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Chapter 4: Problem 15

Would the weight density of water be different on the Moon than it is on Earth? What about the mass density?

Short Answer

Expert verified
Answer: The weight density of water would be different on the Moon compared to Earth, being 1/6th of its value on Earth due to the difference in gravitational force. However, the mass density of water would remain unchanged, as it does not depend on gravity.

Step by step solution

01

Understand the difference between weight and mass

Mass is a measure of the amount of matter in an object, usually expressed in kilograms (kg). Weight, on the other hand, is the force exerted on an object due to gravity, and is usually expressed in newtons (N). The weight of an object can be calculated using the formula: Weight = Mass 脳 Gravity. Since the gravitational force on the Moon is about 1/6th that of Earth's, the weight of an object will be different on the Moon, while its mass remains unchanged.
02

Define weight density and mass density

Weight density is the weight of a substance per unit volume, and it is usually expressed in newtons per cubic meter (N/m^3). To calculate the weight density, we can use the following formula: Weight Density = Mass Density 脳 Gravity, where mass density (or simply 'density') is the mass of a substance per unit volume, expressed in kilograms per cubic meter (kg/m^3). The mass density does not depend on gravity and therefore remains constant, regardless of the location.
03

Compare the weight density of water on Earth and Moon

Earth's gravitational force is about 6 times greater than that on the Moon. Therefore, the weight density of water on the Moon would be 1/6th of its value on Earth. Since mass density does not change, the mass density of water on Earth and the Moon will stay the same.
04

Conclusion

The weight density of water would be different on the Moon compared to Earth due to the difference in gravitational force. It would be about 1/6th of its value on Earth. However, the mass density of water would remain unchanged, as it does not depend on gravity.

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