The Bennett Mechanical Comprehension test II (BMCT II) is one of the most popular mechanical aptitude assessment tools used by thousands of corporations all over the world. It is a tricky screening mechanical test and therefore, very effective.

This course will help you increase your Bennett Mechanical Aptitude test results by up to 10 points, meet the passing score of the behavioral assessment, and get your dream job. All this will happen within 5 hours of video-based BMCT study section and computer-based practicing with our Bennett Mechanical Comprehension practice tests. Compared to the average 36% passing rate, our BMCT students enjoy an outstanding 84% passing rate.

**✓** **Deep video-based learning** - Every module of the Bennett Mechanical Comprehension test course covers the topics in the test in great depth. We make use of video-based guides in order to maximize your learning.

**✓** **Preparation for any level of difficulty** - The difficulty faced on the Bennett Mechanical test can vary. In order to make sure you are 100% covered for any question you could encounter, we have designed our course to teach you everything from the ground up.

**✓** **Lighting fast tactics** - There are 14 question types on the BMCT test. This course offers the optimal strategy for answering every one of these questions.

**✓** **How to approach mechanical questions effectively** - this course is structured to build you mechanical knowledge in such a way that develops your intuitive understanding of mechanical concepts.

If you’ve been asked to take the Bennett Mechanical Comprehension test, you probably don’t have a lot of time between now and sitting the course.Time is short, and you need a quick fix..

Whether you are confident with mechanical concepts or haven’t looked at them since high school, this course has something to offer.

This Bennett Mechanical Aptitude Test Preparation Course is perfect for:

- Inexperienced test-takers who need to learn the mechanical concepts covered in the BMCT from scratch and to practice Bennett Mechanical Comprehension tests.
- Individuals who are well-versed with mechanical concepts who wish to sharpen their skills and jog their memory in order to maximise their chances of success.

This course has been meticulously designed, making use of years of expertise in order to put together the most comprehensive and concise BMCT preparation course available on the market. Our in-house mechanical and educational specialists have composed the text-based and video Bennett Mechanical Comprehension test study guides on this course in order to ensure that you are equipped with everything you could possibly need for the test.

The old Bennett Mechanical Comprehension test form S & T were discontinued on May 2019. Ever since, the only actual version of the BMCT test is the Bennett Mechanical Comprehension Test - II (BMCT-II).

The Bennett Mechanical Comprehension test II is administered by a wide variety of employers to screen out unsuitable candidates. Harsh time restrictions and a wide range of mechanical concepts covered make what might look like a simple mechanical comprehension test into quite a challenging obstacle. If you’ve applied for a job position and have been asked to take this test, there won’t be any do-overs. You need to get this right, and you need to get it right the first time. This course is the essential resource for maximising your chance at test success and landing your dream career.

One of the largest difficulties when learning mechanical concepts is visualization. Frequently, test-takers will struggle to visually understand the concepts presented when reading it in simple text. In order to combat this and maximize your learning potential, we have produced a series of video guides for this course. Using video-based guides alongside our written content, you will be on the fast-track to test success. This course is the only BMCT course on the market which comprehensively covers these topics in a video-based format.

Being asked to take a test you’ve never taken can be pretty daunting. Taking a test you’ve not performed so well on in the past can also be a scary prospect. Our expect in-house mechanical experts understand this, and have produced this course with that in mind. While many test-takers are tripped up on numerous time traps and unfamiliar question types, this BMCT study guide is focused on helping you get to the right answer in the most time-efficient way possible.

What sets this course apart from the others is a comprehensive approach to teaching the concepts. While other courses on the market focus almost entirely on practice tests with very little actual instructional content, we offer a written and video guide for all 14 question types on the actual test and curated Bennett Mechanical Comprehension practice tests, presented in an accessible and easy-to-understand curriculum so that you can spend less time deciphering the course and more time preparing for the test.

The Bennett Mechanical Comprehension test II (BMCT II) is one of the most popular mechanical aptitude assessment tools used by thousands of corporations all over the world. It is a tricky screening mechanical test and therefore, very effective.

This course will help you increase your Bennett Mechanical Aptitude test results by up to 10 points, meet the passing score of the behavioral assessment, and get your dream job. All this will happen within 5 hours of video-based BMCT study section and computer-based practicing with our Bennett Mechanical Comprehension practice tests. Compared to the average 36% passing rate, our BMCT students enjoy an outstanding 84% passing rate.

