Photon stopping an object travelling at 10m/s

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The discussion revolves around the momentum of a photon and its ability to stop an object moving at 10 m/s through elastic reflection. It highlights the conservation of energy and momentum principles, leading to the conclusion that for the object to be stopped, its mass must be zero. The calculations show that the change in momentum of the photon is critical, with equations indicating that the mass of the object can be derived from the photon's momentum. The conversation emphasizes the importance of correctly applying these conservation laws to understand the interaction between the photon and the object. Ultimately, the analysis reveals a misunderstanding in the initial assumptions about the object's mass.
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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?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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