Question

# A 150-lbm astronaut took his bathroom scale (a spring scale) and a beam scale (compares masses) to the moon where the local gravity is g = 5.48 ft/s^2. Determine how much he will weigh (a) on the spring scale and (b) on the beam scale. Answers: (a) 25.5 lbf, (b) 150 lbf

Solution

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To calculate the weight shown on the spring scale we have to multiply the given values of the mass of the astronaut with the gravitational acceleration of the Moon and then express the result in adequate units considering that $1\:\text{lbf} = 32.174\:\dfrac{\text{lbm}\cdot\text{ft}}{\text{s}^{2}}$.

\begin{align*} F_{\text{spring}}&=mg\\ &=150\:\text{lbm}\cdot5.48\:\dfrac{\text{ft}}{\text{s}^{2}}\\ &=\boxed{25.55\:\text{lbf}} \end{align*}

As far as the beam scale is concerned, it is not under the influence of the gravitational acceleration, therefore it will show the same reading as on Earth.

\begin{align*} F_{\text{beam}}=\boxed{150\:\text{lbf}} \end{align*}

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