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- 8 Mechanical Instructional videos
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- 200 Practice questions with explanations
- Suitable for all applicants to companies administering any mechanical test

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- Question 1 of 50
##### 1. Question

**A movable pulley is a simple machine which halves the force necessary to lift a load, while a fixed pulley can only change the direction of force. It cannot change the magnitude of force. In this regard, calculate the mechanical advantage of the system shown in the figure below.**CorrectIncorrect - Question 2 of 50
##### 2. Question

**If the big wheel (A) turns 3 times at clockwise direction, how many times and in which direction does the small one (B) turn?**CorrectIncorrect - Question 3 of 50
##### 3. Question

**If gear A rotates in the clockwise direction, what will the direction of wheels B, C and D be?**CorrectIncorrect - Question 4 of 50
##### 4. Question

**Which statement below is WRONG about springs?**CorrectIncorrect - Question 5 of 50
##### 5. Question

**A football player kicks a football at a velocity of 50.0 m/s, making an angle of 37º with the horizontal. What is the time of flight of the ball? Take the value of g = 9.81 m/s2. Write everything you calculate at 3 s.f.****(sin 37º =0,6 cos37º =0.8)**

CorrectIncorrect - Question 6 of 50
##### 6. Question

**Centripetal force is proportional to**CorrectIncorrect - Question 7 of 50
##### 7. Question

**A 12N force is required to turn a screw of body diameter equal to 6mm and 1mm pitch. Calculate the driving force acting on the screw. Write the answer at 3 s.f.**CorrectIncorrect - Question 8 of 50
##### 8. Question

**Which statement is CORRECT about air pressure?**CorrectIncorrect - Question 9 of 50
##### 9. Question

**The advantage/s of a series circuit to a parallel one is that**CorrectIncorrect - Question 10 of 50
##### 10. Question

**A load of 300 N is held with a force of 1200 N. If the force is acting at a point 25 cm away from the fulcrum, what is the length of the lever in metres?**CorrectIncorrect - Question 11 of 50
##### 11. Question

**How many revolutions does the wheel M make when K completes 4 revolutions?**CorrectIncorrect - Question 12 of 50
##### 12. Question

**What is the rotation velocity and direction of wheel C if the wheel A makes 30 rot / min? (RA = 3RB and RC = 2RB).**

CorrectIncorrect - Question 13 of 50
##### 13. Question

**If the weight of each pulley is equal to the load, what is the ratio between the pulling force F and the load L? (F / L = ?)**CorrectIncorrect - Question 14 of 50
##### 14. Question

**Which statement is WRONG about springs?**CorrectIncorrect - Question 15 of 50
##### 15. Question

**The second half (while falling down) of the vertical component of a complete ballistic trajectory is:**CorrectIncorrect - Question 16 of 50
##### 16. Question

**Which statement is WRONG about circular motion?**CorrectIncorrect - Question 17 of 50
##### 17. Question

**What class of levers does the inclined plane represent?**CorrectIncorrect - Question 18 of 50
##### 18. Question

**If a liquid becomes twice denser and the depth of an immersed object in this liquid halves, the liquid’s pressure:**CorrectIncorrect - Question 19 of 50
##### 19. Question

**What is the main difference between a cell and a capacitor?**CorrectIncorrect - Question 20 of 50
##### 20. Question

**We use __?__ to measure a specific gas pressure**CorrectIncorrect - Question 21 of 50
##### 21. Question

**What happens to the current passing through the main branch in the circuit shown in the figure if one the bulbs smashes?**CorrectIncorrect - Question 22 of 50
##### 22. Question

**Which statement about levers is CORRECT?**CorrectIncorrect - Question 23 of 50
##### 23. Question

**Pedals of a bicycle are 8 inches long and the wheel diameter is 48 inches. What is the mechanical advantage of this bicycle?**CorrectIncorrect - Question 24 of 50
##### 24. Question

**How many inches must one pull the rope down in order to lift the load in the figure by 28 inches?**CorrectIncorrect - Question 25 of 50
##### 25. Question

**The two projectiles in figure are fired from the points K and L at the same instant. What is the relation between u****1****and u****2****, if both of them are to land on the same point P and at the same instant as in figure?**CorrectIncorrect - Question 26 of 50
##### 26. Question

**What would happen to the distance Earth-Sun if one year became 400 days without any change in the gravitational force?**CorrectIncorrect - Question 27 of 50
##### 27. Question

