How To Calculate Mechanical Advantage
Mechanical advantage calculations
In this chapter, you lot will acquire how to calculate the amount of mechanical advantage lever systems and gear systems give.
You lot volition also acquire how to summate the speed with which a gear in a gear organization volition rotate if y'all know how many teeth each gear has, and the speed with which the other gear is rotating.
Calculate the mechanical advantage of a lever
In the previous chapter, you learnt that you can summate a quantity to say exactly how big or smallthe mechanical reward is. This quantity is a ratio.It is calculated by dividing the output force by the input strength.
A ratio of 1 to iv is written as one:4. This is simply another way to write the fraction ¼.
Yous also use a ratio to write the scale of a drawing.
You besides learnt that if the output force is greater than the input force, the mechanical reward (MA) is greater than 1: MA > 1.
Await at the lever in Figure 2. This lever is making the output force bigger, so you lot can say that it is giving us a mechanical reward. In that location are two "arms" on a lever: the input arm and the output arm. The lever below shows the input arm in blue and the output arm in red.
The input arm is sometimes called the "effort arm".
The "output arm" is sometimes chosen the load arm.
Calculations about a lever
On the lever in a higher place, the input arm is 40 cm long and the output arm is ten cm long. The input arm on this lever has been moved upwards by 4 cm. Study the picture then answer the questions.
one. When the input arm is moved up by 4 cm, how far does the output arm motion down?
2. When the input arm is moved up by 2 cm, how far does the output arm motion downward?
iii. How far do you recollect the output arm will move if the input arm was moved up past 12 cm?
4. Now you tin confirm what you lot take already worked out. Use the values in Effigy 2 to calculate the ratio of the length of the output arm to the length of the input arm.
five. Use the values in Effigy 2 to calculate the ratio of the output distance to the input distance.
6. Summate the ratio of the output distance to the input distance when the input altitude is 2 cm. Use your answer from Question 2 higher up to help you.
seven. Summate the ratio of the output distance to the input altitude when the input altitude is 12 cm. Use your answer from Question 3 above to aid you.
viii. What tin you say about the value of all of these ratios?
The ratio of input arm and output arm in levers
If the input arm is 400 cm long and the output arm is 100 cm long, then the output distance will always be:
If you lifted this lever by 20 cm, then:
This lever gives yous a mechanical advantage because the input distance is larger than the output altitude. We know that a lever with a larger input distance and a smaller output altitude volition requite a mechanical advantage, so we tin can say that:
| Input altitude ÷ output altitude = length of input arm ÷ length of output arm = mechanical advantage (MA) | But we also know that: Input distance ÷ output distance = output force ÷ input force = mechanical advantage (MA). |
The ratio input arm altitude : output arm distance is the same as the ratio output force : input force, and this is the mechanical advantage.
A lever with an input arm 400 cm long and the output arm 100 cm long will give a mechanical advantage of:
This means that the output forcefulness will always be four times larger than the input strength; and the input force will e'er exist 4 times less than the output forcefulness.
Consider the force needed to continue a weight of xx kg from falling due to gravity. If this weight is on the output side of the lever discussed above, then what weight is needed on the input side of the lever to residual information technology?
Weight on input side = ¼ × 20 kg = v kg
Mechanical advantage
Calculations about a lever
Look at the lever in Figure 3. The lever is pushed down to crush a can.
ane. How practise y'all know that this lever will crush a can more than easily than by mitt?
2. With the can in the position shown, calculate the mechanical reward that this lever volition give.
3. If you need an output force of 20 "units of force"to vanquish the tin can, how much input force doyou demand?
Length can exist measured in units of metres, and mass tin can be measured in units of kilograms.
You will later on learn in physics well-nigh how force is measured in units of "Newtons". Merely for the moment, you tin can telephone call information technology "units of force", or "units".
4. The designer decides to make it fifty-fifty easier to crush the can. She moves the can closer to the fulcrum. This reduces the output arm to 15 cm. Recalculate the mechanical reward of the lever.
5. Recalculate the new input strength needed to beat out the can with an output force of 20 units.
Summate the distance reward of a lever
Look at the lifting system in Figure 4. It uses a hydraulic cylinder for the input strength. It is a arrangement that could be used for lifting an engine out of a machine.
