kinetic-and-potential-energy

Kinetic energy

There are many different forms of energy including, but not limited to, heat energy, light energy, chemical energy and nuclear energy. Two forms of energy which are of particular interest in mechanics are kinetic energy (KE) and potential energy (or gravitational potential energy, GPE). Elastic potential energy is also considered when dealing with springs and strings.

What is kinetic energy?

• A particle has kinetic energy when it is moving

• Kinetic energy is a scalar quantity, it cannot be negative

• The work done by a resultant force that acts to move an object in a particular direction will be equal to the change in kinetic energy of the object

How is kinetic energy calculated?

• A particle can only have kinetic energy when it is moving

• If a particle with mass, m kg is moving with speed v m s^-1 then its kinetic energy can be calculated using the formula

• If the particle is moving in two dimensions with the velocity vector v then kinetic energy can be calculated in two ways

  • Using the formula on each component individually and finding the sum of the KE in each component

  • Finding the magnitude of the velocity to get the speed and then using the formula for KE

• Kinetic energy is measured in joules (J)

  • 1 Kilojoule = 1000 joules (1 kJ = 1000 J)

How can we link the work done to a change in kinetic energy?

• The work done by the resultant force is equal to the change in kinetic energy

  • This is the final kinetic energy minus the initial kinetic energy

  • The formula for the change in kinetic energy is

where u is the initial velocity and  v is the final velocity

• This is often written as 

• Newton’s Second Law () and the suvat equation <img alt=”v squared space equals space u squared space plus space 2 a s” data-mathml='<math ><semantics><mstyle mathsize=”16px”><msup><mi>v</mi><mn>2</mn></msup><mo> </mo><mo>=</mo><mo> </mo><msup><mi>u</mi><mn>2</mn></msup><mo> </mo><mo>+</mo><mo> </mo><mn>2</mn><mi>a</mi><mi>s</mi></mstyle><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“language”:”en”,”fontFamily”:”Times New Roman”,”fontSize”:”18″}</annotation></semantics></math>’ height=”20″ role=”math” src=”data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20xmlns%3Awrs%3D%22http%3A%2F%2Fwww.wiris.com%2Fxml%2Fmathml-extension%22%20height%3D%2220%22%20width%3D%2299%22%20wrs%3Abaseline%3D%2216%22%3E%3C!–MathML%3A%20%3Cmath%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmstyle%20mathsize%3D%2216px%22%3E%3Cmsup%3E%3Cmi%3Ev%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmsup%3E%3Cmi%3Eu%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmi%3Es%3C%2Fmi%3E%3C%2Fmstyle%3E%3C%2Fmath%3E–%3E%3Cdefs%3E%3Cstyle%20type%3D%22text%2Fcss%22%3E%40font-face%7Bfont-family%3A’math1564b4c0e54101ac57a0cb68c16’%3Bsrc%3Aurl(data%3Afont%2Ftruetype%3Bcharset%3Dutf-8%3Bbase64%2CAAEAAAAMAIAAAwBAT1MvMi7iBBMAAADMAAAATmNtYXDEvmKUAAABHAAAADxjdnQgDVUNBwAAAVgAAAA6Z2x5ZoPi2VsAAAGUAAABK2hlYWQQC2qxAAACwAAAADZoaGVhCGsXSAAAAvgAAAAkaG10eE2rRkcAAAMcAAAADGxvY2EAHTwY