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Energy is the capacity to do work. The unit of energy is J (Joule) which is also kg m2s2 (kilogram meter squared per second squared) Energy can be in many forms! Here we look at Potential Energy (PE) and Kinetic Energy (KE). Potential Energy and Kinetic Energy A hammer: when raised up has potential energy (the energy of position or state) when falling down has kinetic energy (the energy of motion) a raised hammer has PE due to gravity. fuel and explosives have Chemical PE a coiled spring or a drawn bow also have PE due to their state A moving car has a lot of kinetic energy From PE to KE These skydivers have potential energy due to being high up.After they jump this potential energy getsconverted into kinetic energy (and heat) as they speed up. PendulumFor a good example of PE and KE have a play with a pendulum.Gravitational Potential Energy When the PE is due to an objects height then: PE due to gravity = m g h Where: m is the objects mass (kg) g is the gravitational field strength of 9.8 ms2 near the Earths surface h is height (m) Example: This 2 kg hammer is 0.4 m up. What is its PE?PE = m g h = 2 kg × 9.8 ms2 × 0.4 m = 7.84 kg m2s2 = 7.84 J Kinetic Energy The formula is: KE = ½ m v2 Where m is the objects mass (kg) v is the objects speed (ms) Example: What is the KE of a 1500 kg car going at suburban speed of 14 ms (about 50 kmh or 30 mph)? KE = ½ m v2 KE = ½ × 1500 kg × (14 ms)2 KE = 147,000 kg m2s2 KE = 147 kJ Lets double the speed! Example: The same car is now going at highway speed of 28 ms (about 100 kmh or 60 mph)? KE = ½ m v2 KE = ½ × 1500 kg × (28 ms)2 KE = 588,000 kg m2s2 KE = 588 kJ Wow! that is a big increase in energy! Highway speed is way more dangerous. Double the speed and the KE increases by four times. Very important to know A 1 kg meteorite strikes the Moon at 11 kms. How much KE is that? KE = ½ m v2 KE = ½ × 1 kg × (11,000 ms)2 KE = 60,500,000 J KE = 60.5 MJ That is 100 times the energy of a car going at highway speed. From PE to KE When falling, an objects PE due to gravity converts into KE and also heat due to air resistance. Lets drop something! Example: We drop this 0.1 kg apple 1 m. What speed does it hit the ground with? At 1 m above the ground its Potential Energy is PE = m g h PE = 0.1 kg × 9.8 ms2 × 1 m PE = 0.98 kg m2s2 Ignoring air resistance (which is small for this little drop anyway) that PE gets converted into KE: KE = ½ m v2 Swap sides and rearrange: ½ m v2 = KE v2 = 2 × KE m v = √( 2 × KE m ) Now put PE into KE and we get: v = √( 2 × 0.98 kg m2s2 0.1 kg ) v = √( 19.6 m2s2 ) v = 4.427... ms Note: for velocity we can combine the formulas like this: Velocity from KE: v = √( 2 × KE m ) Put in formula for PE: v = √( 2 × mgh m ) Cancel mm: v = √( 2gh ) The mass does not matter! It is all about height and gravity. For our earlier example: v = √( 2gh ) v = √( 2 × 9.8 ms2 × 1 m ) v = 4.427... ms Summary Energy is the ability to do work Potential Energy (PE) is stored energy due to position or state PE due to gravity = m g h Kinetic Energy (KE) is energy of motionKE = ½ m v2 Copyright © 2020 MathsIsFun.com Potential energy is energy an object has because of its position relative to some other object. When you stand at the top of a stairwell you have more potential energy than when you are at the bottom, because the earth can pull you down through the force of gravity, doing work in the process. When you are holding two magnets apart they have more potential energy than when they are close together. If you let them go, they will move toward each other, doing work in the process. The formula for potential energy depends on the force acting on the two objects. For the gravitational force the formula is P.E. = mgh, where m is the mass in kilograms, g is the acceleration due to gravity (9.8 m s2 at the surface of the earth) and h is the height in meters. Notice that gravitational potential energy has the same units as kinetic energy, kg m2 s2. In fact, all energy has the same units, kg m2 s2, and is measured using the unit Joule (J).
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