Machines and MA Page
Simple machines ► Means a machine that only uses the forces directly applied and accomplishes its work with a simple motion. ► Basic simple machines include gears(wedge) screw, pulleys, wheel and axle, ramp (inclined plane) lever
Simple machines ► Input force is the force that you apply ► Output force is the force that does the action
Mechanical Advantage ► MA of a Lever MA lever = L input L output L stands for length
Mechanical Advantage ► Of pulleys is due to force of tension ► Noted as the amount of ropes ► MA = output force ► input force
Mechanical Advantage ► Input gear is the one you turn or apply forces to ► Output gear is connected to the output of the machine ► Gear ration is the ratio of output turns to input turns ► MA = input torque divided by output torque or the inverse of gear ratio
Mechanical Advantage ► MA = distance along the ramp divided by the height of the ramp ► Friction causes high MA of ramps to not work
Mechanical Advantage ► Screw is a simple machine that turns rotating motion into linear motion ► MA = average circumference of the thread divided by the vertical distance is the head of the screw
Work ► Always done in a parallel direction ► W= fd ► W= Fd cosine of the angle ► W = mgd or mgh ► Input work never equals output work because of friction
Energy ► Energy is the ability to make things change. ► Work is the action of making things change.
Forms of Energy ► Mechanical energy ► Light energy ► Nuclear energy ► Electrical energy ► Chemical energy ► Thermal energy ► Pressure energy
Potential energy ► Means that something is capable of becoming active. ► Calculate Potential energy or E p ► E p = mgh ► Rate of work = mgh divided by time (s)
Kinetic energy ► Energy of motion ► Kinetic energy equals E k ► E k = ½ mv 2
Deriving the formula for Ek ► Step 1 Work is force times distance, but force is mass times acceleration. The work done on an object is therefore its mass X acceleration X distance. ► W =Fd =(ma) X d = mad
Deriving the formula for Ek ► 2. The kinetic energy formula involves only mass and speed. In chapter 4 you found a relationship between distance traveled acceleration, and time. ►. D = 1/2at 2
Deriving the formula for Ek ► 3. Replacing distance in the equation for work and combining similar terms creates: ► W = ma(1/2at 2 ) = 1/2ma 2 r 2
Deriving the formula for Ek ► 4. When an object starts from at rest with constant acceleration, its speed is equal to its acceleration multiplied by the time it has been accelerating. Mathematically, v =at, therefore v 2 =a 2 r 2. This is the result that is needed. Replace the a 2 r 2 with v 2 and the resulting work is exactly the formula for kinetic energy.
Deriving the formula for Ek ► v = at v 2 = a 2 r 2 ► W = ½ma 2 r 2 W = ½mv 2
Law of conservation of energy ► Energy can never be created or destroyed only changed from one form to another