Example 01:

In a lever, the effort arm is 60 cm and load arm is 40 cm. Find its mechanical advantage:

Given: Effort arm = E.A. = 60 cm, Load arm = L.A. = 40 cm

To Find: Mechanical advantage = M.A. =?

Solution:

M.A. = E.A. / L.A. = 60 /40 = 1.5

Ans: Mechanical advantage of lever is 1.5

Example 02:

A crowbar of length 120 cm has its fulcrum situated at a distance of 20 cm from the load. Calculate the mechanical advantage of the crowbar.

Crowbar is class I lever

Given: Effort arm = E.A. = 100 cm, Load arm = L.A. = 20 cm

To Find: Mechanical advantage = M.A. =?

Solution:

M.A. = E.A. / L.A. = 100 /20 = 5

Ans: Mechanical advantage is 5

Example 03:

A pair of scissors has its blades 15 cm long, while its handles are 7.5 cm long. Find its mechanical advantage:

Given: Effort arm = E.A. = 7.5 cm, Load arm = L.A. = 15 cm

To Find: Mechanical advantage = M.A. =?

Solution:

M.A. = E.A. / L.A. = 7.5 /15 = 0.5

Ans: Mechanical advantage of is 0.5

Example 04:

A pair of scissors has its blades 15 cm long, while its handles are 7.5 cm long. Find its mechanical advantage:

Given: Effort arm = E.A. = 7.5 cm, Load arm = L.A. = 15 cm

To Find: Mechanical advantage = M.A. =?

Solution:

M.A. = E.A. / L.A. = 7.5 /15 = 0.5

Ans: Mechanical advantage of is 0.5

Example 05:

If the mechanical advantage of a lever is 10, Find the effort required to lift a box weighing 2500 N?

Given: Mechanical advantage = M.A. = 10, Load = W = 2500 N

To Find: Effort = P =?

Solution:

M.A. = W/P

P = W/M.A. = 2500/10 = 250 N

Ans: Effort required is 250 N

Example 06:

If a lever has a mechanical advantage of 0.5, and a person weighing 600 N sat on the effort arm, how heavy of a person could be lifted who sat on the other end?

Given: Mechanical advantage = M.A. = 0.5, Effort = P = 600 N

To Find: Load = W =?

Solution:

M.A. = W/P

W = M.A. x P = 0.5 x 600 = 300 N

Ans: A person of weight 300 N can be lifted.

Example 07:

A force of 50 N is required to cut a metal sheet. A shears used for cutting the metal sheet has its blades 5 cm long, while its handle is 10 cm long. What effort is needed to cut the sheet?

Given: Load = W = 50 N, Effort arm = E.A. = 10 cm, Load arm = L.A. = 5 cm

To Find: Effort = P =?

Solution:

Mechanical advantage = Effort arm/Load arm

M.A. = 10 / 5 = 2

Now, M.A. = W/P

P = W/M.A. = 50/2 = 25 N

Ans: Effort needed to cut sheet is 25 N.

Example 08:

A crowbar 2 m long is pivoted about a point 10 cm from its tip. What is the least force which must be applied at the other end to displace a load of 1000 N.

Given: Load = W = 1000 N, Effort arm = E.A. = 2 m – 10 cm = 1.9 m, Load arm = L.A. = 10 cm = 0.1 m.

To Find: Effort = P =?

Solution:

Mechanical advantage = Effort arm/Load arm

M.A. = 1.9 / 0.1 = 19

Now, M.A. = W/P

P = W/M.A. = 1000/19 = 52.6 N

Ans: Effort = 52.6 N.

Example 09:

The diagram below shows a lever in use. (a) To which class of lever does it belong? (b) If AB =1 m, AF= 0.4 m, find its mechanical advantage. (c) Calculate the value of E.

Solution:

The fulcrum lies between the effort and load, hence it is class I lever.

M.A. = E.A / L.A. = 0.6/0.4 = 1.5

M.A. = W/P

P = W/M.A. = 150/1.5 = 100 N

Ans: It is class I lever, mechanical advantage is 1.5, and effort required to lift 150 N load is 100 N.

