How Does Light Absorption Affect the Oscillation Period of a Pendulum?

[Tanya Sharma]

Homework Statement

A small plate of mass m is suspended by a light string of length l .A monochromatic light beam starts falling on it and is completely absorbed. If the energy falling on the plate per unit time is W, then find the time period of oscillation?

Homework Equations

The Attempt at a Solution

I feel the light falling on the disk exerts some force on the disk .If it is a constant force then the equilibrium position is shifted.

But I am unable to relate the energy falling on the plate with the force it exerts.

I would be grateful if someone could help me with the problem.

 

[Saitama]

Homework Statement

A small plate of mass m is suspended by a light string of length l .A monochromatic light beam starts falling on it and is completely absorbed. If the energy falling on the plate per unit time is W, then find the time period of oscillation?

Homework Equations

The Attempt at a Solution

I feel the light falling on the disk exerts some force on the disk .If it is a constant force then the equilibrium position is shifted.

But I am unable to relate the energy falling on the plate with the force it exerts.

I would be grateful if someone could help me with the problem.

Suppose $n$ photons strike the plate per second. Can you work out the change in momentum of these photons and the force acting on the plate?

Do you know of a relation between energy and number of photons?

You should be able to work out the force acting due to photons with the two equations you get.

 

[ehild]

If you have found the average force the light exerts, find the equilibrium position of the plate in terms of W and mg, then the net force on the plate when it is displaced from that equilibrium position. ehild

 

[Tanya Sharma]

Thank you Pranav...

Thanks ehild...

 

[HalfLostAndSearching]

I would approach this problem by first defining some key variables and equations. The time period of oscillation, T, is the time it takes for the pendulum to complete one full swing. It can be calculated using the equation T = 2π√(l/g), where l is the length of the string and g is the acceleration due to gravity.

In this case, the falling light beam is providing energy to the pendulum, causing it to oscillate. The energy, W, falling on the plate per unit time can be expressed as power, P, which is equal to W/t. This power is related to the force, F, exerted on the plate by the light beam through the equation P = Fv, where v is the velocity of the plate.

To determine the force exerted by the light beam, we can use the equation F = dp/dt, where dp is the change in momentum over time. The change in momentum can be calculated using the equation dp = m(vf - vi), where m is the mass of the plate, vf is the final velocity (zero in this case), and vi is the initial velocity (also zero).

Combining these equations, we can express the force exerted by the light beam as F = m(vf - vi)/t. This force will cause the pendulum to oscillate, and we can use the equation F = ma to find the acceleration, a, of the pendulum. Substituting this into the equation for the time period, T = 2π√(l/g), we can solve for T in terms of the variables given in the problem.

Overall, the time period of oscillation will depend on the length of the string, the mass of the plate, the energy falling on the plate per unit time, and the acceleration due to gravity. By manipulating the equations and plugging in the given values, we can find the time period of oscillation for this specific scenario.