**A screw is a combination of:**CorrectIncorrect - Question 28 of 50
##### 28. Question

**What is the pressure exerted on the ground if a 400 N object is placed on the conic platform as shown in the figure? The weight of conic platform is negligible.**CorrectIncorrect - Question 29 of 50
##### 29. Question

**We must put a __?__ before an expensive circuit component to prevent it from burning by the excessive current.**CorrectIncorrect - Question 30 of 50
##### 30. Question

**Why can we not use the equation P = ρ · g · h for calculating the air pressure at a height h taking as a reference level the upper part of the atmosphere?**CorrectIncorrect - Question 31 of 50
##### 31. Question

**In parallel combination of bulbs, when a bulb smashes, the other bulbs:**CorrectIncorrect - Question 32 of 50
##### 32. Question

**An electric iron gets hotter but the cable carrying the current to the iron is cool. This, because:**CorrectIncorrect - Question 33 of 50
##### 33. Question

**Which statement regarding magnets is CORRECT?**CorrectIncorrect - Question 34 of 50
##### 34. Question

**What kind of lever is the hydraulic crane shown in the figure?**CorrectIncorrect - Question 35 of 50
##### 35. Question

**Which term is NOT related to gears?**CorrectIncorrect - Question 36 of 50
##### 36. Question

**In which direction does the 4****th****wheel rotate if the first wheel rotates clockwise?**CorrectIncorrect - Question 37 of 50
##### 37. Question

**A uniform rod can be hold in equilibrium with the help of a system of pulleys as in the figure. What is the weight of the rod if the force F=3N? (Remember that the weight of the rod acts at the center of gravity of the rod which is at its middle).**CorrectIncorrect - Question 38 of 50
##### 38. Question

**What is the load shown in the figure in Newtons if the springs are all identical (k = 4000N/m each) and the total extension of all springs is 20cm?**CorrectIncorrect - Question 39 of 50
##### 39. Question

**Which quantity remains constant during a ballistic trajectory?**CorrectIncorrect - Question 40 of 50
##### 40. Question

**Which statement is CORRECT?**CorrectIncorrect - Question 41 of 50
##### 41. Question

**A wooden rectangular object is 15cm high as shown in the figure. What is the pressure exerted by the object on the ground given that the density of wood is 600 kg / m****3****? Take g = 9.81 m/s****2****. Write the answer as a whole number.**CorrectIncorrect - Question 42 of 50
##### 42. Question

**Electrons in a circuit flow from a place where there are __?__ electrons to a place where there are __?__ electrons.**CorrectIncorrect - Question 43 of 50
##### 43. Question

**A gas has a volume of 10 lt****and a pressure of 4 atm initially. If after a process its volume becomes 20***It,***what will its final pressure be in cm-Hg?**CorrectIncorrect - Question 44 of 50
##### 44. Question

**Which of the following does NOT use magnetism to operate?**CorrectIncorrect - Question 45 of 50
##### 45. Question

**Which method is NOT used to make a magnet?**CorrectIncorrect - Question 46 of 50
##### 46. Question

**Belts usually are made from materials that __?__ friction.**CorrectIncorrect - Question 47 of 50
##### 47. Question

**Which statement is wrong regarding the situation shown in the figure below? The event occurs from left to right.**CorrectIncorrect - Question 48 of 50
##### 48. Question

**What is the rotation speed (in km/h) of a given point on the Earth’s surface? The radius of Earth is about 6370 km. Write the answer as a whole number.**CorrectIncorrect - Question 49 of 50
##### 49. Question

**What value does the voltmeter in the circuit shown in the figure read?**CorrectIncorrect - Question 50 of 50
##### 50. Question

**Which of the following materials can become a magnet?**CorrectIncorrect - Engineers
- Energy and Utilities
- General Labor
- Industrial/Technical Sales
- Installation/Maintenance/Repair
- Machine Operators/Machinists
- Manufacturing and Production
- Mechanics
- Skilled Trades
- Vocational/Technical Students
- Introduction to the BMCT
- Course Structure
- Time Management Factor
- The Right Approach

**1****2****3****4****5****Not categorized 0%****1****2****3****4****5****Answered****Review****Question 1 of 5****1. Question****The long side of a crowbar (up to the turning point) has a length of 0.80 m. it is**

