In a region of space where gravitational forces can be...

In a region of space where gravitational forces can be neglected, a sphere is accelerated by a uniform light beam of intensity $6.0 \mathrm{~mW} / \mathrm{m}^{2}$. The sphere is totally absorbing and has a radius of $2.0 \mu \mathrm{m}$ and a uniform density of $5.0 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3} .$ What is the magnitude of the sphere's acceleration due to the light?

Key Concepts

Force and Acceleration

The force on an object due to radiation pressure is found by multiplying the pressure by the area over which the light is absorbed. According to Newton’s second law, the acceleration of the object can then be calculated by dividing this force by the object's mass. This relationship ties together the effect of light pressure with the dynamics of motion.

Momentum Transfer from Light

The momentum transfer from light occurs when photons impart momentum to an object they interact with. For a totally absorbing surface, each photon gives up its entire momentum, making the force experienced by the object proportional to the light's intensity, and this concept is key to understanding how the object is accelerated through the beam.

Geometric and Mass Considerations

When dealing with spherical objects, it is important to consider the cross-sectional area (?r^2) that intercepts the light beam as well as the mass determined by the volume and density of the sphere. These geometric and mass-related calculations are essential for quantifying the acceleration produced by the force due to radiation pressure.

Radiation Pressure

Radiation pressure is the pressure exerted by electromagnetic radiation upon any surface due to the transfer of momentum from the light to the object. For a perfectly absorbing surface, the pressure is given by the intensity of the light divided by the speed of light (I/c), which is fundamental in determining the force exerted on the object by the light.

Intensity of Light

Intensity represents the power per unit area carried by a light beam. It directly influences the radiation pressure experienced by an object; higher intensities result in greater radiation pressure, and thus larger forces are applied to objects exposed to the beam.

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