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Force exerted on the palm of your hand by a beam of light

3
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Compute the force exerted on the palm of you hand by the beam from a 1.0W flashlight. (a) if your hand absorbs the light, and (b) if the light reflects from your hand.

What would the mass of the particle that exerts that same force in each case would be if you hold it at earth's surface?

On the problem I used E = pc to solve part (a). My lack of understanding lies in part (b). Where I am told that the momentum change is twice the amount. I do not understand.

[P][/total] = [P][/1] + [P][/2]

Shouldn't [P][/1] cancel with [P][/2] since the momentum of [P][/2] is moving in the opposite direction?
 

Nugatory

Mentor
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4,857
Shouldn't [P][/1] cancel with [P][/2] since the momentum of [P][/2] is moving in the opposite direction?
The momentum was P and changed to be -P. Thus, the change in momentum was the change from +P to -P and that's 2P.... The difference between 3 and -3 is 6.
 
3
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The momentum was P and changed to be -P. Thus, the change in momentum was the change from +P to -P and that's 2P.... The difference between 3 and -3 is 6.
So i should look at this as +P - (-P) = 2P ?
 

Nugatory

Mentor
12,365
4,857
So i should look at this as +P - (-P) = 2P ?
Yes.

Footnote:
Or you could look at it as (-P) - P = -2P, depending on whether you're defining the towards-your-hand direction to be the positive direction or the negative direction. Either way, the change in momentum is going to be the final momentum minus the initial momentum. The important thing with vector quantities like forces, momenta, velocities is that whatever convention you use, you use it consistently. Note that in this problem the force exerted on (and acceleration and resulting velocity of) your hand will have a positive sign under one convention and a negative sign under the other, but either way it will point from the palm to the back of your hand.
 
3
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or (-P) - P = -2P, depending on whether you're defining the towards-your-hand direction to be the positive direction or the negative direction, but either way, the change in momentum is going to be the final momentum minus the initial momentum. The important thing with vector quantities like forces, momenta, velocities is that whatever convention you use, you use it consistently.
THANK YOU! I get it now.
 

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