Photon stopping an object travelling at 10m/s

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SUMMARY

The discussion centers on the physics of stopping an object moving at 10 m/s using the momentum of a photon, defined as ħk, where k is the wave vector. The conservation of momentum and energy equations are applied, leading to the conclusion that for the object to be stopped by elastic reflection of the photon, its mass must be zero. The calculations involve the relationship between the momentum of the photon before and after the collision and the kinetic energy of the object. The final derived equation indicates that the mass of the object is directly related to the wave vector of the photon and its velocity.

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Homework Statement



The momentum of a photon is ħk, where k is the wave vector. Assume an object moving at 10m/s, objects of which mass can be stopped by elastic reflection of the photon.

Homework Equations



Conservation of energy and momentum
p = ħk = h/λ

The Attempt at a Solution



Assume the photon is traveling in the opposite direction to the object. Then the mass of the object has to be 0. I feel I'm missing something?
 
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Mr.A.Gibson said:
Assume the photon is traveling in the opposite direction to the object. Then the mass of the object has to be 0.
How did you conclude this?

Hint: What's the change in momentum of the photon?
 
Doc Al said:
How did you conclude this?

conservation of momentum,
<br /> p_b+10m=p_a<br />
subscripts refers to photons momentum before and after collision.

Then from conservation of energy
<br /> \frac{1}{2}mv^2+cp_b=cp_a<br />
substitute in the first equation and velocity of the object to give
<br /> 50m+cp_b=c(p_b+10m)<br />
<br /> 50m=10cm<br />
only valid if m=0
 
Last edited:
Doc Al said:
Hint: What's the change in momentum of the photon?

2ħk = 10m

m = ħk/10

Makes sense, what did I mess up in the first place then?
 

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