**used to pull out a nail from a board. The nail is 5 cm away from the turning point.**

**Calculate the force to be used if the nail can take a maximum force of 3000 N.****Correct****Incorrect****Question 2 of 5****2. Question****A wheelbarrow weighs 20 kg when empty. A 600 N load is carried using it. The load is concentrated at a point which horizontally is 50 cm away from the wheel. The wheelbarrow, which is 2m long, has also its center of mass at this point. How much easier do we lift the load instead of carrying it on shoulders? (Take the gravity equal to 10 m/s2 if needed)****Correct****Incorrect****Question 3 of 5****3. Question****A third class lever has a mechanical advantage****Correct****Incorrect****Question 4 of 5****4. Question****Which one of the following are correct for levers?****I.If there is a gain in force, there is a loss in distance****II.The mechanical advantage is the ratio of the load to the force****III. In simple machines there is a gain in work****Correct****Incorrect****Question 5 of 5****5. Question****Which diagram below shows the working principle of pliers?****A.****B.****C.****Correct****Incorrect****What are levers?***They can change the direction of a force*- They can change the magnitude of force
- They can change both of the above
- The part that tends to rotate the system anticlockwise (in the figure above, the force F
_{1}exerted perpendicular to the rigid rod at the distance d_{1}from the pivot, tends to rotate the rigid bar anticlockwise. - The part that tends to rotate the system clockwise (in the figure above, the force F
_{2}exerted perpendicular to the rigid rod at the distance d_{2}from the pivot, tends to rotate the rigid bar clockwise. - Pivot located between load and force,
- Load located between pivot and force, and
- Force acting between pivot and load
- They can change the direction of a force
- They can change the magnitude of force
- They can change both of the above
- Pivot located between load and force, (L-P-F or F-P-L) [First class levers]

(Examples of first class levers include seesaw, can-opener, scissors, equal-arm balance, crowbar etc.) - Load located between pivot and force, and (P-L-F or F-L-P) [Second class levers]

(Examples of second class levers include wheelbarrow, can-opener, nutcracker etc.) - Force acting between pivot and load (P-F-L or L-F-P) [Third class levers]

(Examples of third class levers include sugar tongs, tweezers, forearm etc.) - What are levers? – Theoretical background
- Equation of levers
- Mechanical advantage
- Types of levers – First, Second, Third Class
- Practice Questions

- What are gears? – Theoretical background
- Thumb rules in meshed gears
- Practice Questions
- Systems of gears
- Rack and Pinion
- Relationship between the radius of the gear and its velocity of rotation

- What are wheels? – Theoretical background
- Mechanical advantage of wheels
- Combination of wheels and gears
- Advantages and limitations of wheel (and gear) systems
- Practice Questions

- What are pulleys? – Theoretical background
- Types of pulleys – Fixed, Moveable, Combined
- Block and Tackle
- Practice Questions

- What are springs? – Theoretical background
- Combination of Springs – Series, Parallel, Mixed
- Practice Questions

- What is ballistics? - Theoretical background
- Equations of ballistics
- Practice Questions

- What is circular motion? - Theoretical background
- Directions of Rotation
- Centripetal and centrifugal force
- Centripetal acceleration
- Practice Questions

- Wheel and Axle
- Inclined Plane
- Screw
- Wedge
- Practice Questions

- What is Pressure? – Theoretical Background
- Solid pressure
- Liquid Pressure
- Applications of hydrostatic pressure
- Practice Questions

- Gas Pressure – Theoretical Background
- Air pressure – Evidence of air pressure
- How to measure air/gas pressure? – Apparatus and Units
- Pressure and Volume relation in gases
- Practice Questions

- Electric Charges
- Electric Circuits
- Electric Current
- Ohm’s Law
- What does resistance depend upon?
- Symbols of electric circuit elements
- Practice Questions

- Combination of resistors – Series, Parallel, Complex
- Advantages and disadvantages of series and parallel combination of resistors
- Practice Questions

- Theoretical background
- Mechanical vs Electric Power
- Power and efficiency
- Electric energy & Joule’s Law
- Joule or kWh? – Cost of electricity
- Practice Questions

- Magnets – Theoretical & Historical background
- Classification of magnets
- Magnetic poles - Magnetic force - Magnetic field lines
- Theory of magnetism
- Magnetism in use
- How to make a magnet?
- Practice Questions

