Hydraulic Advantage What are the advantages of Hydraulics Calculating MA SR and E Hydraulic Demo Take a look at the two syringes at the front of the room Make your predictions as to what will happen in terms of inputoutput force and distance ID: 773747
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Hydraulic Advantage What are the advantages of Hydraulics Calculating MA, SR, and E
Hydraulic Demo Take a look at the two syringes at the front of the room Make your predictions as to what will happen in terms of input/output force and distance
Calculating Hydraulic Advantage There is a mechanical advantage when using hydraulics to lift a load We calculate this advantage using the same formulas that we have used in the past MA = F output SR = d input E = MA x 100 F input d output SR
Hydraulic Lifting Devices Input piston… Input Force and Distance Output piston… Output Force and Distance
Hydraulic Lifting Devices Hydraulic lifting devices have an input piston for the input force & distance and an output piston for the output force & distance Calculating MA and SR all depend on the Surface Area Ratio (SAR) The ratio in size difference between the two pistons will determine the MA and SR
The Big Idea If you can calculate the SAR, the MA, or the SR, then you have your answers for the other two. The three values will always be the same!!! SAR = MA = SR
Hydraulic Lifting Devices If we have a small area making up the input piston which has an area of 1 m² And… if the output piston has an area made up of 9 of the same units (9 m²)… The SAR is 1:9 because the output piston is 9 times larger than the input piston Small Area for the input piston Large Area for the output piston
SAR Example Calculation Surface Area Ratio = Area of Large Piston (output) Area of Small Piston (input) SAR = A Output piston A Input piston SAR = 9 m² 1 m² SAR = 9 Small Area for the input piston Large Area for the output piston The large piston is 9 x larger than the small piston
Hydraulic Lifting Devices Here we have a small 10 N force applied to the input piston (1 m²) The output piston has an area made up of 9 of the same units (9 m²)… Therefore we multiply the input force by 9 to find out what the output force will be 10 N
F output Example Calculation Example If we apply 10 N of force to the input piston, then we need to multiply that by 9 to know what the output force is. Therefore… Output Force = Input force x Surface Area Ratio Output Force = Input force x SAR Output Force = 10 N x 9 Output Force = 90 N 10 N 90 N
F input Example Calculation Example If we were given the output force and we needed to calculate the input force, we would now divide rather than multiply because the input force is smaller than the output force. Therefore… Input Force = Output force ÷ Surface Area Ratio Input Force = Output force ÷ SAR Input Force = 90 N ÷ 9 Input Force = 10 N 10 N 90 N
Calculating Mechanical Advantage Example We now know that the input force is 10 N and the output force is 90NTherefore we can now calculate Mechanical Advantage MA = F output Finput MA = 90 N 10 N MA = 9 90 N 10 N
The Trade Off The disadvantage is that the output distance will only be 1/9 th of our input distanceWe gain Mechanical Advantage, but we “trade off” when it comes to Speed Ratio 18 cm What would the output distance be if we had an input distance of 18 cm?
Hydraulic Lifting Devices Example If we push down on the input piston for a total distance of 18 cm, then the output distance will be 1/9 th of 18 cm Therefore… Output distance = Input distance Surface Area Ratio Output distance = 18 cm 9 Output distance = 2 cm 18 cm 2 cm
Calculating Speed Ratio Example We now know that the input distance is 18 cm and the output distance is 2 cmTherefore we can now calculate Speed Ratio SR = d input doutput SR = 18 cm 2 cm SR = 9 18 cm 2 cm
Surface Area Ratio is the Key! As we have now calculated, the SAR, MA and SR are all the same If you can calculate the surface area of both pistons and figure out what the ratio is between them, then you automatically know what the MA and SR will be
Should we x or ÷ When deciding whether to multiply or divide by the SR for MA or SAR… you need to visualize the system and decide if the value you are calculating will be less than your starting value, or more If it should be less, you ÷ If it should be more, you x
If you are given Input Force…x If you are given Input Distance… ÷ If you are given Output Force… ÷ If you are given Output Distance… x
Example Question N N What formula do you have enough information given below to complete the calculation for?
What is the Mechanical Advantage of this hydraulic system? What is the Speed ratio of the System? N Example Question N
What is the Mechanical Advantage of this system? MA = F output F input MA = 1200 N 40 N MA = 30 Example Question Answers
If the Mechanical Advantage of the hydraulic system is 30… What is the Speed ratio and Surface Area Ratio of the System? N Example Question N
What is the Speed Ratio and Surface Area ratio of this system? SR and SAR = the same as MA… 30 Example Question Answers Ratio of 30 between the 2 pistons
How large would the area of the output piston have to be if the in put piston is 0.5 m² N Example Question N
How large would the area of the output piston have to be if the input piston is 0.5 m² 0.5 m² x 30 = 15 m² Example Question Answers
If the Output distance the van was lifted was 1.75 m, then what would the input distance be? N Example Question N
If the Output distance the van needed to be lifted was 1.75 m, then what would the input distance be? 1.75m x 30 = 52.5 m Example Question Answers
What will the pressure in the system be as the person is applying her 40 N of force to an area of 0.5 m²? N N Example Question
What will the pressure in the system be as the person is applying her 40 N of force to an area of 0.5 m²? Pressure = Force Area P = F ÷ A P = 40 N ÷ 0.5 m² P = 80 pa Example Question Answers
We know the van is applying a force of 1200 N, and we calculated the area of that piston to be 15 m². Calculate the pressure to see if is the same as the one you calculated for the input piston? Should they be the same? Why? N N Check your Answer
What will the pressure in the system be as the Van is applying it’s 1200 N of force to an area of 15 m²? Pressure = Force Area P = F ÷ A P = 1200 N ÷ 15 m² P = 80 pa Example Question Answers Pascal's Law states that pressure is distributed equally in all directions… in this case, both the person and the van have pressures calculated as 80 pa
Home Work Take some time to look at the worksheet and practice some of the example questions This sheet will be marked in class so if you are having troubles, make sure you ask for help or come in after school