91Ó°ÊÓ

Density is a fundamental concept in physics and describes how compact the mass in a substance is. It's defined as mass per unit volume and is crucial in understanding buoyancy.
For liquids, density determines their ability to support objects floating or sinking in them. The formula to calculate density is:

• \( \rho = \frac{m}{V} \)

where:

• \( \rho \) is the density
• \( m \) is the mass
• \( V \) is the volume.

In our exercise, we calculate the density of a rock to find a liquid density where it would float. A key point here is that an object will float if the density of the liquid is equal to or greater than the object's density.
This has real-world implications. For example, ice floats on water because ice is less dense than liquid water. Understanding density can provide insights into why certain materials behave the way they do when submerged in liquids.

Tension is the force exerted by a string, cable, or similar object when it is pulled tight by forces acting from opposite ends. In our exercise, tension comes into play when the rock is hanging and submerged in water.
When a submerged object is attached to a string, the tension in the string changes due to the buoyant force acting on the object. The formula to calculate tension, when a submerged object is present, is:

• \( T = W - F_{\text{buoyant}} \)

where:

• \( T \) is the tension in the string
• \( W \) is the gravitational force (weight of the object)
• \( F_{\text{buoyant}} \) is the buoyant force.

In the exercise, we find tension was 12.8 N, which indicates the presence of a buoyant force trying to lift the rock, making the tension less than the actual weight if it was in air. This is a perfect demonstration of how tension and buoyancy interact in practical scenarios.

Gravitational force is the force by which a planet or other celestial body attracts objects toward its center. On Earth, this force creates weight. In this exercise, gravitational force is a crucial component in determining the weight of the rock.
The formula to calculate the gravitational force (or weight) of an object is:

• \( W = m \cdot g \)

where:

• \( W \) is the weight or gravitational force
• \( m \) is the mass of the object
• \( g \) is the acceleration due to gravity (approximately \( 9.81 \text{ m/s}^2 \) on Earth).

Understanding gravitational force helps us comprehend how much an object weighs and how it will behave in different fluids based on its weight and the buoyant forces acting upon it. This force is why objects have weight and is essential in equations used to explore buoyancy and flotation in various contexts.