An astronaut has a mass of 70 kg. a. What is the weight of the astronaut on Earth at sea level? b. What are the mass and the weight of the astronaut on the Moon, and on Mars? c. What is the ratio of the pressure exerted by the astronaut’s shoe on Earth

a. On Earth at sea level, the weight of the astronaut can be calculated by using the formula W = mg, where m is the mass and g is the acceleration due to gravity. At sea level, g is \approx imately 9.81 m/s?, so the weight of the astronaut is W = 70 kg x 9.81 m/s? = 686.7 N. b. The mass of the astronaut will remain the same on the Moon or Mars, as mass is an intrinsic property of an object and does not change with location. However, the weight of the astronaut will vary based on the strength of gravity at those locations. On the Moon, the acceleration due to gravity is about 1/6th of that on Earth, or \approx imately 1.62 m/s?. Therefore, the weight of the astronaut on the Moon would be W = 70 kg x 1.62 m/s? = 113.4 N. On Mars, the acceleration due to gravity is about 0.38 times that on Earth, or \approx imately 3.71 m/s?. Therefore, the weight of the astronaut on Mars would be W = 70 kg x 3.71 m/s? = 259.7 N. c. The pressure exerted by the astronaut's shoe on a surface depends on the weight of the astronaut and the area of the shoe in contact with the surface. Since the mass of the astronaut is the same on both Earth and Mars, the weight of the astronaut will be different due to the difference in gravitational acceleration. Therefore, the ratio of the pressure exerted by the astronaut's shoe on Earth to Mars will be the same as the ratio of their weights. Using the weights obtained in part b, the ratio would be: Pressure on Earth / Pressure on Mars = Weight on Earth / Weight on Mars Pressure on Earth / Pressure on Mars = 686.7 N / 259.7 N Pressure on Earth / Pressure on Mars = 2.644 Therefore, the pressure exerted by the astronaut's shoe on Earth is \approx imately 2.6 times greater than that on Mars.