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Chapter 4: Problem 46

Find and compare the weight of a \(65-\mathrm{kg}\) man on Earth with the weight of the same man on (a) Mars, where \(g=3.7 \mathrm{N} / \mathrm{kg}.\) (b) Venus, where \(g=8.9 \mathrm{N} / \mathrm{kg} ;\) and (c) Earth's Moon, where \(g=1.6 \mathrm{N} / \mathrm{kg}.\)

Short Answer

Expert verified
Answer: The 65 kg man weighs the least on Earth's Moon, with a weight of 104 N.

Step by step solution

01

Calculate the weight on Earth.

Recall that the gravitational acceleration on Earth is approximately \(9.81 \mathrm{N} / \mathrm{kg}.\) We'll first calculate the weight of the man on Earth. Weight on Earth = Mass * Gravitational Acceleration on Earth Weight on Earth = \(65 \mathrm{kg} * 9.81 \mathrm{N} / \mathrm{kg} = 637.65 \mathrm{N}\)
02

Calculate the weight on Mars.

Next, we'll calculate the weight of the man on Mars using the given gravitational acceleration of \(3.7 \mathrm{N} / \mathrm{kg}.\) Weight on Mars = Mass * Gravitational Acceleration on Mars Weight on Mars = \(65 \mathrm{kg} * 3.7 \mathrm{N} / \mathrm{kg} = 240.5 \mathrm{N}\)
03

Calculate the weight on Venus.

Now, we'll calculate the weight of the man on Venus using the given gravitational acceleration of \(8.9 \mathrm{N} / \mathrm{kg}.\) Weight on Venus = Mass * Gravitational Acceleration on Venus Weight on Venus = \(65 \mathrm{kg} * 8.9 \mathrm{N} / \mathrm{kg} = 578.5 \mathrm{N}\)
04

Calculate the weight on Earth's Moon.

Finally, we'll calculate the weight of the man on Earth's Moon using the given gravitational acceleration of \(1.6 \mathrm{N} / \mathrm{kg}.\) Weight on Moon = Mass * Gravitational Acceleration on Moon Weight on Moon = \(65 \mathrm{kg} * 1.6 \mathrm{N} / \mathrm{kg} = 104 \mathrm{N}\)
05

Compare the weights on each celestial body.

We have calculated the man's weight on Earth, Mars, Venus, and Earth's Moon. Let's now compare these weights: - Weight on Earth: 637.65 N - Weight on Mars: 240.5 N - Weight on Venus: 578.5 N - Weight on Moon: 104 N The man weighs the most on Earth (637.65 N) and the least on Earth's Moon (104 N).

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