Chapter 4: Problem 13

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 due to the difference in local gravitational field strength. However, the mass density of water would remain the same, as it depends solely on mass and volume, which are constant regardless of location.

Step by step solution

Define weight density and mass density

Weight density (sometimes referred to as specific weight) is the ratio of the weight of a substance to its volume. It is commonly expressed in newtons per cubic meter (N/m³). Mass density (also known as density) is the mass of a substance divided by its volume, typically expressed in kilograms per cubic meter (kg/m³).

Understand the difference between mass and weight

Mass is the amount of matter in an object, measured in kilograms. Weight, on the other hand, is the force on an object due to gravity and is equal to the mass of the object multiplied by the acceleration due to gravity (Newtons). While mass is a scalar quantity and remains constant regardless of the object's location, weight is a vector quantity and depends on the local gravitational field strength.

Analyze the effect of gravity on weight density and mass density

Since weight depends on the local gravitational field strength, an object's weight is different on the Moon compared to Earth due to the Moon's weaker gravity. Therefore, the weight density of a substance, being dependent on weight and volume, would also be different on the Moon compared to Earth. On the other hand, mass density is dependent solely on an object's mass and volume, and since the mass of a substance is constant irrespective of its location, the mass density of water will be the same on Earth as it would be on the Moon.

Conclude the answer

The weight density of water would indeed be different on the Moon than it is on Earth, due to the difference in local gravitational field strength. However, the mass density of water would remain the same, as it depends solely on mass and volume, which are constant regardless of location.

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

Short Answer

Step by step solution

Define weight density and mass density

Understand the difference between mass and weight

Analyze the effect of gravity on weight density and mass density

Conclude the answer

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