CBSE Class 10 Physics Work Energy and Power Notes Set 20

Work

In physics, work is done when a force moves its point of application. Work = force × distance moved along the force. The SI unit is the joule (newton metre). 1 joule is done when a force of 1 N moves a body 1 m in its own direction. In CGS units work is measured in erg and 1 J = 10⁷ erg.

If the force F acts at an angle θ to the direction of motion, only the component F cos θ helps the motion, so work = (F cos θ) d. Lifting a mass m through a height h needs work mgh.

Energy: Kinetic and Potential

Energy is the capacity to do work and has the same units as work. Kinetic energy is energy of motion, K.E. = ½ m v². Potential energy is energy of position or shape; for a body at height h above the ground P.E. = mgh. A body lying on the ground has no gravitational P.E. because h = 0. If the speed is doubled, K.E. becomes four times.

Example. A body of mass m falls freely from height h. At the top its energy is all potential, mgh. Half way down its P.E. is mgh/2 and the other half has become kinetic energy.

Power

Power is the rate of doing work: P = W / t. Its unit is the watt (1 W = 1 J/s). 1 kW = 1000 W and 1 horse power = 746 W. Example: a man of 60 kg wt climbs 25 stairs of 20 cm each (5 m) in 3 s. Work = 60 × 9.8 × 5 = 2940 J, so power = 2940 / 3 = 980 W.

Conservation of Energy

A stone falling from a tower loses P.E. and gains an equal amount of K.E., so its total energy stays the same. In general, energy can neither be created nor destroyed; it only changes from one form to another. An electric motor changes electrical into mechanical energy, a dynamo does the reverse, an incandescent bulb turns electrical energy into light (and much heat), and a heat engine turns heat into mechanical energy.

Conversions are not always complete. Mechanical energy can be changed completely into heat (friction, Joule's experiment) but heat can be changed into mechanical energy only in part.

Joule's Experiment and the Mechanical Equivalent of Heat

In Joule's experiment falling weights turn paddle wheels in a calorimeter of water. The potential energy lost by the weights, 2mgh for two equal weights, appears as heat in the water and calorimeter, heat = mass × specific heat × rise in temperature. If heat is counted in calories, the ratio W/H is a constant, J = 4.2 joule per calorie (more exactly 4.18). This is the mechanical equivalent of heat. 1 kilocalorie = 4200 J.

Example. Two weights of 250 g each fall 50 m and all the energy warms water by 1°C. Then 2 × 0.25 × 9.8 × 50 = m × 4200 × 1, so m = 245 / 4200 = 0.0583 kg = 58.3 g.

Heat Engines

A heat engine takes heat from a hot source, turns part of it into work and gives the rest to a colder body. In an external combustion engine (steam engine) the fuel burns outside the cylinder; in an internal combustion engine (petrol or diesel) it burns inside. At best about 40 per cent of the heat becomes work.

A diesel engine compresses air alone; the heat of compression ignites the diesel oil sprayed in at the end of the stroke, and the efficiency is a little higher than that of a petrol engine.