1. Simple Machines

2.  MACHINE A machine is a device by means of which work can be performed easily or in a convenient manner. A machine can be used : To lift heavy loads by applying little force. To enlarge magnitude of force To increase rate of work done To change the direction of force Example of simple machines are : Lever, pulley, inclined plane, wedge, screw etc.  EFFORT OR POWER The power directly applied to a machine to lift a load is called Effort or Power. It is denoted by ‘P’.  LOAD OR WEIGHT The weight lifted by a machine is called Load. It is denoted by ‘W’.

3.  The ratio of weight (load) lifted by a machine to the force(effort) applied on a machine is called mechanical advantage of the machine. Greater the value of mechanical advantage of a machine, more easier is the work done. Mathematically,  M.A = load/effort  OR  M.A = W/P  UNIT:  It has no unit.  INPUT  Amount of work done on a machine by a given effort (force) is called input of a machine.  Input = effort x distance through which effort acts OR  input = P x d  OUTPUT  Amount of work done by a machine on the load (weight) is called output of the machine.  Output = load x distance covered by the load OR  Output = W x D  EFFICIENCY  The ratio of output of a machine to the input of machine is called its efficiency.  h = output/input h = (W x D)/(P x d) Efficiency in h = (W x D)/(P x d )x100  UNIT:  It has no unit.

4. An ideal machine is a hypothetical machine whose output is equal to its input. For an ideal machine  output = input  Efficiency of an ideal machine is 100% because there is no loss of energy in an ideal machine due to friction or any other means that can waste useful energy.  M.A of an ideal machine is d / h.

5.  Lever is a simple machine which is used to lift heavy bodies or heavy load in a very easy way. Lever consists of a rigid bar capable to rotate about a fixed axis called fulcrum. Effort is applied at one end of the bar and weight can be lifted from the other end.

6.  There are three kinds of lever depending upon the positions of load, effort and fulcrum.  FIRST KIND OF LEVER  In the first kind of lever, the fulcrum F lies between effort (P) and load (W). SECOND KIND OF LEVER In the second kind of lever, load (W) lies between effort (P) and fulcrum (F). THIRD KIND OF LEVER In the third kind of lever, effort (P) lies between load (W) and fulcrum (F). Example: forceps, jaws, human forearm, firetong.

7.  Consider the example of a lever of 1st kind. In equilibrium position torque of effort is always equal to the torque of load. I.e. Clockwise torque = Anti clockwise torque Torque of effort = torque of load OR effort x effort arm = weight x weight arm P x OA = W x OB OA = W x OB/P W/P = OA/OB but [W/P = M.A.] M.A = OA/OB OR M.A. = Effort arm / weight arm This equation shows that mechanical advantage of lever can be increased: By increasing effort arm. By decreasing weight arm

8.  A pulley is a simple machine. It consists of a wheel mounted on an axis which is fixed to a frame called block. The wheel is free to rotate. With the help of pulley we can lift heavy loads very easily by applying little force and also change the direction of force. FIXED PULLEY If the block of the pulley is fixed to a strong beam or ceiling, the pulley will not move and is called a “Fixed Pulley”.

9.  In fixed pulley, the effort ‘P’ is applied which is equal to the load ‘W’, if we ignore weight of rope and force of friction between rope and pulley then :  effort = load  P = W  Dividing both sides by P  P/P = W/P W/P = 1  Since [W/P = M.A]  M.A = 1  This shows that fixed pulley can only change the direction of force but it will lift load equal to the effort applied on it.

10.  In a moveable pulley, one end of the rope which passes around the pulley is tied to a firm support ‘O’ and effort ‘P’ is applied to the other end. The load is hung from the hook of the block. As the load is applied by two segments of rope,  the effort becomes twice of the applied value i.e. EFFORT = 2 x P In equilibrium condition we have Load = Effort W = 2P Dividing both sides by P W/P = 2 but [W/P = M.A] thus M.A. = 2 This shows that a moveable pulley can lift a load double the effort.

11.  Any smooth plane surface which makes an angle q with the horizontal surface is called an “Inclined plane”. Where 0 o < q <90 o or values of q lies between 0 o and 90 o USES OF INCLINED PLANE It is a simple machine and is used to raise heavy loads by applying little effort.

