91Ó°ÊÓ

Light intensity is a measure of the power of light per unit area, which is crucial when understanding radiation pressure. In this exercise, light intensity is given as \[ I = 6.0 \, \text{mW/m}^2 = 6.0 \times 10^{-3} \, \text{W/m}^2 \]This tells us how much energy is hitting a square meter region per second. The higher the intensity, the more energy is being transferred to the surface it hits.

Since radiation pressure is the pressure exerted by light on any surface, it is directly related to light intensity. For our sphere, which is totally absorbing the light, the pressure can be obtained as:\[ P = \frac{I}{c} \]where:

• \( I \) is the intensity of the light.
• \( c \) is the speed of light, approximately \( 3.0 \times 10^8 \, \text{m/s} \).

By understanding these elements, we can appreciate how light exerts force—important for calculating the sphere's acceleration.

Calculating the volume of a sphere is key to determine its mass when given its density.

In geometrical terms, volume of a sphere with radius \( r \) is calculated as:\[ V = \frac{4}{3} \pi r^3 \]In our problem, the sphere's radius \( r \) is \( 2.0 \, \mu\text{m} = 2.0 \times 10^{-6} \, \text{m} \). Substituting into the formula gives us:\[ V = \frac{4}{3} \pi (2.0 \times 10^{-6})^3 \, \text{m}^3 \]Calculating this volume helps us find out how much space the sphere occupies, and with the density known, it aids in finding the sphere's mass—necessary for applying Newton's second law later.

• Volume gives a three-dimensional measure of space.
• Knowing this, we can accurately determine the amount of material within the sphere.

Newton's Second Law of Motion forms the backbone of dynamics, describing how the velocity of an object changes when a force is applied. It is expressed as:\[ F = m \times a \]This tells us that the force \( F \) acting on an object is the product of its mass \( m \) and its acceleration \( a \). Understanding this law is fundamental to solving problems such as the one in this exercise.

Here's how we set up the problem:

• First, we calculate the force \( F \) exerted by light on the sphere using radiation pressure.
• Then, we find the mass \( m \) of the sphere using its density and volume.
• Finally, rearrange the formula to solve for acceleration \( a \): \( a = \frac{F}{m} \).

By substituting the values for force and mass from our calculations, we can find the sphere's acceleration. This concept underlines how different physical quantities such as force, mass, and acceleration interrelate and how they can be computed when an external force like light interacts with a material object.