Example 10:

The diagram below shows a lever in use. (a) To which class of lever does it belong? (b) If AB =1.2 m, AF= 0.2 m, find its mechanical advantage. (c) Calculate the value of E.

Solution:

The fulcrum lies between the effort and load, hence it is class I lever.

M.A. = E.A / L.A. = 1/0.2 = 5

M.A. = W/P

P = W/M.A. = 180/5 = 36 N

Ans: It is class I lever, mechanical advantage is 5, and effort required to lift 180 N load is 36 N.

Example 11:

A man uses a crowbar of length 1.5 m to raise a load of 750 N by putting a sharp edge below the bar at a distance 1 m from his hand. (a) Draw a diagram of the arrangement showing the fulcrum (F), load (L) and effort (E) with their directions. (b) State the kind of lever. (c) Calculate i) mechanical advantage and (ii) the effort needed.

Solution:

The fulcrum lies between the effort and load, hence it is class I lever.

M.A. = E.A / L.A. = 1/0.5 = 2

M.A. = W/P

P = W/M.A. = 750/2 = 375 N

Ans: It is class I lever, mechanical advantage is 2, and effort required to lift 750 N load is 375 N.

Example 12:

A pair of scissors is used to cut a piece of a cloth by keeping it at a distance 8.0 cm from its rivet and applying an effort of 100 N by fingers at a distance 2.0 cm from the rivet. (a) Find: (i) the mechanical advantage of scissors and (ii) the load offered by the cloth. (b) How does the pair of scissors act: as a force multiplier or as a speed multiplier?

Given: Load arm = L.A. = 8.0, Effort arm = E.A. 2.0 cm, Effort = P = 100 N,

To Find: Mechanical advantage = M.A. =?, Load = W = ?

Solution:

M.A. = E.A / L.A. = 2.0/8.0 = 0.25

M.A. = W/P

W = P x M.A. = 100 x 0.25 = 25 N

As M.A. < 1 scissor is acting as speed multiplier

Ans: Mechanical advantage is 0.25, and load offered by cloth is 25 N. The scissor is acting as speed multiplier.

Example 13:

A lever of length 9 cm has its load arm 5 cm long and the effort arm is 9 cm long. (a) To which class does it belong? (b) Draw diagram of the lever showing the position of fulcrum F and directions of both the load L and effort E. (c) What is the mechanical advantage and velocity ratio if the efficiency is 100%? (d) What will be the mechanical advantage and velocity ratio if the efficiency becomes 50%?

Given: Load arm = L.A. = 5cm, Effort arm = E.A. = 9 cm,

To Find: M.A. =? V.R. =? When Efficiency = 100 %, M.A. =? V.R. =? When Efficiency = 50 %

Solution:

In this case, effort arm is equal to lever length and it is also more than the load arm. it means load is between fulcrum and effort. It is class II lever.

M.A. = E.A./L.A. = 9/5 = 1.8

Efficiency = (M.A/V.R.) x 100

V.R. = (M.A. x 100)/Efficiency

When efficiency is 100%

V.R. = (1.8. x 100)/100 = 1.8

When efficiency is 50%

V.R. remains the same, M.A. decreases

M.A.. = (Efficiency x V.R.)/100

M.A. = (50 x 1.8)/100 = 0.9

Ans: When efficiency is 100 %, M.A. = 1.8 and V.R. = 1.8

When efficiency is 50 %, M.A. = 0.9 and V.R. = 1.8

Example 14:

The diagram below shows a lever in use. (a) To which class of lever does it belong? (b) If FA = 80 cm, AB = 20 cm, find its mechanical advantage. (c) Calculate the value of E

Solution:

In this case, the effort is between the fulcrum and the load, it is class III lever.

L.A. = 80 + 20 = 100 cm

M.A. = E.A./L.A. = 80/100 = 0.8

M.A. = W/P

P = W/M.A. = 50/0.8 = 62.5 N

Ans: It is a class III lever, M.A. = 0.8, Effort = 62.5 N

Example 14:

The diagram below shows a lever in use. (a) To which class of lever does it belong? (b) If FA = 80 cm, AB = 20 cm, find its mechanical advantage. (c) Calculate the value of E if load is 50 N

In this case, the load is between the fulcrum and the effort, it is class II lever.

