Simple machines
IMA ideal mechanical advantage
theory-based calculation, friction does not apply, ratio of distance traveled by effort and resistance force. Used in efficiency and safety factor design. IMA=De/Dr (De= distance traveled by effort force Dr= distance traveled by resistance force
Rotational equilibrium
when the sum of all moments on a lever equals 0; the state in which the sum of all the clockwise movement equals the sum of all the counterclockwise moments about a pivot point. To find rotational equilibrium, set the counterclockwise motions equal to the clockwise motions. (Effort moment=resistance moment)
HOW TO REMEMBER THE CLASS OF A LEVER:
you can determine the class of a lever by looking at the middle of the length. Here is what's in the middle of each lever class: First class- fulcrum Second class- resistance Third class- Effort
MA can never be less than or equal to:
zero
Moment
The turning effect of a force about a point equal to the magnitude of the force times the perpendicular distance from the point to the line of action from the force. Basically, the moment (of a lever) is the distance of the effort force to the fulcrum (or resistance force to the fulcrum) times the force (M=de x F) or (dr x F).
Example of effort arm length applied to a screwAMA:
If using a wrench, the effort arm distance would be the length of the wrench.
Efficiency
In a machine, the ratio of useful energy output to the total energy input, or the percentage of the work input that is converted to work output. Percent of efficiency=(AMA/IMA)100. Plugged in: (2.00/2.44)100= 82.0% No machine is 100 percent efficient
Pulley
a lever consisting of a wheel with a groove in its rim that is used to change the direction and magnitude of a force exerted by a rope or cable.
AMA actual mechanical advantage
experimental based, friction losses are considered, for efficiency calculations, ratio of force magnitudes AMA IS LESS THAN OR EQUAL TO IMA Fr/Fe=ama (f=force)
Pitch of a screw:
the distance between threads and linear distance traveled by one rotation of the screw Example: 1/4" 13 UNC If 13 threads, the pitch is 1/13 of an inch (the middle number in the description)
The MA (not AMA) of any lever is:
the distance from the fulcrum to the effort divided by the distance from the fulcrum to the resistance. (de/dr)
How to find Lever AMA
(AMA=Fr/Fe): this is the ratio of applied resistance force to applied effort force. EXAMPLE: resistance force=32 pounds, effort force=16 pounds, resistance to fulcrum=2.25in, effort to. fulcrum=5.5in. AMA=32/16=2:1 ratio. To convert the AMA into IMA, you must divide the length of the effort to the fulcrum by the length between the resistance to the fulcrum. IMA=5.5/2.25=2.44:1 ratio. IMA is larger than AMA because IMA does not include friction and other forces. This makes sense because if you have more friction, it would be harder to move something thus requiring more effort.
Work
(Fd) The force applied on an object times distance the object travels parallel to the force; The product of the effort times the distance traveled will be the same regardless of the system mechanical advantage (Work=Force x distance)
How to find Lever IMA
(IMA=De/Dr): both effort and resistance forces will travel in a circle if unopposed. Circumference=2pr (2 times pi times the radius). or in simple terms: The distance from the fulcrum to the effort divided by the distance from the resistance to the fulcrum. (De/Dr)
IMA of a screw is:
(circumference of effort arm travel)/distance INTO the surface it penetrates IMA= circumference/pitch
Static equilibrium
A condition where there are no net external forces acting upon a particle or rigid body and the body remains at rest or continues at a constant velocity.
Inclined plane
A flat surface set at an angle or incline with no moving parts Able to lift objects by pushing or pulling the load IMA=length/height or Length of ramp/vertical length AMA=Weight of object being pushed (resistance)/effort force (force applied to object).
Lever
A rigid bar used to exert a pressure or sustain a weight at one point of its length by the application of a force at a second point and turning on a fulcrum at a third.
Wheel and axle
A wheel and a lever arm fixed to a shaft, called an axle. The wheel and axle move together as a simple lever to lift or move an item by rolling. It is important to know which is applying the effort and resistance force - wheel or axle. Both effort and resistance forces will travel in a circle if unopposed. De= pi x [diameter of effort (wheel or axle)] Dr= pi x [diameter of resistance (wheel or axle)] AMA=Resistance force/Effort force IMA=effort diameter/resistance diameter EXAMPLE: axle diameter=6in, Wheel diameter=20in. What is the IMA of the wheel if the axle is driving the wheel (effort from axle)? 6/20= .3= .3:1= 3:10 ratio What is the IMA of the wheel if the wheel is driving the axle (effort from wheel)? 20/6= 3.33= 3.33:1 ratio
Screw
An inclined plane wrapped around a cylinder, forming the path and pitch •A wheel and axle used to create rotary motion Properties •Change rotary motion into linear motion •Used as a threaded fastener •Large MA •Large amount of friction loss The more threads, the less effort needed A screw is just a circular inclined plane.
