Energy, Work, and Machines

What is work?  Put a book over your head, are you working?  Hold a pencil out straight from your body, are you working?  From a physics standpoint, no. Work is the product of the force and the objects distance, W = Fd  Force x Time changes momentum  Force x Distance changes energy

What are we doing then?  Energy is being expended, a force is being exerted but, without any net displacement, no work is done, no energy is changed.  What about a planet orbiting the sun? Is work being performed?  Remember, a force perpendicular to an object does not change its speed, only its direction.

What if?  What if you push against a wall?  What if you push a flat cart along the ground at a constant speed?  What if you say forget it, jump out of a plane and are in free fall?  Ultimately, work can be defined as a change in kinetic energy where  KE = ½ mv 2

Kinetic Energy  From the equation we can see that an increase in mass or speed results in an increase in kinetic energy, similar to momentum.  Notice that velocity is squared, therefore a small increase in speed results in a large increase in kinetic energy.

So?  The definition of energy is the ability to cause change, in relation to an object either in itself or its surroundings. Kinetic energy is the energy of motion, potential energy at rest. Energy is measured in quanta, we’ll get to that later.  The work energy theorem states that work is a change in kinetic energy or W = KE  This states that work is accomplished when there is a net change in kinetic energy  Work is accomplished with any change in energy, W = E

James Prescott Joule  English Dude, 1800’s, discovered relationship between work and the change in energy.  Joule, also known as a Newton - Meter is equal to a force of 1 Newton acting over a distance of 1 meter. It is a unit of energy  Lifting an apple a distance of 1 meter is approximately 1 Joule

What if?  What if I am pushing a car at an angle of 25 degrees from the horizontal.  Remember a force acting in the direction of motion does work. A force acting perpendicular to the direction of motion does no work.  In this case work is a function of the angle.

Still What if  W = Fdcos0  The sine of the angle is the y component and vertical or perpendicular forces do no work  Gravity and normal forces do not contribute to work. The cosine of 90 is 0  Friction opposes motion and 180 degrees would be opposite of motion, the cosine of 180 is -1

More work  It should be noted that the area under a graph of force versus displacement curve illustrates work.

What about time?  You lift 100lbs over your head but take 60 seconds to get it there. Your buddy lifts the same weight the same distance in 1 second. Work performed is the same. However your buddy is obviously stronger or he has more power.  Power is work done divided by the time it takes to do it of P = w/t

Power  Power is measured in watts, 1 joule of energy in 1 second. Watts are typically measured in kilowatts  Energy and power are not the same thing the smallest device can use a tremendous amount of energy given enough time. Power is how fast a device can use or transfer energy

More Power!!!!!  If power is equal to work divided by time then it can also be said that:  P = Fd/t of P = Fv since v equals d/t  Machines incorporate these variables to maximize power. You need the proper amount of force and speed

Machines  A machine is any device that changes either the direction or magnitude of the applied force or both.  If the machine increases the magnitude of the applied force it gives us a mechanical advantage, the resistance force divided by the effort force.  MA = F r /F e

Mechanical Advantage  If the MA is greater than 1, the machine provides a mechanical advantage or increase in the applied force.  Machines can increase force but it cannot increase energy. All machines lose energy through heat, friction, etc.  An ideal machine transfers all the energy

Ideal Mechanical Advantage  While MA can be written as resistance force over effort force it can also be written as output work Wo / input work Wi or  F r D r / F e D e  Ideal mechanical advantage is calculated  IMA = d e /d r  Notice, MA is Fr/Fe and IMA is de/dr

Machines  Machines are never ideal, this is a measure of the maximum possible amount of work.  Efficiency of machines can be measured in two ways:  Efficiency = Wo/Wi x 100 or  Efficiency = MA/IMA x 100

More Machines  A simple machine is one that does work with only one movement.  There are six basic types: Lever, inclined plan, wedge, screw, pulley, and wheel & axle.  Lever, increases applied force Le/Lr and changes direction  3 types 1 st class fulcrum in the middle  2 nd class, fulcrum resistance and effort  3 rd class, fulcrum effort and resistance  The human body is composed of several levers.

Simple machines  Pulleys, single pulley changes direction, a movable pulley or multiple pulleys decrease the effort force, increasing the applied force.  Wheel and axle, similar to a lever attached to a shaft, increases your applied force  IMA = Rw/Ra

More simple machines  Inclined plane, allows you to cover more distance with less force.  IMA = length of slope/height of slope  Screw, is an inclined plane wrapped around a post  Wedge, is an inclined plane with two or more sloping sides, change the direction of the force

Machines, Machines, Machines  A compound machine is a combination of any two or more simple machines  Most “machines” are compound  The MA for a compound machine is the combination of MA’s for each simple machine MA = MA1 + MA2