pivot (fulcrum) effort force (F e ) is applied to effort arm (l e ) Levers

output force (F r ) is applied to resistance arm (l r ) output force is sometimes called the resistance force or load Levers

Law of Moments states then when the torques are equal, the lever will be stationary, and: Levers F e l e = F r l r

mechanical advantage: Levers AMA = FrFr FeFe IMA = lele lrlr

First-class: the fulcrum is between the resistance and effort forces Kinds of Levers

IMA may be more or less than 1. Kinds of Levers

Second-class: the resistance is between the fulcrum and effort force IMA > 1 Kinds of Levers

Third-class: the effort force is between the fulcrum and the resistance IMA < 1 Kinds of Levers

Levers are generally limited in movement. Wheels are modified levers, with the fulcrum at the center. Wheels can function as 2 nd or 3 rd -class levers. Wheels and Pulleys

A pulley is a grooved wheel that turns on an axle. For a single fixed pulley: Wheels and Pulleys d in = d out IMA = d in d out = 1

For a movable pulley: Wheels and Pulleys IMA = FrFr FeFe = 2 A movable pulley doubles the effort force.

block and tackle system has both fixed and moveable pulleys IMA of a block and tackle system is equal to the number of ropes supporting the load. Wheels and Pulleys

In the real world, the work put out by any machine is always less than the work put into it. Efficiency is a way to measure how much input work became output work. Mechanical Efficiency

Efficiency is notated by the Greek letter eta (η). Mechanical Efficiency η = IMA AMA × 100% Stationary pulley systems are nearly 100% efficient.