Work, Energy, Power and Simple Machines

What you need to know

• Work is done when a force moves its point of application through a distance in the direction of the force: W = F d cos theta, where theta is the angle between the force and the displacement. A man carrying a load on his head along a level road does no work against gravity, because the force is vertical and the motion horizontal.
• Energy is the capacity to do work, and both are measured in joules. One joule is the work done when a force of one newton moves a body through one metre in the direction of the force.
• Kinetic energy is the energy a body has by virtue of its motion, KE = (1/2)mv^2. Potential energy due to position is PE = mgh; elastic potential energy stored in a stretched spring is (1/2)ke^2.
• The principle of conservation of energy states that energy can neither be created nor destroyed but only converted from one form to another. For a body falling freely, the loss in potential energy equals the gain in kinetic energy, so mgh = (1/2)mv^2 and v = sqrt(2gh).
• Power is the rate of doing work or the rate of transfer of energy, P = W/t, measured in watts. For a body moving at steady velocity against a resisting force, P = F v.
• Energy forms you must be able to name and convert between: mechanical, heat, light, sound, electrical, chemical, nuclear and solar. A torch converts chemical to electrical to light and heat; a generator converts chemical to mechanical to electrical.
• A machine is any device that allows a force applied at one point (the effort) to overcome a force at another point (the load). Machines do not create energy; they trade force against distance.
• Mechanical advantage MA = load / effort, velocity ratio VR = distance moved by effort / distance moved by load, and efficiency = (MA/VR) x 100 per cent, which is also (work output / work input) x 100.
• No practical machine is 100 per cent efficient, because some work input is always spent overcoming friction between moving parts and lifting the movable parts of the machine itself. Efficiency improves with lubrication and lighter moving parts.
• For a lever, the principle of moments gives load x load arm = effort x effort arm, so MA = VR for an ideal lever. First-class levers have the fulcrum between load and effort (scissors, seesaw, pliers); second-class have the load between (wheelbarrow, nutcracker); third-class have the effort between (forceps, the human forearm, a fishing rod).
• For a block and tackle pulley system, the velocity ratio equals the number of pulleys, or more precisely the number of rope sections supporting the movable block. A single fixed pulley has VR = 1 and merely changes the direction of the effort.
• For an inclined plane, VR = length of plane / vertical height = 1/sin(theta). For a screw jack, VR = 2 pi R / pitch, where R is the length of the handle. For a wheel and axle, VR = radius of wheel / radius of axle.
• In a hydraulic press, the velocity ratio is the ratio of the areas, A(large)/A(small), and the pressure is transmitted equally throughout the liquid, which is Pascal's principle used as a force multiplier.
• A moment of a force about a point is force times perpendicular distance from the point, measured in N m. A body in equilibrium obeys both conditions: the sum of the forces is zero and the sum of clockwise moments about any point equals the sum of anticlockwise moments.