UNIT D: MECHANICAL SYSTEMS
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1 1 UNIT D: MECHANICAL SYSTEMS Science 8 2 Section 2.0 AN UNDERSTANDING OF MECHANICAL ADVANTAGE AND WORK HELPS IN DETERMINING THE EFFICIENCY OF MACHINES. 1
2 3 MACHINES MAKE WORK EASIER Topic WHAT WOULD BE EASIER: DRIVING STRAIGHT UP A MOUNTAIN? DRIVING UP A MOUNTAIN ON ROADS THAT BEND BACK AND FORTH? 2
3 5 MACHINES MAKE WORK EASIER A machine can make work easier by increasing the amount of force that you exert on an object. A person alone could not exert enough force to lift a heavy object, such as a car. But using a machine the lever would make it possible. The scientific explanation is that the lever provided mechanical advantage. #1 6 MECHANICAL ADVANTAGE The mechanical advantage of a machine is the amount by which a machine can multiply a force. The more a machine multiplies force, the greater its mechanical advantage. #2 3
4 7 MECHANICAL ADVANTAGE The force applied to the machine is called the input force. The force the machine applies to the object is called the output force. Input and output forces are measured in Newtons. #2 8 CALCULATING MECHANICAL ADVANTAGE You can calculate the mechanical advantage of a machine if you know the input and output forces. Mechanical Advantage (MA) = Output force Input force = F out F in The mechanical advantage is actually a ratio of forces in the mechanical device. For this reason, mechanical advantage is also called the force ratio of the machine. #3 4
5 9 EXAMPLE It takes 45 N to lift a 180 N box with a pulley. What is the mechanical advantage of the pulley? Note: In order to actually lift the box, you must put in 45 N = the input force! MA = MA = 180 N 45 N MA = 4 Output force Input force #4 10 SPEED RATIO Calculating the speed ratio is another way of analyzing how machines work. Speed measures the distance an object travels in a given amount of time. A measure of how the speed of the object is affected by a machine is called the speed ratio. #5 5
6 11 CALCULATING SPEED RATIO The speed ratio is calculated by dividing the input distance by the output distance. Speed Ratio (SR) = Where d = distance Input distance Output distane = d in d out #5 12 EXAMPLE You lift a weight by 1 m when you pull a rope attached to a pulley by 4 m. SR = SR = 4 m 1 m SR = 4 Input distance Output distance What is the speed ratio of the pulley? #6 6
7 13 SPEED RATIO EXPLAINED The speed ratio of 4 means that the part of the pulley where you apply the input force moves four times faster than the part where the output force is the load that you are lifting. 14 PULLEYS: LESS FORCE BUT GREATER DISTANCE An advantage of pulleys is that they multiply the force you exert. A disadvantage of pulleys is that you have to pull much farther than the load actually moves. #7 7
8 15 THE EFFECT OF FRICTION Friction is a force that opposes motion. It is caused by the surface roughness of materials. A rough surface creates more friction than a smooth one. Friction opposes motion, so an extra force is needed to overcome friction whenever you move an object. #8 16 EFFICIENCY Friction does not affect the speed ratio, but it does affect the mechanical advantage of a device, so it also affects its efficiency. Efficiency is a measurement of how well a machine or device uses energy. Efficiency (%) = Mechanical Advantage Speed Ratio Efficiency (%) = MA SR #9 8
9 17 EXAMPLE: CALCULATING EFFICIENCY A pulley has a speed ratio of 3 and a mechanical advantage of 2. Calculate the % efficiency. Round your answer to the nearest hundredth. Efficiency (%) = MA SR 100 Efficiency (%) = Efficiency (%) = 66.67% #10 18 HOMEWORK! Check and Reflect Page 286 # 2 5 (Reference Book pg. 11) 9
10 19 THE SCIENCE OF WORK Topic THE MEANING OF WORK In the scientific sense, work is done when a force acts on an object to make the object move. It s important to remember that movement is needed before you can say that work has been done. 10
11 21 HOW MUCH WORK IS BEING DONE? The amount of work done depends on two things: the amount of force exerted on the object the distance the object moved in the direction of the applied force #11 22 CALCULATING WORK #12 The amount of work done can be calculated using the following formula: Where: W = F d F = Force exerted on an object; measured in Newtons (N) d = distance; measured in metres (m) W = Work; measured in Newton metre (N m), which is also known as a joule (J). 11
12 23 EXAMPLE: CALCULATING WORK You exert a force of 50 N to lift a chair onto your desk which is 0.4 m high. How much work did you do? W = F d W = 50 N 0.4 m W = 20 N m or 20 J #13 24 ENERGY AND WORK Energy and work are closely related because without energy, there would be no work. When you ride your bicycle, you exert a force on the pedals. The force you apply to the pedals causes the bicycle to move. In a car, the energy to drive the wheels comes from gasoline. #14 12
