CBSE Class 10 Physics Simple Machines Notes Set 14

Simple Machines

A simple machine is a device that lets us apply a force at a convenient point to overcome another force somewhere else. The force we apply is the effort P and the force we overcome is the load W. The ratio load / effort is the mechanical advantage (M.A.). It can be greater than, equal to or less than one depending on the machine. The five simple machines are the lever, pulley, inclined plane, wedge and screw.

The Lever and its Three Orders

A lever is a rigid bar that turns about a fixed point called the fulcrum F. In equilibrium, load × load arm = effort × effort arm, so M.A. = effort arm / load arm.

First order: the fulcrum lies between load and effort (scissors, crowbar, see-saw). M.A. may be more than, equal to or less than 1.

Second order: the load lies between the fulcrum and the effort (nut cracker, wheelbarrow). M.A. is always greater than 1.

Third order: the effort lies between the fulcrum and the load (charcoal tongs, forearm). M.A. is always less than 1; the gain is in speed and range of movement.

Pulleys, Wheel and Axle

A single fixed pulley only changes the direction of the effort, so M.A. = 1. A single movable pulley has two rope segments supporting the load, so M.A. = 2 for a light pulley; if the pulley weighs w, the effort is (W + w)/2. In the first system of pulleys, with n movable pulleys, M.A. = 2ⁿ. In a wheel and axle of radii R and r, M.A. = R / r because it is a first order lever whose effort arm is R and load arm is r.

The Inclined Plane

To lift a load W through a height h we may pull it along a ramp of length l. Without friction, W × h = P × l, so P = W h / l = W sin(angle) and M.A. = l / h = 1 / sin(angle). A gentle slope gives a large M.A. but the effort travels a long way. For a vertical plane, M.A. = 1.

The Screw and the Screw Jack

One full turn of a screw moves it forward by the pitch d, the distance between two neighbouring threads. If the effort acts at a radius r from the axis, one turn takes it through 2 π r, so M.A. = 2 π r / d. A long handle and a fine pitch give a large M.A., which is the principle of the screw jack used to lift cars.

Velocity Ratio and Efficiency

Velocity ratio V.R. = distance moved by the effort / distance moved by the load. By the principle of work, an ideal machine gives W d2 = P d1, so M.A. = V.R. In a real machine friction makes M.A. smaller than V.R. and

Efficiency = work output / work input = M.A. / V.R. × 100%, always below 100%.

Example. In a wheel and axle the load is 4 kg wt and the effort 2 kg wt; the radii of wheel and axle are 8 cm and 2 cm. M.A. = 4/2 = 2. V.R. = 8/2 = 4 (one turn: the effort moves 2 π × 8, the load 2 π × 2). Efficiency = 2/4 = 50%.

Moments and the Centre of Gravity

The moment of a force about a point is force × perpendicular distance of the point from the line of action of the force. A body in rotational equilibrium has clockwise moments equal to anticlockwise moments. If a rod is supported away from its centre, its own weight acts at its centre of gravity G and must be included. Example: a rod of weight 0.4 kg wt, G 50 cm from the fulcrum at one end, carries 2 kg wt at 30 cm from the fulcrum and is held up by a string 60 cm from the fulcrum. Moments about F: T × 0.6 = 2 × 0.3 + 0.4 × 0.5 = 0.8, so T = 1.33 kg wt.

The centre of gravity is the point where the whole weight of a body may be taken to act. For a triangular lamina it is the meeting point of the medians, for a rectangle the meeting point of the diagonals, for a disc its centre. A body is in stable equilibrium if tilting raises its centre of gravity (and the vertical through G stays inside the base), unstable if tilting lowers it, and neutral if the height stays the same (a funnel or ball rolling on a table). A low centre of gravity and a wide base give stability.

Atmospheric Pressure and the Barometer

Pressure = thrust / area. Its SI unit is N/m², called the pascal (Pa). Air has weight and presses on every surface; a barometer measures this pressure. In a mercury barometer a glass tube about 90 cm long, filled with mercury, is inverted in a mercury cup. The mercury falls until its column is about 76 cm high at sea level, leaving a vacuum above it. The pressure is P = h d g = 0.76 × 13600 × 9.8 = 1.013 × 10⁵ Pa.

An aneroid barometer has no liquid and can be graduated in height to act as an altimeter, because pressure falls with height. The same pressure supports a water column 76 × 13.6 = 1033.6 cm = 10.34 m high.