Energy calculations

Energy calculations

Energy is measured using the unit Joules, J.
The kinetic energy of a moving object is \(0.5\times\text{mass}\times\text{(speed)}^2\). This can be written as \(E_k=\frac{1}{2}mv^2\) where:
- \(E_k\) is the kinetic energy in J
- \(m\) is the object’s mass in kg
- \(v\) is the object's speed in m/s.
The elastic potential energy stored in a spring that has been stretched is given by \(0.5\times\text{spring constant}\times\text{(extension)}^2\). This can be written as \(E_e=\frac{1}{2}ke^2\) where:
- \(E_k\) is the elastic potential energy in J
- \(k\) is the spring constant of the spring in N/m
- \(e\) is the extension of the spring in m.
The gravitational potential energy stored in an object raised above ground level is given by \(\text{mass}\times\text{gravitational field strength}\times\text{height}\). This can be written as \(E_p=mgh\) where:
- \(E_p\) is gravitational potential energy in J
- \(m\) is the mass of the object in kg
- \(g\) is the gravitational field strength in N/kg
- \(h\) is the height raised in m.
The energy transferred due to a temperature change is given by \(\text{mass}\times\text{specific heat capacity}\times\text{temperature change}\). The specific heat capacity of a substance is the energy to raise the temperature of one kilogram of the substance by one degree Celsius. This equation can be written as \(\Delta E = mc\Delta \theta\) where:
- \(\Delta E\) is the thermal energy transferred in J
- \(m\) is the mass of the object heated or cooled in kg
- \(c\) is its specific heat capacity of the object in J/kg °C
- \(\Delta\theta\) is the temperature change in °C

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