All of the following affect the climate of an area except
2 answers:
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Answer:
Minimum number of photons required is 1.35 x 10⁵
Explanation:
Given:
Wavelength of the light, λ = 850 nm = 850 x 10⁻⁹ m
Energy of one photon is given by the relation :
....(1)
Here h is Planck's constant and c is speed of light.
Let N be the minimum number of photons needed for triggering receptor.
Minimum energy required for triggering receptor, E₁ = 3.15 x 10⁻¹⁴ J
According to the problem, energy of N number of photons is equal to the energy required for triggering, that is,
E₁ = N x E
Put equation (1) in the above equation.
Substitute 3.15 x 10⁻¹⁴ J for E₁, 850 x 10⁻⁹ m for λ, 6.6 x 10⁻³⁴ J s for h and 3 x 10⁸ m/s for c in the above equation.
N = 1.35 x 10⁵
a)
The equation which gives the position of a simple harmonic oscillator is:
where
A is the amplitude
is the angular frequency, with k being the spring constant and m the mass
t is the time
Let's start by calculating the angular frequency:
The amplitude, A, can be found from the maximum velocity of the spring:
So, the equation of motion is
b) t=0.10 s, t=0.52 s
The potential energy is given by:
While the kinetic energy is given by:
The velocity as a function of time t is:
The problem asks as the time t at which U=3K, so we have:
However, , so we have
with two solutions:
c) 3 seconds.
When x=0, the equation of motion is:
so, t=0.
When x=1.00 m, the equation of motion is:
So, the time needed is 3 seconds.
d) 0.097 m
The period of the oscillator in this problem is:
The period of a pendulum is:
where L is the length of the pendulum. By using T=0.628 s, we find