- Identifying the Relationship of Each Figure
- Figure Movement Tracking
- Two-Figure Analogy
- Six-Figure Analogy
- Coloration Time Trap
- Practice Questions

- Sequence Type Identification
- Inversion Sequences
- Rotation Sequences
- Positioning Sequences
- Counting Sequences
- Size Sequences
- The Right Approach
- Practice Questions

- Conforming Figure Question Type
- Outlying Figure Question Type
- Key Attribute Discernment
- The Three-Step Approach
- Practice Questions

- Word Problems Question Types
- Percentages Problems
- Rate and Ratio Problems
- Age Calculation Problems
- Time Trap Avoidance
- One-Variable Problems

- Linear Series
- Geometric Series
- Compound Series
- Layered Series
- Squared Series
- Exponential Series
- Practice Questions

- Ordering Types
- Fraction Ordering
- Mixed Value Ordering
- Formula-Type Problems
- Practice Questions

- Practice Test 1
- Practice Test 2
- Practice Test 3

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Hi, and welcome to PrepTerminal’s Bennett Mechanical Comprehension Test course. In the following modules, we’ll walk you through every concept contained within the BMCT through a comprehensive series of guides composed by industry experts who have closely studied the BMCT in order to ensure that this course is the most up-to-date preparation resource on the market.

These guides contain in-depth explanations of the concepts covered by the BMCT, as well as the best methods required to solve questions on the BMCT test quickly and effectively.

Time management is an essential skill in this test, and as such we have composed our guides with an emphasis on this so that you won’t be caught unprepared when taking the real test.

In this module, we will discuss the contents of the test, and the structure of the course. We’ll lay out the rationale behind creating this course, what makes it unique, and how best to study from it. After this, we’ll finish up with some of our best test-taking tips to get you started off on the right foot.

As you go through the modules, take your time - there is a lot of information to digest due to the nature of this test, and it’s vital that you absorb all of it to the best of your ability if you’re to maximize your performance in this test. It may be that you find yourself needing to pause and review parts of the videos or read the text transcript in order to consolidate your understanding; this is perfectly normal and is in fact encouraged so that you can be sure you haven’t missed any important details along the way.

Last but not least - we’re very pleased to see you here. We hope you enjoy the course, and that it’ll be of great benefit to you. Good luck!

**Test Structure**

The questions on the BMCT course can vary in difficulty, though the concepts covered are not so advanced that a college education would be required to manage them - in fact, these questions are at a sixth-grade level. That being said, a learned knowledge of the concepts covered is a huge asset when it comes to understanding exactly how to approach questions quickly and subsequently achieving a high score.

On top of this, the time restriction is rather challenging. The test is comprised of 55 questions, which are to be answered within 25 minutes, meaning in order to complete the entire test you must answer each question, on average, within 25 seconds.

It is important to understand that the expectation on this test is not to score a full 55/55. Rather, candidate scores are compared to a range of ‘norm groups’. The current norm groups as of 2018 are:

Because of this variety of norm groups, the score against which you will be compared varies depending on the job position applied for. To that end, your focus should be on achieving the best score you possibly can in order to rank well compared to your norm group.

Because you’ll need to judiciously skip time-consuming questions, even one wrong answer could have a catastrophic effect on your overall score. After all, every point counts on the BMCT. As such, when you are faced with a question, you must think critically and make decisions quickly. Success is contingent upon your capacity to work efficiently and intelligently; pre-existing knowledge is not as much of a factor.

By following the guidelines and methodology that we laid out for you, you’ll be able to easily filter out the questions which are and aren’t worth spending time on and guess strategically for a higher score. By understanding how test-takers design the test, we seek to ensure that you’ll be more than prepared when test day comes.

The BMCT test is far more challenging than it seems. Far too often, hardworking and talented individuals are being turned away from jobs they were otherwise qualified for simply because their test scores were too low.

While the BMCT can be useful as a general metric of mechanical comprehension, many highly competent individuals fail the test for no reason other than their unfamiliarity with the types of questions and time traps. The strategy and super quick tactics conveyed in our modules help test-takers solve questions well within the time constraints and immediately recognize & avoid time traps, thus allowing you to save precious time which can make the difference between success and failure in your exam.

We have created this course so that busy people such as yourself can prepare for this test as quickly as possible. Whether you’ve been out of school for a few years, or are just nervous, we seek to provide promising candidates the tools they need to effectively take on this challenging psychometric test.

