Machines

Q: Define mechanical advantage and velocity ratio. Why do neither of them have a unit?

Mechanical advantage is the ratio of the load to the effort; velocity ratio is the ratio of the velocity of the effort to the velocity of the load, or the distance moved by the effort to the distance moved by the load in the same time. Each is a ratio of two quantities of the same kind (two forces, or two distances), so the units cancel.

Q: State four purposes for which a simple machine is used, with one example of each.

As a force multiplier (a car jack); to change the direction of the effort (a single fixed pulley on a well); to gain speed (fire tongs or a fishing rod); to apply the effort at a convenient point (a hand-pump handle or a spanner).

Q: Derive the relation between the efficiency, mechanical advantage and velocity ratio of a machine.

η = Wo / Wi = (L dL)/(E dE) = (L/E) ÷ (dE/dL) = MA/VR.

Q: Why is the mechanical advantage of a practical machine always less than its velocity ratio?

Some work input is always wasted against friction and in lifting the moving parts, so η < 1. Since MA = η × VR, MA must be less than VR.

Q: A machine is oiled so that friction falls. What happens to its MA, VR and efficiency?

MA increases, because a smaller effort is needed for the same load. VR is unchanged, because it depends only on the geometry of the machine. Efficiency increases, since η = MA/VR.

Q: Name the class of each lever and say what lies in the middle: (a) a pair of scissors, (b) a nutcracker, (c) a pair of sugar tongs.

(a) First class, fulcrum in the middle. (b) Second class, load in the middle. (c) Third class, effort in the middle.

Q: Why is the MA of a second class lever always greater than 1, and that of a third class lever always less than 1?

In a second class lever the load lies between the fulcrum and the effort, so the effort arm is always longer than the load arm and MA = lE/lL > 1. In a third class lever the effort lies between the fulcrum and the load, so the effort arm is always shorter and MA is less than 1.

ICSE Class 10 · Physics · Chapter 3

What this chapter covers

Machines as force multipliers
Mechanical advantage
Velocity ratio
Work input, work output and efficiency
Relation between efficiency, mechanical advantage and velocity ratio
The lever and its principle
The three classes of levers
Levers in the human body
Single fixed pulley
Single movable pulley
Block and tackle system

Key definitions

Effort is the force applied to a machine to make it do useful work, and it is written as E.

Load is the resisting force that a machine overcomes, such as the weight lifted or the friction pushed against, and it is written as L.

Mechanical advantage is the ratio of the load to the effort for a machine, and it is written as MA.

Velocity ratio is the ratio of the velocity of the effort to the velocity of the load in a machine, and it is written as VR.

Work input is the work done on a machine by the effort, equal to the effort multiplied by the distance moved by the effort, and it is written as W_i.

Work output is the work done by a machine on the load, equal to the load multiplied by the distance moved by the load, and it is written as W_o.

Efficiency is the ratio of the useful work output to the work input of a machine, and it is written as η (the Greek letter eta).

An ideal machine is a machine whose moving parts are weightless and frictionless, so that its work output equals its work input and its efficiency is 1, or 100%.

The fulcrum is the fixed point about which a lever turns.

The effort arm is the perpendicular distance of the line of action of the effort from the fulcrum.

The load arm is the perpendicular distance of the line of action of the load from the fulcrum.

A first class lever is a lever in which the fulcrum lies between the effort and the load.

