# Calculating Force Exerted by Photons on a Small Space Vehicle

• Amith2006
In summary, the problem involves using a lamp emitting blue light to move a 50 kg space vehicle in free space. The solution involves considering the particle nature of light and calculating the number of photons emitted per second and their individual momentum. The total force exerted on the vehicle is found using Newton's second law, which results in an acceleration of 6.8 x 10^(-9) m/sec^2. However, there may be a discrepancy in the calculation of the force depending on whether the photons are being absorbed or reflected.
Amith2006

## Homework Statement

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)
= p(dn/dt)
= 3.4 x 10^(-7) N
Therefore,
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
= 2pN
= 3.32 x 10^(-6) N

Well what you have done is tried to calculate the momentum change of the photon when what you want is the momentum imparted to the ship by the photons.

Amith2006 said:

I don't see how you got your number from computing 2pN. If you use their values of p and N, you should get twice their result. They apparently assumed the photons are being absorbed, while you are assuming they are being reflected, so your force is twice as much as theirs. That will give you a factor of 2 difference between your result and theirs.

You are right. I never thought about it. Thanks.

## What is the force exerted by photons?

The force exerted by photons refers to the amount of push or pull that a photon, which is a particle of light, exerts on an object. It is a form of electromagnetic force and is measured in newtons (N).

## How is the force exerted by photons calculated?

The force exerted by photons can be calculated using the equation F = dp/dt, where F is the force, dp is the change in momentum, and dt is the change in time. This equation is known as the impulse-momentum theorem and is derived from Newton's second law of motion.

## Is the force exerted by photons a constant value?

No, the force exerted by photons is not a constant value. It depends on various factors such as the intensity of light, the distance between the photon and the object, and the properties of the object (such as its reflectivity). The force can also vary depending on the direction of the photon's travel and the angle at which it strikes the object.

## Can the force exerted by photons be measured?

Yes, the force exerted by photons can be measured using specialized instruments such as a photonic force microscope or a radiation pressure balance. These instruments use the principles of electromagnetism to accurately measure the force exerted by individual photons.

## What are the real-world applications of understanding the force exerted by photons?

Understanding the force exerted by photons is crucial in a variety of fields, such as astronomy, optics, and photonics. It helps in understanding the behavior of light and its interactions with matter, which is essential in developing technologies such as solar panels, fiber optics, and laser technology. It also plays a significant role in the study of celestial bodies and the universe.

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