While the BMCT is difficult, anybody can succeed if they are armed with a proven test-taking strategy and well-prepared tactics for the BMCT’s 14 different question categories. We believe that nobody should be turned away from their dream job or institution just because they didn’t know what to expect from a standardized test.

This is one of the only online courses devoted solely to the BMCT test. Being far more than a cursory review, our test prep modules are deeply focused upon the skills you need for success. Avoiding extraneous tips, needless steps and general nonsense, our resources are both incredibly comprehensive and extremely practical.

Our goal in this course is not only to teach you the mechanical concepts on the BMCT - you can find this kind of help anywhere in abundance. Rather, this course is produced with the intention of arming you not only with the concepts required, but also the techniques for proper application in the context of this test for the quickest solution.

In this course, we explain exactly how to approach every one of the 14 different question types within the given time limit. Our step-by-step video tutorials show you the shortcuts you should be using at every opportunity.

In this course, we explain exactly how to approach every one of the different question types within the given time limit.

To get started with your study, move on to the next module to begin learning about the BMCT question types in detail.

Thanks for choosing Prepterminal to be your partner in test success, and once again, good luck!

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Questions involving levers require the candidate to identify the correct position in which a force must be applied in order to establish the equilibrium between two parts of levers which have opposite tendencies of rotation. In addition, they require one to figure out the missing force at one side of the system to set the equilibrium, if the distances from the turning point are given.

Another important point of this module is working out the resultant turning effect (moment) of force if the equilibrium cannot be established. The situation can be more complex if the weight of the lever is also included in the calculations.

In the test, it is very important to approach questions with some urgency as time is extremely limited. One should take care not to linger too long on any single question as it takes up valuable time which would be better-allocated on other, more approachable questions. While this guide will explore the means by which to approach the questions regarding levers, it is vital that if you cannot identify a path to a solution within 10-12 seconds you take an educated guess and move on to the next question. Spending too much time on any single question can cost precious time which is better spent elsewhere on less challenging problems.

First, let’s have a quick view on levers, before entering into details, which will be discussed when the types of levers are explained.

**Levers** are one of the simplest types of simple machines. As such, they possess the main properties of simple machines, i.e.:

Levers consist on a rigid bar which can turn around a fixed point. This turning point is known as pivot or fulcrum.

The turning point divides the system into 2 main parts:

Thus, the equilibrium is settled when the turning effects (moments) caused by the two forces applied at the given distances from the turning point, cancel each other. In simplest words, the condition of equilibrium in this case is

Total clockwise moment of force=Total anticlockwise moment of force

**1.2 Equation of levers**

The mathematical equation of the abovementioned rule is

where

F_{1⊥} and F_{2⊥} are the components of acting forces on both sides of the bar which are perpendicular to the bar length, while d1 and d2 are the distances of the points where the forces act to the fulcrum.

In general, a lever is used to lift a load L using a force F. Therefore, instead of writing F_{1}, F_{2}, d_{1} and d_{2}, we can write L for F_{1}, dL for d_{1}, F for F_{2} and d_{L} for d_{2}.

Hence, the equation of levers becomes

L×d_{L}=F×d_{F}

For example, if the load in the figure below is 20N and the distance of the center of gravity of the load from the turning point is 2 m, the magnitude of force F will be

**1.3** **Mechanical advantage **

Another important quantity regarding levers is Mechanical Advantage (MA). It is calculated by the equation

It calculates how many times easier we can lift a load using the lever than if we simply lifted it by arms.

In our example, the mechanical advantage is

This means we can lift the load 2 times easier when using the lever instead of carrying it by hand.

**1.4 Types of levers**

We determine the class of the lever by noting the relative positions of the load (L), pivot (P) and force (F).

The three possible combinations are:

Each of these combinations gives a different class of levers.

**1.4.1 First class levers**

** A first class lever **is used to lift heavy loads with small forces. It has a fulcrum between the force and the load as in the figure of the previous example

If the system is in equilibrium there are two equal turning effects but in opposite directions. According to the law of levers we can write

The force applied to the lever can also be calculated from the law of conservation of energy. Look at the figure below:

Giving that

Work done on the load=Work done by the force

we obtain

From the similarity of triangles, we obtain

where k is a constant. Hence, we obtain

Substituting the last expression in the equation (1), we obtain

Simplifying k, we obtain

which is identical with the equation (2).