Key points

A machine lets an effort applied at one point overcome a load at another point more conveniently; it never gives more work than is put in.
Simple machines are used as force multipliers, to change the direction of effort, to gain speed, or to apply effort at a convenient point.
Mechanical advantage MA = L/E; velocity ratio VR = V_E/V_L = d_E/d_L; both have no unit.
Work input W_i = E × d_E, work output W_o = L × d_L, and efficiency η = W_o/W_i.
η = MA/VR, so MA = η × VR; for every practical machine η < 1 and MA < VR; for an ideal machine MA = VR.
Friction and the weight of moving parts lower MA and efficiency but never change VR.
The principle of a lever: load × load arm = effort × effort arm; for an ideal lever MA = VR = effort arm / load arm.
First class: fulcrum in the middle, MA can be more than, equal to or less than 1 (scissors, crowbar, beam balance).
Second class: load in the middle, MA always more than 1 (wheelbarrow, nutcracker, bottle opener).
Third class: effort in the middle, MA always less than 1, used for speed (fire tongs, fishing rod, forearm).
In the body: nodding the head is first class, rising on the toes is second class, lifting with the forearm is third class.
Single fixed pulley: VR = 1, ideal MA = 1; it only changes the direction of effort.
Single movable pulley: VR = 2, ideal MA = 2; with pulley weight w, E = (L + w)/2.
Block and tackle with n pulleys: VR = n, ideal MA = n; with lower block weight w and no friction, η = L/(L + w).

Questions answered

Define mechanical advantage and velocity ratio. Why do neither of them have a unit?

Mechanical advantage is the ratio of the load to the effort; velocity ratio is the ratio of the velocity of the effort to the velocity of the load, or the distance moved by the effort to the distance moved by the load in the same time. Each is a ratio of two quantities of the same kind (two forces, or two distances), so the units cancel.

State four purposes for which a simple machine is used, with one example of each.

As a force multiplier (a car jack); to change the direction of the effort (a single fixed pulley on a well); to gain speed (fire tongs or a fishing rod); to apply the effort at a convenient point (a hand-pump handle or a spanner).

Derive the relation between the efficiency, mechanical advantage and velocity ratio of a machine.

η = W_o / W_i = (L d_L)/(E d_E) = (L/E) ÷ (d_E/d_L) = MA/VR.

Why is the mechanical advantage of a practical machine always less than its velocity ratio?

Some work input is always wasted against friction and in lifting the moving parts, so η < 1. Since MA = η × VR, MA must be less than VR.

A machine is oiled so that friction falls. What happens to its MA, VR and efficiency?

MA increases, because a smaller effort is needed for the same load. VR is unchanged, because it depends only on the geometry of the machine. Efficiency increases, since η = MA/VR.

Name the class of each lever and say what lies in the middle: (a) a pair of scissors, (b) a nutcracker, (c) a pair of sugar tongs.

(a) First class, fulcrum in the middle. (b) Second class, load in the middle. (c) Third class, effort in the middle.

Why is the MA of a second class lever always greater than 1, and that of a third class lever always less than 1?

In a second class lever the load lies between the fulcrum and the effort, so the effort arm is always longer than the load arm and MA = l_E/l_L > 1. In a third class lever the effort lies between the fulcrum and the load, so the effort arm is always shorter and MA is less than 1.

Give one example of each class of lever in the human body, naming the fulcrum.

First class: nodding the head, fulcrum at the joint of the skull with the top of the spine. Second class: rising on the toes, fulcrum at the balls of the feet. Third class: lifting a load with the forearm, fulcrum at the elbow.

Past board exam questions

ICSE 2027 sample paper · 1 mark

The Velocity Ratio (V.R.) of a block and tackle system of three pulleys with the effort in upward direction is:

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ICSE 2027 sample paper · 2 marks

Match the movement of the body part in Column A to the class of lever in Column B. | Column A | Column B | |---|---| | (a) Nodding head | 1. Class III | | (b) Lifting body weight on your toes | 2. Class II | | | 3. Class I |

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(a) Nodding head – 3. Class I (the fulcrum, at the top of the spine, lies between the load and the effort) (b) Lifting body weight on your toes – 2. Class II (the load lies between the fulcrum at the toes and the effort of the calf muscles)

ICSE 2027 sample paper · 3 marks

A bar of length 120 cm is used as a lever to raise a load placed at point P. Seven equidistant points are marked along the bar: P, Q, R, S, T, U, and V, each 20 cm apart. You are permitted to place the fulcrum at any of the marked points and exert the effort at a different point. (The load acts downward at P, at one end of the bar; V is at the other end.) (a) Specify the fulcrum and effort points that yield the greatest mechanical advantage. (b) Based on the lever arrangement identified in part (a), calculate the maximum mechanical advantage using the distances given. (c) To which class of lever does this arrangement belong?

