Photon stopping an object travelling at 10m/s

[Mr.A.Gibson]

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?

 

[Doc Al]

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?

 

[Mr.A.Gibson]

How did you conclude this?

conservation of momentum,
$$p_b+10m=p_a$$
subscripts refers to photons momentum before and after collision.

Then from conservation of energy
$$\frac{1}{2}mv^2+cp_b=cp_a$$
substitute in the first equation and velocity of the object to give
$$50m+cp_b=c(p_b+10m)$$
$$50m=10cm$$
only valid if m=0

 

[Mr.A.Gibson]

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?