E.A. = FA + AB = 80 + 20 = 100 cm

M.A. = E.A./L.A. = 100/80 = 1.25

M.A. = W/P

P = W/M.A. = 50/1.25 = 40 N

Ans: It is a class II lever, M.A. = 1.25, Effort = 40 N

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A simple machine is a mechanical device that makes our life easier. If a force is applied at one point, the simple machine transmits it to another point with a convenient change of magnitude and direction. In this article we shall study the terminology associated with the simple machines.

Types of Machine:

The basic machines are

• Lever
• Inclined plane
• Pulley (Special case of levers)
• Wheel and axle (Special case of levers)
• Wedge (Special case of the inclined plane)
• Screw (Special case of the inclined plane)
• Gear

Functions of Simple Machine:

• Applying force at a convenient point: Instead of applying force directly to the wheels of a bicycle, it is easier and more convenient to apply it to the pedals.
• Applying force in a convenient direction: It is difficult to lift a bucket full of water directly, but the task becomes very easy if the force is applied in a downward direction using a pulley.
• By applying small effort to lift large loads: In such case machine is said to be used as a force multiplier. e.g. a screw jack used to lift a car or a truck.
• To change the speed of motion of a body: In such a case the machine is said to be used as a speed multiplier. e.g. Gears in an automobile are used to change the speed of the automobile.

Defining a Simple Machine:

Depending upon the above mentioned functions of simple machines we can define simple machine as follows: “A simple machine is a device by which we can either overcome a large resistive force (or load) at some point by applying a small force (or an effort) at convenient point and in a desired direction or by which we can obtain a gain in speed”.

Terminology:

Load (L):

A resistive force to be overcome by a machine is called a load. Its S.I. unit is newton (N)

Effort (E):

An external force applied to a simple machine to overcome a load is called an effort. Its S.I. unit is newton (N)

Load Point:

The point where the energy is obtained by overcoming the load, is called the load point.

Effort Point:

The point at which the energy is supplied to a machine by applying the effort, is called the effort point.

Mechanical Advantage (M.A.):

The ratio of load (L) to overcome to the magnitude of the effort (E) is called a mechanical advantage. It is also called as leverage.

As it is ratio of same type of physical quantities, the mechanical advantage is unit less and dimension less quantity.

• If the effort needed is less than the load, the machine has mechanical advantage greater than 1. In such case the machine acts as a force multiplier.
• If the effort needed is greater than the load, the machine has mechanical advantage less than 1. In such case the machine helps in gaining speed.
• If the effort needed is equal to the load, the machine has mechanical advantage equal to 1. Generally, in such cases the machine is used to change the direction of the effort.

Velocity Ratio:

The ratio of a distance travelled by the effort to the distance travelled by the load in given time is called velocity ratio.

As it is ratio of same type of physical quantities, the velocity ratio is unit less and dimension less quantity.

• If the distance travelled effort is more than the distance travelled by load, the machine has velocity ratio greater than 1. In such case the machine acts as a force multiplier.
• If the distance travelled effort is less than the distance travelled by load, the machine has velocity ratio less than 1. In such case the machine helps in gaining speed.
• If the distance travelled effort is equal to the distance travelled by load, the machine has velocity ratio equal to 1. Generally, in such cases the machine is used to change the direction of the effort.

Work Input:

The energy supplied to a machine is called work input. Its S.I. unit is joule (J).

Work Input = Effort (E) X Distance traveled by an effort (s)

Work Output:

The useful work done by a machine is called work output. Its S.I. unit is joule (J).

Work Output = Load (L) X Distance traveled by a load (l)

Efficiency:

The ratio of the useful work output to the actual work input of the machine is called efficiency.

For a machine, of a given design, the velocity ratio does not change, but due to friction and weight of the moving parts of machine mechanical advantage and the efficiency decrease.