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(a) Fulcrum at Q and effort at V. (b) Load arm = PQ = 20 cm; effort arm = QV = 100 cm. M.A. = effort arm/load arm = 100/20 = 5. (c) Class I lever (the fulcrum is between the load and the effort).

ICSE 2026 sample paper · 1 mark

Anita used a single movable pulley to lift a bucket of water from a well. She lubricates the pulley. Which of the following statements is true regarding the performance of the pulley used?

Mechanical Advantage decreases and efficiency increases.
Velocity Ratio increases and efficiency decreases.
Mechanical Advantage remains unchanged and efficiency increases.
Velocity Ratio remains unchanged and efficiency increases.

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Velocity Ratio remains unchanged and efficiency increases.

ICSE 2026 sample paper · 6 marks

Complete the following by choosing the correct answers from the bracket: (a) A ___________ [Class II/Class III] lever will always have M.A. > 1. (b) A boy uses a GPS device to locate his missing friend in a crowded area; the system primarily uses __________ [ultraviolet waves / microwaves] to track the location. (c) Unit of specific heat capacity is _______. [kg²m²s⁻²K⁻¹ / m²s⁻²K⁻¹] (d) The threshold of hearing is __________. [0dB, 20Hz] (e) Two copper wires can have different resistivity if they have different __________. [lengths / temperatures] (f) The reaction responsible for the production of energy in the sun is __________. [Nuclear Fusion / Nuclear Fission]

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(a) Class II (the effort arm is always longer than the load arm) (b) microwaves (c) m²s⁻²K⁻¹ (J kg⁻¹ K⁻¹ = kg m² s⁻² kg⁻¹ K⁻¹) (d) 0dB (e) temperatures (resistivity depends on the material and its temperature, not on length) (f) Nuclear Fusion

ICSE 2026 sample paper · 2 marks

Match the movement of the body part in Column A to the class of lever in Column B. | Movement of the body part (Column A) | Class of lever (Column B) | |---|---| | (a) Nodding head | Class III | | (b) Lifting body weight on your toes | Class II | | | Class I |

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(a) Nodding head → Class I (the fulcrum, at the joint of the skull and the spine, lies between the effort of the neck muscles and the load, the weight of the head). (b) Lifting body weight on your toes → Class II (the fulcrum is at the toes, the load—body weight—acts between the toes and the heel, and the effort is applied by the calf muscles at the heel).

ICSE 2026 board paper · 2 marks

Case 1: Lata cuts a potato into two halves, using a cutter which belongs to a Class II lever. She needed effort E1. Case 2: Then she cuts one half of this potato again, but this time she needed effort E2. If E1 > E2 then: (a) In which case (1st or 2nd) was the potato closer to her hand applying the effort? (Assume normal reaction of the surface of the potato is same in both cases) (b) Give a reason for your answer in (a) above.

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(a) Case 1 (1st). (b) In a class II lever the load (potato) lies between the fulcrum and the effort, and by the principle of moments E × effort arm = L × load arm. The effort arm and the load (resistance) are the same in both cases, so the larger effort E1 means a longer load arm: the potato was farther from the fulcrum, i.e. closer to her hand, in case 1.

ICSE 2026 sample paper · 3 marks

A block and tackle system of pulleys has velocity ratio 4. (a) Draw a labelled diagram of the system indicating clearly, the direction of the load and effort. (b) Calculate the potential energy gained by load of 100 kgf, lifted by this pulley to a height of 5 m. (g = 10 ms⁻²)

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(a) Diagram: an upper block with two pulleys fixed to a rigid support and a lower movable block with two pulleys carrying the load L (arrow downwards). One end of a single string is tied to the hook of the upper block; the string passes alternately round the pulleys of the lower and upper blocks, so that 4 segments of string support the lower block, and the free end comes down from the upper block, where the effort E is applied downwards. The tension T in each segment is marked (acting upwards on the lower block). (b) Load = 100 kgf, so m = 100 kg U = mgh = 100 × 10 × 5 = 5000 J