A small spaceship with a mass of only 1.5 ×10^3 kg (including an astronaut) is drifting in oute

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A small spaceship with a mass of only 1.5 ×10^3 kg...

A small spaceship with a mass of only $1.5 \times 10^{3} \mathrm{~kg}$ (including an astronaut) is drifting in outer space with negligible gravitational forces acting on it. If the astronaut turns on a $10 \mathrm{~kW}$ laser beam, what speed will the ship attain in 1.0 day because of the momentum carried away by the beam?

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Key Concepts

Photon Momentum

Photon momentum is the concept that even though photons have no mass, they can carry momentum, which is directly related to their energy by the relation p = E/c. This principle is essential in explaining how light can exert force on objects when emitted or absorbed.

Radiation Pressure

Radiation pressure is the pressure exerted by electromagnetic radiation on a surface due to the transfer of momentum from photons. It is significant in contexts where light or other forms of radiation impart force on materials, leading to observable mechanical effects.

Impulse and Momentum Transfer

Impulse involves the application of force over time, resulting in a change in momentum of an object. In scenarios where momentum is continuously carried away by emitted photons, the cumulative impulse provides a small but measurable change in the object's velocity.

Conservation of Momentum

The conservation of momentum principle states that in the absence of external forces, the total momentum of a system remains constant. When photons are emitted, their momentum must be balanced by an equal and opposite momentum in the emitting object, which results in a recoil or propulsion effect.

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