Ideal Machine:

Ideal machine is that machine in which there is no loss of energy in any manner i.e. the work output is equal to the work input.

Thus, for ideal machine the mechanical advantage of the machine is equal to its velocity ratio and the efficiency of the machine is 100%. In practice there is no ideal machine because for every machine the output energy is always less than the input energy. Thus there is a loss of energy in using the machine.

Actual Machine:

Actual machine is a machine in which the output energy is always less than the input energy i.e. there is a loss of energy in using the machine.

Thus, for actual machine the efficiency is always less than 100%. Thus efficiency of machine is 80% means 20% of the input energy is lost in machine and only 80 % of input energy is converted into useful work.

The reasons for loss of energy in using the machine are as follows:

• The friction between different moving parts in the machine,
• The different parts of machine are not perfectly rigid,
• The string used in machine is not perfectly elastic,
• The different parts of machine have some weight (inertia), and
• The different parts used in machine are not smooth

Principle of a Machine:

 The work output of a machine is equal to the work input. In practice work output of machine is not equal to the work input. Work output of machine is always less than the work input.

Example – 01:

In a machine an effort of 100 N is applied to lift a load of 1000 N. What is its mechanical advantage?

GivenEffort = P = 100 N, Load = W = 1000 N

To Find: Mechanical Advantage = M.A. =?

Solution:

M.A. = W/P = 1000/100 = 10

Ans: Mechanical advantage is 10.

Example 02:

A machine has mechanical advantage 5. It raises a load of 25 N. Calculate the minimum effort required.

Given: Mechanical advantage = M.A. = 5, Load = W = 25 N

To Find: Effort = P =?

Solution:

M.A. = W/P

P = W/M.A. = 25/5 = 5 N

Ans: Efforts required = 5 N

Example – 03:

The mechanical advantage of a machine is 2. It is used to raise a load of 150 N. What effort is needed?

Given: Mechanical advantage = M.A. = 2, Load = W = 150 N

To Find: Effort = P =?

Solution:

M.A. = W/P

P = W/M.A. = 150/2 = 75 N

Ans: Efforts required = 75 N

Example 04:

The mechanical advantage of a machine is 5. How much load it can exert for the effort of 20 N?

Given: Mechanical advantage = M.A. = 5, Effort = P = 20 N

To Find: Load = W =?

Solution:

M.A. = W/P

W = M.A. x P. = 5 x 20 = 100 N

Ans: Load = 100 N

Example 05:

The efficiency of a machine is 50 %. If 300 J of energy given to the machine. What is its output?

Given: Efficiency of machine = 50%, Input energy = 300 J

To Find: Output energy

Solution:

Efficiency = (Output / Input) x 100

Output = (Efficiency x Input) / 100

Output = (50 x 300)/100 = 150 J

Ans: Output of machine is 150 J

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A simple machine is a mechanical device that makes our life easier. If a force is applied at one point, the simple machine transmits it to another point with a convenient change of magnitude and direction. In this article we shall study the terminology associated with the simple machines.

Types of Machine:

The basic machines are

• Lever
• Inclined plane
• Pulley (Special case of levers)
• Wheel and axle (Special case of levers)
• Wedge (Special case of the inclined plane)
• Screw (Special case of the inclined plane)
• Gear

In this article, we shall study levers. Levers are the simplest kind of machine used in daily life.

• Lever: A rigid object that is used with an appropriate fulcrum point to multiply the mechanical force that can be applied to another object. A lever is a rigid, straight or bent bar which is capable of turning about a fixed axis. Lever is assumed to be weightless and frictionless.
• Fulcrum: It is an axis about which the lever turns and passes through a point of the lever.
• Effort Arm (E.A.): The distance between the effort and fulcrum is called an effort arm.
• Load Arm (L.A.): The distance between the load and fulcrum is called a load arm.

Principle of Lever:

Lever works on the principle of moments.

This is an expression for mechanical advantage of a lever.

Thus, mechanical advantage of a lever is equal to the ratio of the length of its effort arm to the length of its load arm.

