Question

an astronaut’s pack weighs 18.5 n when she is on earth but only 3.44 n when she is at the surface of moon. what is the acceleration due to gravity on this moon? express your answer with the appropriate units. g_m = value units

Explanation:

Step1: Find mass of the pack on Earth

Weight on Earth \( W_{e} = 18.5\ N \), acceleration due to gravity on Earth \( g_{e} = 9.8\ m/s^{2} \). Using \( W = mg \), mass \( m=\frac{W_{e}}{g_{e}}=\frac{18.5}{9.8}\ kg \).

Step2: Calculate acceleration on Moon

Mass is constant, weight on Moon \( W_{m} = 3.44\ N \). Using \( W = mg \), acceleration \( g_{m}=\frac{W_{m}}{m}=\frac{W_{m}g_{e}}{W_{e}} \). Substitute values: \( g_{m}=\frac{3.44\times9.8}{18.5} \approx 1.84\ m/s^{2} \).

Answer:

\( 1.84\ m/s^{2} \)