It is desired to move a small 50 kg space vehicle by a lamp which emits 100 watts of blue light(lambda= 4700 Angstrom). If the vehicle is in free space, what will its acceleration?
The Attempt at a Solution
The solution as given in my book is as follows:
Here we take the particle nature of light. Since the emitted light carries momentum the change in momentum per second will be responsible for exerting force on the vehicle.
Suppose the lamp emits N photons per second. Then,
Nhf = Power of lamp
Where h = Planck’s constant, f = frequency of light
On simplification we get,
N= 2.4 x 10^20
Each photon will have a momentum given by,
p = h/lambda
= 1.4 x 10^(-27) N – sec
The total force on the vehicle as per Newton’s 2nd law is,
F = d/dt(Np)
= 3.4 x 10^(-7) N
acceleration = F/mass
= 6.8 x 10^(-9) m/sec^2
I understood till the momentum calculation. I didn’t understand the force calculation. I calculated it in the following way:
The change in momentum of each photon after striking the space vehicle per second= 2p
change in momentum of N photons per second = 2pN
F = dp/dt
= 3.32 x 10^(-6) N
Could somebody please guide me?