A 63-kg astronaut is floating in empty space.
If she shines a 1.0W- flashlight in a fixed direction, how long will it take her to accelerate to a speed of 10m/s ?
If she shines a 1.0W- flashlight in a fixed direction, how long will it take her to accelerate to a speed of 10m/s ?
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The momentum, p, of a single photon is p = E/c where E is the photon energy and c is the speed of light.
If you have many photons, the momentum of the light = (total energy)/c
The momentum produced by the torch each second = (total energy per second)/c = 1.0/(3x10^8) = 3.33x10^-9 Ns for each second.
Because of the conservation of momentum, the astronaut's momentum will increase by this amount (but un the opposite direction) each second
The next step requires you to know the force is the rate of change of momentum.
(If you know some calculus then you should see:
Rate of change of momentum = d(mv)/dt = mdv/dt = ma.
Since F= ma the force = the rate of change of momentum)
F = 3.3x10^-9 N
a = F/m = 3.3x10^-9 / 63 = 5.2x10^-11 m/s²
To reach 10m/s, t = v/a = 10/ (5.2x10^-11) = 1.9x10^11s
(Around 6050 years!)
(The lesson is - don't try propelling yourself by shining a 1W torch!)
If you have many photons, the momentum of the light = (total energy)/c
The momentum produced by the torch each second = (total energy per second)/c = 1.0/(3x10^8) = 3.33x10^-9 Ns for each second.
Because of the conservation of momentum, the astronaut's momentum will increase by this amount (but un the opposite direction) each second
The next step requires you to know the force is the rate of change of momentum.
(If you know some calculus then you should see:
Rate of change of momentum = d(mv)/dt = mdv/dt = ma.
Since F= ma the force = the rate of change of momentum)
F = 3.3x10^-9 N
a = F/m = 3.3x10^-9 / 63 = 5.2x10^-11 m/s²
To reach 10m/s, t = v/a = 10/ (5.2x10^-11) = 1.9x10^11s
(Around 6050 years!)
(The lesson is - don't try propelling yourself by shining a 1W torch!)