**1.4.1.1 Examples of first class levers in daily life**

There are many examples in daily life when the principles of first class levers are applied. Scissors, see-saws, can openers, equal-arm balances and crowbars are all examples of first class levers.

Scissors (first class lever)

Seesaw (first class lever)

Seesaw (first class lever)

Equal-arm balance (first class lever)

Crowbar (first class lever)

**Example:** Calculate the force needed to pull out a nail using a crowbar as in the figure. The nail can take a maximum force of 2000 N.

Solution: Crowbar is a first class lever, so, its fulcrum is As we see, the distance from the load to the turning point (dL) is 15cm = 0.15m and the distance from the force to the turning point (dF) is 1m. The maximum force the nail can take (2000 N) here represents the load L. Thus, for the force F needed to pull out the nail, we have

The mechanical advantage of this crowbar is

The same result can be obtained also by dividing the distance from the turning point. Thus, from the equation

we can write

As you can see, the result is the same in both cases.

**1.4.2 Second class levers**

A second class lever has the load between the force and the fulcrum as shown in the figure below

The equation of a second class lever is the same as for the first class lever, i.e.

And the equation of mechanical advantage is also the same:

The only difference here is that in most cases, force distance is equal to the total length of the lever.

Wheelbarrow, nutcracker and bottle opener are all examples of second class levers. Look at the figures below

Wheelbarrow (second class lever)

Nutcracker (second class lever)

Bottle opener (second class lever)

Example: A man carries a 600N load using a wheelbarrow. What is the force the man applies for the values given in the figure? Find the mechanical advantage of the wheelbarrow? Ignore the weight of wheelbarrow.

Solution: From the figure we can see that dL = 40cm = 0.4 m, dF = 120cm = 1.2m and L = 600N. Thus, using the levers equation

we can work out the force F.

The mechanical advantage of this wheelbarrow is

**1.4.3 Third class levers**

*A third class lever *has the force between the load and the fulcrum, as shown in the figure below

A third class lever also obeys the law of the lever

Sugar tongs, tweezers, forearm etc. are good examples of third class levers.

Sugar tongs and tweezers (third class lever)

Forearm (third class lever)

Example: Calculate the force needed to catch a 20g ball using the tweezers as in the figure above if the length of tweezers is 9 cm and the force is exerted at a point 6 cm from the turning point. What can you say about mechanical advantage of these tweezers? (Take the approximate value of 10 m/s^{2} for gravity in this example).

Solution: first, we have to work out the load L which is equivalent to the weight W. Giving that mass m = 20g = 0.02 kg, we obtain

Now, using the equation of levers

Substituting the values dL = dtotal = 9cm = 0.09m and dF = 6cm = 0.06m, we obtain

The mechanical advantage is

In this case the mechanical advantage is less than 1. This means the force needed to lift the load is greater than the load itself. For this reason, one may think this type of lever is useless as we have to use a greater force than needed to lift the load. However, third class levers are usually used to lift light objects. Thus, the force is also small.

The usefulness of third class levers consist on the fact that they are used when no other options are available. Ethics is also a reason why we use third class levers. It is not ethical

catching the sugar lumps with fingers. On the other hand, you cannot use the hands to move a burning wooden block but you would use tongs for this.

**Important note**: In all the above examples, the weight of levers was not mentioned. It is either very small to be taken in consideration, or it was taken together with the load.

**1.5 Finding the correct approach on the questions involving levers**

The diagram below represents a guide on how to approach the questions about levers.

**1.6 Summary**

Levers are one of the simplest types of simple machines. As such, they possess the main properties of simple machines, i.e.:

The equilibrium is established when the turning effects (moments) caused by the two forces applied at the given distances from the turning point, cancel each other. In simplest words, the condition of equilibrium in this case is

Total clockwise moment of force=Total anticlockwise moment of force

In symbols,

where

L is the load in Newtons,

F is the force in Newtons,

d_{L} is the distance from the load to the fulcrum, and

d_{F}is the distance from the force to the turning point.

The above equation is known as the equation of levers.

We determine the class of the lever by noting the relative positions of the load (L), pivot (P) and force (F).

The three possible combinations are:

Mechanical advantage is an important quantity that shows how easily one can lift a load using the lever rather than carrying it by hand. It is calculated by the equation

In first and second class levers, mechanical advantage is greater than 1, while in the third class levers mechanical advantage is less than 1. This means that in third class levers we have to use a greater force than the load. However, they are very useful in certain situations.