12.  In the figure AB is an inclined plane which makes an angle q with the horizontal plane. A load ‘W’ is being raised from A to B by applying an effort ‘P’. If we neglect the force of friction between load and inclined plane  Output = input Weight x height = effort x distance W x h = P x L W*h/P = L W/P = L/h OR W/P = 1/h/L in right angled DOAB Sin q = OB/AB Sin q = h/L [ perpendicular/hypotenuse = sinq] therefore W/P = 1/sinq but [W/P = M.A.] Thus M.A. = 1/sinq  This expression shows that mechanical advantage of an inclined plane depends upon the value of sinq.

13.  It is a simple machine and is used to lift heavy loads. It has a wheel of larger radius (R) and an axle of smaller radius (r) fixed on the same shaft. Wheel and axle are free to rotate about its shaft.

14.  The effort is applied to the rim of the wheel and the load is raised by a rope wound around the axle.  In one rotation wheel covers a distance of 2pR  In one rotation load is raised by a distance of 2pr  If we neglect force of friction,  Output = input W x 2pr = P x 2pR W/P = 2pR/2pr W/P = R/r  Since [W/P = M.A.]  M.A. = R/r OR M.A. = radius of wheel / radius of axle  This expression indicates that in order to increase the mechanical advantage Radius of :wheel must have a large value. Radius of axle must be smaller than that of wheel.

15.  Wedge is also a type of simple machines. It is used in levers as a fulcrum. It is also used for splitting the wood in to small pieces. It is used as an Ax.  CONSTRUCTION OF WEDGE  A wedge is made of two inclined planes joined together. The effort ‘P’ is applied on the top of the wedge placed over a wood log. The wedge enters the wood and splits it. The reaction forces R1 & R2 are acting perpendicular on the inclined planes of the wedge. These forces and resultant frictional forces are responsible for keeping the wedge inside the wood firmly.

16.  Let us consider that the wedge is in equilibrium under the action of forces three forces R1, P and R2 and neglecting frictional forces. According to figure below the forces P, R1 and R2 are represented by the sides of D XYZ such that effort P the reaction R1 and R2 are represented by XY, YZ, ZX which are the sides of,D XYZ respectively. Mechanical advantage(M.A). = load/effort For equal sides of wedge i.e. = R1 = R2 = R M.A. = R/P M.A = ZX/XY Triangle ABC and triangle XYZ are similar, therefore, ZX=AC and XY=BC M.A. = AC/BC Mechanical advantage = length of inclined surface of wedge/thickness of wedge From above expression it is clear that if the thickness of the wedge is decreased the mechanical advantage of the wedge will increase & if the wedge is more sharper, then the mechanical advantage will increase.

17.  Screw is one of the most important machines. It is used to hold different parts of machines together. It has waste applications in our daily life plus in industries. It is used in every type of device. CONSTRUCTION AND WORKING It simply consists of a threaded rod with a head known as “Screw head”. It has a number of threads. The perpendicular distance between two adjacent threads is known as pitch of screw. The thread of screw can be regarded as a continuous inclined plane wrapped round a cylinder of radius d.

18.  If we apply an effort ‘P’ on the head of screw then it turns one revolution and at the same time the screw moves forward in to the wood or wall through a distance equal to its pitch “h”. The effort ‘P’ moves through a distance 2  d. The screw remains in the wood due to frictional forces between the screw and the wood. A large amount of energy changes in to heat energy during the process of screwing. Let us assume an ideal case when there is no loss of energy then;in this condition  Output = input P x 2  d = W x h W/P = 2  d /h  Hence, the mechanical advantage of the screw will be.  M.A. = 2pd /h  The mechanical advantage of the screw depends upon the following factors. PITCH: In order to increase mechanical advantage of screw we must use a screw of small pitch. RADIUS OF SCREW: Larger is the radius of screw head, greater is the mechanical advantage.

19.  A screw jack is a simple machine. It is used to lift cars or heavy automobiles. It consists of a long screw rod which passes through a threaded block B and a handle. The distance between two consecutive thread is known as pitch of screw.

20.  When an effort is applied to the handle, the effort moves in a circle of radius “d” while “d” is the length of the rod and the block “B” moves up equal to the pitch of the screw jack. If the handle is turned through one complete revolution in a circle of radius “d” the effort moves through a distance 2pd and consequently the load is raised through a height h. Hence, the mechanical advantage is given by:  M.A. = 2pd/h M.A. = Distance through which the effort is moved/height through which the load is raised  We know that the pitch of the screw is very small as compared to the length of the rod, so the mechanical advantage should be very large. Due to frictional force between the different parts of screw jack, the efficiency is less than one. It is due to the reason that a lot heat energy is used for over coming the frictional forces. It should be remembered that in case of screw jack friction is a necessary part of operation, because in the absence of friction, it would unwind at once when applied force is removed.