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When an object is submerged in a fluid, it experiences a reduction in weight known as the apparent weight. This phenomenon is due to the buoyant force that acts upward against gravity. The buoyant force makes objects feel lighter when they are in a liquid, like water.
In the exercise, the apparent weight of the aluminum ingot is the weight it seems to have when submerged in water. To find this, you subtract the buoyant force from the actual weight of the ingot.

• The actual weight in air is 89 N.
• The buoyant force equals the weight of the water displaced by the ingot.
• The formula for buoyant force is: \[ F_{buoyant} = \text{density of water} \times V \times g \]

Subsequently, the apparent weight can be calculated as: \[ W_{apparent} = W - F_{buoyant} \]In our case, the apparent weight is approximately 56.03 N after subtracting the buoyant force of 32.97 N from the initial weight of 89 N.

Density is a measure of how much mass is contained in a given volume. It's an essential concept in physics, especially when dealing with buoyancy and fluid mechanics.
The density is defined by the formula: \( \rho = \frac{m}{V} \), where \( \rho \) is density, \( m \) is mass, and \( V \) is volume.
The density of aluminum is approximately 2700 kg/m³ which is used to calculate the mass of the ingot in the problem. Since the density of water is 1000 kg/m³, we can use this property to predict how much fluid is displaced by the ingot.

• Higher density means more mass in each unit of volume.
• Objects denser than the fluid will sink; less dense objects will float.

This principle helps in determining the buoyant force, which impacts the apparent weight of the object in water. With these insights, students can correctly apply density in related physics problems.

The calculation of volume is crucial to understanding the use of density in physics. To find the volume of an object when the mass and the density are given, you can rearrange the density formula to:
\[ V = \frac{m}{\rho} \]This formula allows you to find the space an object occupies.
In the exercise about the aluminum ingot, once the mass is calculated (using weight divided by gravity), you can then substitute the mass and aluminum density values into this formula to find the volume.

• First, determine the mass using: \( m = \frac{W}{g} \).
• Next, calculate the volume with: \( V = \frac{9.07}{2700} \approx 0.00336 \text{ m}^3 \).

By finding the volume, students can apply it to determine the amount of fluid displaced by the object when submerged, thus calculating buoyant force and apparent weight. Volume calculation is thereby foundational for solving various problems in fluid mechanics.