Question

An equation for potential energy states \(U=m g h .\) If \(U\) is in joules, with \(m\) in \(\mathrm{kg}, h\) in \(\mathrm{m},\) and \(g\) in $\mathrm{m} / \mathrm{s}^{2},$ find the combination of SI base units that are equivalent to joules.

Short answer

Answer: The combination of SI base units equivalent to joules is kg·m²/s².

Step-by-step solution

Write down the equation

The equation for potential energy is given as: \(U = mgh\)

Identify the units of each variable

We are given the units for each variable as: - \(U\): joules - \(m\): kg (mass) - \(h\): m (height) - \(g\): \(\dfrac{m}{s^2}\) (acceleration due to gravity)

Substitute the units into the equation

Replace each variable in the equation with its respective unit: joules = kg * \(\dfrac{m}{s^2}\) * m

Simplify the expression

Multiply the units together: joules = kg * \(\dfrac{m^2}{s^2}\)

Write the final answer

The combination of SI base units that are equivalent to joules is: joules = kg \(\cdot\) m\(^2\) / s\(^2\)