An astronaut, stranded in space 10.0 m from hism spacecraft...

An astronaut, stranded in space 10.0 m from hism spacecraft and at rest relative to it, has a mass (including equipment) of 110 kg. Because he has a 100-W light source that forms a directed beam, he considers using the beam as a photon rocket to propel himself continuously toward the spacecraft. (a) Calculate how long it takes him to reach the spacecraft by this method. (b) What If ? Suppose, instead, that he decides to throw the light source away in a direction opposite the spacecraft. If the mass of the light source is 3.00 kg and, after being thrown, it moves at 12.0 m/s relative to the recoiling astronaut, how long does it take for the astronaut to reach the spacecraft?

Key Concepts

Conservation of Momentum

This concept explains that in the absence of external forces the total momentum of a system remains constant. It is used to analyze how the momentum transfer occurs when a photon beam is emitted or when mass is ejected, as in the case of throwing the light source, to generate a reaction force that propels the astronaut.

Photon Momentum

Photon momentum is based on the fact that even though photons have no rest mass, they carry momentum proportional to their energy. This principle underlies the idea of using a directed light beam as a means of propulsion, where the continuous emission of photons creates a thrust that accelerates the astronaut.

Rocket Propulsion Principles

This involves the idea that expelling mass or energy from a system can produce thrust and result in acceleration. Both the photon rocket method and the mass-ejection scenario utilize these principles, relying on the conservation of momentum to determine the propulsion effects achieved by emitting energy or mass in the opposite direction of travel.

Kinematics in Free Space

Kinematic principles allow the calculation of acceleration, velocity, and travel time when an object is acted upon by a constant force. These laws are applied to determine how long it takes for the astronaut to travel a set distance in an environment free of resistive forces, such as space.

Transcript

00:01 In this example, we're going to be looking at electromagnetic waves, and i'm also going to be looking a little bit at conservation and momentum and a little bit of our kinematics equations.

00:10 So what we have is an astronaut, and she is somehow stranded in space, a distance d of 10 .0 meters from her spaceship.

00:22 And she's realizing that she's carrying a flashlight that has an output of, i'll call that power flashlight, of one.

00:30 100 .0 watts.

00:34 And she wants to use this flashlight as a kind of photon cannon to propel herself back to her spaceship.

00:41 And we want to find out how long this might take her and if it's reasonable.

00:46 All right.

00:47 So let's start with what we know.

00:48 We know force equals mass times acceleration.

00:54 We also know the mass of the astronaut and her equipment equals, i'll call that mass.

01:01 Astronaut, 110 .0 kilograms.

01:06 Okay, so going back to this, force equals mass times acceleration.

01:11 I need to find my acceleration.

01:13 And i need to know my force.

01:15 Luckily, i have a relationship between power and force.

01:19 I know force times velocity equals power.

01:26 Okay, so my force equals my power over my velocity.

01:32 And in this case, we're looking at the velocity of the photon.

01:35 So the velocity is the speed of light.

01:38 And remember, c equals 3 .0 times 10 to the 8 meters per second.

01:46 So i can substitute this expression in for force.

01:50 P over c equals mass times acceleration...

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