The lifting lever at the summit is a third-course lever, because the input is between the fulcrum and the output.
A tertiary-class lever always gives a distance reward. It never gives a mechanical advantage.
1. How long is the input arm on this lever?
2. How long is the output arm?
3. Calculate the mechanicaladvantage that this lever gives.
4. Explain what this MA value tells y'all well-nigh the output and input forces.
five. A person wants to utilise this system to elevator an engine out of a car. He needs the engine to be lifted by 90 cm. How far will the hydraulic cylinder at the input need to move for the engine to be lifted 90 cm at the output?
half-dozen. If the system is designed to elevator objects by 180 cm, how far does the hydraulic cylinder need to movement at the input?
Calculate the speed reward of gears
The gear ratio
The gear ratio, which is also chosen the speed ratio or sometimes the velocity ratio, tells you how the speed of a driven gear will be changed by a commuter gear.
Wait at the two meshed gears in Figure 5. The driver or input gear has 5 teeth. The driven or output gear has 10 teeth.
- If the driver moves ane revolution, it pushes the v teeth on the driven gear.
- If the commuter gear moves by 2 revolutions, then x of the driven gear's teeth are moved. So the driven gear moves 1 revolution. Two driver revolutions give 1 driven gear revolution. And so the turning speed of the driven gear is ½ the turning speed of the driver gear. The speed ratio, which is the aforementioned every bit the gear ratio, is1 : 2 or ½.
- If the commuter gear revolves ten times, so the driven gear volition but revolve 5 times.
Calculations using the gear ratio
The speed of a turning wheel is measured in revolutions per minute, or rpm. Then if the driver gear is turning effectually twice every second, it has a speed of ii rpm. A speed of ii rpm on this system will give a speed of i rpm on the driven gear.
rpm stands for "revolutions per minute".
The gear ratio can be used to work this out:
The speed ratio and mechanical reward
If a gear arrangement gives a speed reward because of its gear ratio, then it will give you a mechanical disadvantage. This means that if a driven gear revolves faster than its driver gear, it gives less turning output force to the machine.
If a driven gear revolves slower than its driver gear, it gives more turning output force to the car.
Speed advantage
When a driven (input) gear makes the driver (output) gear rotate faster, and so the gear system gives a speed reward.
Calculations
i. The gear system in Figure v has v teeth on the driver gear and 10 teeth on the driven gear. Calculate the rpm of the driven gear if the commuter gear rotates at 1 500 rpm.
ii. If a driver gear has 15 teeth and a driven gear has 60 teeth, calculate the gear ratio.
three. Consider a gear system where the driver gear has 25 teeth and the driven gear has 15 teeth.
(a) If the driver gear rotates at 100 rpm, calculate the speed of the driven gear.
(b) What can you say about the output turning force at the driven axle compared to the input turning force at the commuter beam? How does that alter in this system?
Using the gear diameters to summate the gear ratio
The easiest way of computing the speed of a gear system is from the number of teeth on the gear wheels.
However, there is another style of calculating the speed of a gear system:
- If a gear wheel is minor, it volition have a small number of teeth and its bore volition be small-scale.
- If a gear wheel is large, it volition take more teeth and its diameter will be larger.
In Figure v, the diameter of the large driven gear is ix,iv cm and the diameter of the pocket-size driver gear is iv,seven cm.
Annotation: The diameters are measured for the dashed circles in Figure v, since those circles prove where the gear teeth brand contact.
More calculations for you to practice
1. A starter motor of a car has a driver gear with a diameter of 4 cm. Information technology drives a large gear continued to the crankshaft of the engine with a diameter of sixty cm. Calculate the gear ratio of the starter-motor system of this car.
2. If the starter motor turns at three 600 rpm, calculate the speed that the engine turns when the car starts.
3. Exercise you remember the turning output forcefulness that makes the engine turn is greater than, or less than, the turning input force of the electric starter motor?
Next calendar week
Side by side week, you will learn how to depict gear systems. You volition besides write pattern briefs for gear systems with an exact speed reward and an verbal mechanical advantage.
How To Calculate Mechanical Advantage,
Source: http://www.mstworkbooks.co.za/technology/gr8/gr8-technology-12.html
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