Final answer:
The mass of the astronaut's pack is approximately 1.835 kg, which remains the same on both the Earth and the Moon. This determination is made using the provided weights on each celestial body and the known gravitational accelerations.
Step-by-step explanation:
The mass of an astronaut's pack on the moon can be found by using the relationship between weight and mass. Weight is the force of gravity on an object and is calculated by the equation Weight = mass × gravitational acceleration. Since weight and gravitational acceleration vary depending on the location, whereas mass remains constant, we can use the weights given for the Earth and the Moon to determine the mass, considering Earth's gravitational acceleration is approximately 9.81 m/s² and the Moon's is about 1.63 m/s².
The astronaut's pack weighs 18.0 N on Earth, and if we divide this by Earth's gravitational acceleration, we calculate the mass (Mass = Weight / gravitational acceleration). So, the mass of the pack on Earth and on the Moon (since mass doesn't change with location) is:Mass = 18.0 N / 9.81 m/s² = approximately 1.835 kg
Despite the pack's weight being only 3.64 N on the Moon, its mass remains 1.835 kg because mass is an intrinsic property of the object and doesn't depend on the location.