13 25 MACHINES: INPUT VS. OUTPUT WORK INPUT The work input is the work needed to use or operate a machine. W in = F in d in WORK OUTPUT The work output is the work done by the machine. W out = F out d out #15 26 WORK AND FRICTION Recall that a machine s mechanical advantage does not equal to speed ratio in real situations. The reason is friction. Friction is also the reason that work input does not equal work output in real situations. It affects a machine s efficiency. #16 13
14 27 CALCULATING EFFICIENCY Efficiency can also be calculated using work input and work output. Efficiency = Work output Work input 100 #17 28 EXAMPLE: CALCULATING EFFICIENCY A pulley requires an input force of 10.4 N. You pull the rope 2.0 m. The output force to move an object by 1.0 m is 20.0 N. What is the efficiency of the pulley? Round to the nearest percent. (Hint: Solve for Work out and Work in first.) W out = F out d out W out = (20.0 N) (1.0 m) W out = 20.0 J Efficiency = Work out Work in 100 Efficiency (%) = 20.0 J 100 = 96% 20.8 J W in = F in d in W in = (10.4 N) (2.0 m) W in = 20.8 J #18 14
15 29 HOMEWORK! Check and Reflect Page 292 # 1-4, 6-9 (Reference Book pg ) 30 THE BIG MOVERS - HYDRAULICS Topic
16 31 RECALL: HYDRAULIC SYSTEMS Most machines that move very large objects use a hydraulic system that applies force to levers or gears. A hydraulic system uses a liquid under pressure to move loads. A hydraulic system increases the mechanical advantage of the levers in machines. #19 32 RECALL: PRESSURE Recall that pressure is a measure of the amount of force applied to a given area. It can be written as an equation: p = F A Where p is pressure, F is force, and A is area. The unit of measurement for pressure is the pascal (Pa). #20 16
17 33 THE WORLD S GREATEST LAW OKAY FINE, 2 ND GREATEST LAW (AFTER GRAVITY) Pascal discovered that pressure applied to an enclosed fluid is transmitted equally in all directions throughout the fluid. This effect is known as Pascal s Law. #21 34 EXAMPLE: A SIMPLE HYDRAULIC JACK WORKS BECAUSE OF PASCAL S LAW. The first piston is the input piston. This piston is used to apply the force to the fluid, which creates pressure in the fluid. The fluid transfers the pressure equally in all directions. So the pressure on the output piston equals the pressure at the input piston. 17
18 35 PISTONS AND PRESSURE In hydraulic systems, the pressure is created using a piston. A piston is a disk that fits tightly inside a cylinder. As the disk moves inside the cylinder, it either pushes fluid out or draws fluid into the cylinder. 36 PISTONS AND PRESSURE The pressure in the fluid provides the mechanical advantage that makes hydraulic systems so useful. #21 18
19 37 CALCULATING MECHANICAL ADVANTAGE OF A HYDRAULIC JACK You can calculate the mechanical advantage of a hydraulic jack if you know the input and output forces. Recall that the formula for calculating mechanical advantage is: MA = Output force Input force #22 38 EXAMPLE: CALCULATING MECHANICAL ADVANTAGE In a hydraulic jack, the input force is 20 N and the output force is 500 N. Calculate the mechanical advantage. MA = MA = 500 N 20 N MA = 25 Output force Input force The jack s mechanical advantage is 25. #23 19
20 39 PRESSURE AND MECHANICAL ADVANTAGE The reason for the large mechanical advantage in a hydraulic system is the ability of the fluid to transmit pressure equally. From Pascal s law, we know that the pressure the small piston creates is the same everywhere in the fluid. 40 PRESSURE AND MECHANICAL ADVANTAGE So, p small = p large according to Pascal s Law. But p = F A : p small = p large, so F small A small = F large A large We can use this ratio to solve for unknown values in hydraulic systems. #24 20
21 41 EXAMPLE: HYDRAULIC SYSTEM CALCULATIONS In a hydraulic system, a small piston has an area of 4 cm 2. A large piston has an area of 100 cm 2. You exert a force of 20 N on the small piston. What force is exerted on the large piston? F small A small = F large A large 20 N = x 4 cm cm 2 Use cross-multiplication or equivalent fractions to solve. x = 500 N The force exerted on the large piston is 500 N. #25 42 A DISADVANTAGE The mechanical advantage of hydraulic systems has a similar shortcoming to levers. To increase the force on the output piston, the input piston has to move a greater distance. #26 21
22 43 HOMEWORK! Check and Reflect Page 300 # 1-4 Assess Your Learning Page 303 # 1-3, 5 (Reference Book pg ) 22
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