1. The smallest shift you can reliably measure on the screen is about 0.2 grid units. This shift corresponds to the precision of
1 answer:
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Answer:
The probability of finding the proton at the central 2% of the well is almost exactly 4%
Explanation:
If we solve Schrödinger's equation for the infinite square well, we find that its eigenfunctions are sinusoidal functions, in particular, the ground state is a sinusoidal function for which only half a cycle fits inside the well.
let be the well's length, the boundary conditions for the wavefunction are:
And Schrödinger's equation is:
The solution to this equation are sines and cosines, but the boundary conditions only allow for sine waves. As we pointed out, the ground state is the sine wave with the largest wavelength possible (that is, with the smallest energy).
here the leading constant is just there to normalise the wavefunction.
Now, if we know the wavefunction, we can know what the probability density function is, it is:
So in our case:
And to find the probability of finding the particle in a strip at the centre of the well of width 2% of L we only have to integrate:
If we do a substitution:
We get the integral:
This integral can be computed analytically, and it's numerical value is .0399868, that is, almost a 4% probability.
The period of a simple pendulum is given by
where
L is the pendulum length
g is the acceleration of gravity
If we move the same pendulum from Earth to the Moon, its length L remains the same, while the acceleration of gravity g changes. So we can write the period of the pendulum on Earth as:
where
is the acceleration of gravity on Earth, while the period of the pendulum on the Moon is
where
is the acceleration of gravity on the Moon.
If we do the ratio of the two periods, we get
but the gravity acceleration on the Moon is 1/6 of the gravity acceleration on Earth, so we can write
and we can rewrite the previous ratio as
so the period of the pendulum on the Moon is
where
L is the pendulum length
g is the acceleration of gravity
If we move the same pendulum from Earth to the Moon, its length L remains the same, while the acceleration of gravity g changes. So we can write the period of the pendulum on Earth as:
where
where
If we do the ratio of the two periods, we get
but the gravity acceleration on the Moon is 1/6 of the gravity acceleration on Earth, so we can write
so the period of the pendulum on the Moon is
F = normal force by each board on each side
W = weight of the board in between acting in down direction = 95.5 N
f = frictional force in upward direction by each board
= coefficient of friction = 0.663
Using equilibrium of force in Upward direction
f + f = W
f = W/2
f = 95.5/2 = 47.75 N
frictional force is given as
f = F
47.75 = (0.663) F
F = 72.02 N