If a single rope is threaded multiple times through a system of pulleys:
IMA= number of strands opposing the force of the load.
MA can be:
IMA and AMA.
Simple machines
Mechanisms that manipulate magnitude of force and distance.
The 6 simple machines are...
Pulley, wheel and axel, wedges, levers, and screws,and inclined planes
Compound Machines
Simple machines working in combination to complete a task If one simple machine is used after another, the mechanical advantages multiply.
Torque
a force that produces of tends to produce rotation or torsion (nearly the same as a moment).
Wedge
Wedge: •Functions as a moving inclined plane •Tapers to a thin edge and is used for splitting, raising heavy bodies, or for tightening by being driven into something It can be used to separate two objects or portions of an object, lift up an object, or hold an object in place.
Block and tackle
a combination of fixed and movable pulleys to provide MA and a change of direction for effort force.
To find the distance traveled by a number of revolutions for a wheel given a circumference:
diameter x pi x number of revolutions= distance traveled
To calculate the mechanical advantage of a wedge:
divide the length (height) of the wedge by the width of the wedge. Therefore, the longer the wedge is the less force you need to input. AMA=resistance force/effort force Ima= depth of penetration (AKA height of wedge) /width (the opposite side of the penetration point.
First class lever
fulcrum located in the middle (EFFORT, FULCRUM, RESISTANCE). Between the effort and the resistance forces. Effort and resistance forces are applied to the lever arm in the same direction. This is the only lever class that can have an MA greater than or less than 1. MA=1 when the fulcrum is directly in the middle of the effort and resistance. MA<1 when the distance between the resistance and the fulcrum is longer than the distance between the effort and the fulcrum. MA>1 when the distance between the fulcrum and the resistance is shorter than the distance between the effort and the fulcrum. EXAMPLE OF A FIRST-CLASS LEVER: A hammer pulling a nail from a board.
Fixed pulley:
functions as a first-class lever with an IMA of 1; changes the direction of force (pull down, goes up).
Movable pulley:
functions as a second-class lever with an IMA of 2; force directions stay constant (pull up, goes up).
Static equilibrium equation
height x resistance force= length of ramp (hypotenuse) x effort force
To find the max weight able to be pulled by a pulley:
multiply the number of strands by the effort force.
To find how much cable is pulled:
multiply the number of strands by the height of the building (or length from the resistance to the start of the pulley system).
AMA of a screw:
resistance (going in)/effort (from screw) (1200pounds/35pounds) = 34.29:1 ratio
When asked to find out the number of pulleys and you get a decimal:
round up if the answer is not perfect! (8.33 is 9 strands)
Second class lever
the fulcrum is located at one end of the lever (FULCRUM, RESISTANCE, EFFORT). Resistance is located between the fulcrum and the effort force. This time, the resistance force and the effort force are exerted in opposite directions. This lever always has a mechanical advantage of greater than 1 (MA>1). EXAMPLE OF A CLASS 2 LEVER: resistance=100 pounds, fulcrum to resistance=2.5ft, fulcrum to effort=5ft. The MA of this system would be 2. The amount of effort you would need to put in would be 50 pounds (divide the MA by the resistance to get the effort force). (Wheel barrel)
Third class lever
the fulcrum is located at one end of the lever and the effort force is located between the fulcrum and resistance (RESISTANCE, EFFORT, FULCRUM). The resistance force and the effort force are in opposing directions. This type of lever always has a mechanical advantage of less than 1 (MA<1). EXAMPLE OF A CLASS 3 LEVER: resistance=100 pounds, fulcrum to resistance=5ft, effort to fulcrum=2.5ft. The MA of this system would be .5 (since 2.5/5 equals .5) and the amount of effort force would need to be 200 pounds. (Tweezers)
Mechanical advantage (MA) is...
the ratio of the magnitude of the resistance and effort forces; Ratio of distance traveled by the effort and the resistance force; Calculated ratios allow designers to manipulate speed, distance, force, and function. MA=output force/input force, MA=input arm distance/output arm distance, output force= MA x input force The measure of how much effort is decreased by the simple machine
If MA is less than 1:
•Proportionally greater effort force is required to overcome the resistance force •Proportionally less effort distance is required to overcome the resistance force
If MA is greater than 1:
•Proportionally less effort force is required to overcome the resistance force •Proportionally greater effort distance is required to overcome the resistance force