This relation is also known as the law of levers.

• If effort arm = Load arm, then M.A. = 1
• If effort arm > Load arm, then M.A. > 1
• If effort arm < Load arm, then M.A. < 1

Thus, mechanical advantage of lever can be increased by increasing effort arm or decreasing load arm.

Types of Levers:

Depending upon the relative position of the load, the effort and the fulcrum levers have three types: a) Class I levers, b) Class II levers, and c) Class III levers.

Class – I (First Order) Lever:

In this type of levers the fulcrum lies between the load and the effort. It is to be noted that the fulcrum need not be at the midpoint between the load and the effort.

Examples: A see-saw, pliers, scissors, crowbar, Handle of a common water pump, bicycle hand brakes, claw hammer, nodding of human head, etc.

Characteristics of Class – I Lever:

• Fulcrum lies in between load and effort.
• If E.A. > L.A. then M.A. > 1 If E.A. < L.A. then M.A. < 1 If E.A. = L.A. then M.A. = 1
• Generally, this type of lever acts as a force (effort) multiplier.

Notes:

• When effort arm > Load arm, the mechanical advantage and velocity ratio are greater than 1 and the lever acts as a force multiplier. For example, in shears used to cut metal sheets have much longer handles as compared to its blades.
• When effort arm = Load arm, the mechanical advantage and velocity ratio are equal to 1. For example, in physical balance, the effort arm and load arm are equal in lengths.
• When effort arm < Load arm, the mechanical advantage and velocity ratio are less than 1 and it helps in gaining speed. For example, in a pair of scissors blades are longer  as compared to its handles.

Why there is a need of long handles for spanners?

Spanner is a class – I lever and we know if effort arm is greater than load arm, then M.A. > 1. When handle is long, small effort can be used to overcome large loads. Thus with longer handle oar, spanners can be used with less effort.

Why does oar used to row a boat has longer handle?

An oar used to row a boat is Class – I lever and we know if effort arm is greater than load arm, then M.A. > 1. When handle is long, small effort can be used to overcome large loads. Thus with longer handle oar, the boat can be rowed with less effort.

Explain why scissors for cutting cloth may have blades longer than the handles, but shears for cutting metals have short blades and long handles.

The cloth is thin, and can be cut very easily but here gain of speed is required, which is obtained by having mechanical advantage less than one. i.e. by making effort arm of smaller than the load arm. Hence scissors for cutting cloth may have blades longer than the handles.

Metal plates require large force to cut them. Hence here force multiplier is required, which is obtained by having mechanical advantage greater than one. i.e. by making effort arm of scissors larger than the load arm. Hence shears for cutting metal may have short blades and long handles.

Class – II (Second Order) Lever:

In this type of levers the Load is lies between the effort and the fulcrum.

Examples:Diving board, door knob, paddle, nut cracker, wheel barrow, bottle opener, oar of a boat. hand flour grinder,

Characteristics of Class – II Lever:

• Load lies in between fulcrum and effort.
• Effort arm is always greater than the load arm, hence the M.A. of class – II lever is always greater than 1. Thus Class II levers always act as force multiplier.
• This type of lever acts as a force (effort) multiplier.

What is a reason that the handle is provided at the rim of a hand flour mill?

A hand flour mill is a class – II lever, and we know that for class – II lever, the effort arm is always greater than the load arm. Hence M.A. > 1. Thus more mechanical advantage can be obtained by increasing effort arm. It can be done by providing the handle at the rim of the hand flour mill. Thus applying small effort, large loads can be overcome.

Class – III (Third Order) Lever:

In this type of levers the effort is applied between the load and the fulcrum.

Examples:Fire tong, boat paddle, Stapler, broom, fishing rod, Ice tong, tweezers, hammer

Characteristics of Class – III Lever:

• Effort lies in between fulcrum and load.
• Effort arm is always less than the load arm, hence the M.A. of class – III lever is always less than 1. Hence it is used for gaining speed. Larger displacement of load is obtained by small displacement of effort.
• This type of lever acts as a speed multiplier.

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