Classwork Series and Exercises {Physics- SS2}: Machines

Introduction

A machine is essentially a device or tool which allows a force (or effect) applied at one point to overcome a resisting force (or load) at another point.

Consider a simple machine such as a screw. We apply a small turning force at the head and the screw is able to move through a block of wood, against a large resisting force provided by the wood. Generally a machine enables us to overcome a large resistance or load by applying a small effort. A machine enables us to do work more easily and conveniently than it could be done without it. For example, it is easier to roll a drum of oil up an inclined plane onto a lorry than to raise it vertically without the inclined plane.

Examples of machines are the lever, pulleys, pliers, wheel barrows, nut crackers, the inclined plane, the wedge, wheel and axle, screw jack and so on. Many complicated machines are made up of two or more machines.

Before discussing the working principles of simple machines we need to define some terms that apply to the working of the machines.

Mechanical Advantage (MA) or Force Ratio (FR)

We define Effort as the force applied to a machine and Load as the force or resistance overcome by the machine. The ability of a machine to overcome a large load through a small effort is known as its Mechanical Advantage (MA) or Force Ratio. It is given by:

MA = Load/Effort

Suppose a load of 20 N is raised by an effort of 4 N, then

MA = Loads/Effort = 20/4 = 5

W e see that the MA is the ratio of the two forces, load and effort, hence it is sometimes referred to as Force Ratio. The load is the output force and the effort is the input force. Mechanical Advantage can also be defined by

MA = Output force/ Input force

The mechanical advantage of a machine is influenced by friction in the parts. In the presence of friction part of the effort applied will be used to overcome friction and another part will be used to overcome the resistance or lift a load. Hence more effort will be required to overcome a load. A machine that has no friction is called an ideal machine or a perfect machine.

This is defined as the ratio of the distances moved by the effort and load in the same time interval.

V.R = distance moved by effort (a)/distance moved by load (l)

The velocity ratio depends on the geometry of the machines. It is independent of friction. For an ideal or perfect machine, Work done by machine = work done on machine

\ load x distance moved by load = effort x distance moved by effort

Or load/effort = distance moved by effort (a)/ distance moved by load (l) = velocity ratio

Hence for an ideal or perfect machine mechanical advantage = velocity ratio.

Efficiency (E_f)

The efficiency (E_f) of a machine is defined as:

E_f = Useful work done by the machine/Work put into the machine

Usually, the efficiency of a machine is expressed as a percentage:

E_f = Useful work done by the machine/Work put into the machine x 100%

Since work (W) is given by

W = Load (L)/Effort (E) x distance moved by load (l)/distance moved by effort (e) x 100%

= L/E x l/e = L/E ¸ e/l

= Mechanical Advantage/Velocity x 100%

E_f = MA/VR x 100%

A perfect or ideal machine has 100% efficiency. This means that all the work done by the effort is wholly used to overcome the load. In practical machines the efficiency is usually less than 100% because of friction in the moving parts of the machine. In such practical machines, part of the effort applied is used to overcome frictional forces which are always present. Thus the useful work done by the machine is less than the work done by the effort on the machine.

Types of Machines

1. The Lever

 The lever is one of the simplest machines known. With it we can overcome a large resistance by the application of a small force.

It consists of a steel bar or rigid rod supported at the fulcrum or pivot about which it can rotate. An effort (E) applied at one point of the lever lifts a load (L) or overcomes a resistance at some other points.

The lever operates on the principle of moments.

Types of Levers

There are three classes of levers: First order, Second order and Third order. The classification is dependent on the relative positions of the effort, load and fulcrum.

The First Class Lever

In the first order of levers; the fulcrum or pivot is between the load and the effort. Examples of such levers are (i) the crowbar, a pair of scissors or pincers, claw hammers and pliers. Velocity ration is usually greater than 1 but could be less or equal to 1.

The Second Class Lever

The Third Class Lever

In a Type 3 Lever, the effort is between the pivot (fulcrum) and the load.

Examples of common tools that use a type 3 lever include:

 

The Pulley System

A pulley is a wheel with a groove along its edge, where a rope or cable can be placed. It uses the principle of applying force over a longer distance, and also the tension in the rope or cable, to reduce the magnitude of the necessary force. Complex systems of pulleys can be used to greatly reduce the force that must be applied initially to move an object.

The pulley is one of the so-called “simple machines” from which many more complex machines are derived. With a single fixed-axis pulley, the ideal mechanical advantage is just N=1. You get the convenience of being able to redirect the effort force F_e, so that you can stand clear of the load. With a suspended pulley as in the middle illustration, the upward forces in the two ropes is equal, and therefore each supports half of the load, giving an IMA of N=2.

With a four-pulley set as shown, you have four ropes supporting the load, so the effort force F_e that establishes the rope tension is just one-fourth of the load in the ideal case, so IMA=4. All these force relationships are obtained from the force equilibrium condition, which in this case just amounts to “forces up = forces down” at any cross-section of the system.

EXERCISES

Lets see how much you’ve learnt, attach the following answers to the comment below

A block and tackle system of pulleys consisting of 4 pulleys is used to raise a load of 500 N through a height of 20 m. If the total work done against friction in the pulley is equivalent to 800 J, calculate

1. The total work done by the effort A. 10000 J B. 10800 J C. 12000 J  D. 8000 J
2. The efficiency of the system A. 90 % B. 97 % C.  92.6 %  D. 40.5 %
3. The effort applied A. 176 N B. 145 N  C. 153 N  D. 167 N
4. How many classes of levers exist in this topic? A. One B. Two C.  Three  D. Four
5. Type one lever items include all, except A. Hammer’s claw B. Scissors  C. Screw Driver  D. Plier

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