We intend to observe two distant equal brightness stars whose angular separation is 50.0 × 10-7 rad. Assuming a mean wavelength
2 answers:
Answer:
13.4cm
Explanation:
According to Rayleigh’s criterion the angular resolution to distinguish two objects is given by:
θ = 50.0*10^-7 rad
λ: wavelength of the light = 550nm
b = diameter of the objective
By doing b the subject of the formula and replacing the values of the angle and wavelength you obtain:
hence, the smallest diameter objective lens is 13.4cm
Answer:
0.134 m
Explanation:
Given:
θ=50.0 × 10-7
λ=550 nm
angular resolution to distinguish two objects developed by Lord Rayleigh is given by:
θ= 1.22 λ/d
where λ is the wavelength of light (or other electromagnetic radiation) and D is the diameter of the aperture, lens, mirror, etc., with which the two objects are observed.
d= 1.22 λ/θ
d= (1.22 x 550 x ) / 50 x
d=0.134 m
Therefore, the smallest diameter objective lens that will resolve the stars is 0.134 m
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There is a missing data in the text of the problem (found on internet):
"with force constant<span> k=</span>450N/<span>m"
a) the maximum speed of the glider
The total mechanical energy of the mass-spring system is constant, and it is given by the sum of the potential and kinetic energy:
</span>
<span>where
k is the spring constant
x is the displacement of the glider with respect to the spring equilibrium position
m is the glider mass
v is the speed of the glider at position x
When the glider crosses the equilibrium position, x=0 and the potential energy is zero, so the mechanical energy is just kinetic energy and the speed of the glider is maximum:
</span>
<span>Vice-versa, when the glider is at maximum displacement (x=A, where A is the amplitude of the motion), its speed is zero (v=0), therefore the kinetic energy is zero and the mechanical energy is just potential energy:
</span>
<span>
Since the mechanical energy must be conserved, we can write
</span>
<span>from which we find the maximum speed
</span>
<span>
b) </span><span> the </span>speed<span> of the </span>glider<span> when it is at x= -0.015</span><span>m
We can still use the conservation of energy to solve this part.
The total mechanical energy is:
</span>
<span>
At x=-0.015 m, there are both potential and kinetic energy. The potential energy is
</span>
<span>And since
</span>
<span>we find the kinetic energy when the glider is at this position:
</span>
<span>And then we can find the corresponding velocity:
</span>
<span>
c) </span><span>the magnitude of the maximum acceleration of the glider;
</span>
For a simple harmonic motion, the magnitude of the maximum acceleration is given by
where
is the angular frequency, and A is the amplitude.
The angular frequency is:
and so the maximum acceleration is
d) <span>the </span>acceleration<span> of the </span>glider<span> at x= -0.015</span><span>m
For a simple harmonic motion, the acceleration is given by
</span>
<span>where x(t) is the position of the mass-spring system. If we substitute x(t)=-0.015 m, we find
</span>
<span>
e) </span><span>the total mechanical energy of the glider at any point in its motion. </span><span>
we have already calculated it at point b), and it is given by
</span>
"with force constant<span> k=</span>450N/<span>m"
a) the maximum speed of the glider
The total mechanical energy of the mass-spring system is constant, and it is given by the sum of the potential and kinetic energy:
</span>
<span>where
k is the spring constant
x is the displacement of the glider with respect to the spring equilibrium position
m is the glider mass
v is the speed of the glider at position x
When the glider crosses the equilibrium position, x=0 and the potential energy is zero, so the mechanical energy is just kinetic energy and the speed of the glider is maximum:
</span>
<span>Vice-versa, when the glider is at maximum displacement (x=A, where A is the amplitude of the motion), its speed is zero (v=0), therefore the kinetic energy is zero and the mechanical energy is just potential energy:
</span>
<span>
Since the mechanical energy must be conserved, we can write
</span>
<span>from which we find the maximum speed
</span>
<span>
b) </span><span> the </span>speed<span> of the </span>glider<span> when it is at x= -0.015</span><span>m
We can still use the conservation of energy to solve this part.
The total mechanical energy is:
</span>
<span>
At x=-0.015 m, there are both potential and kinetic energy. The potential energy is
</span>
<span>And since
</span>
<span>we find the kinetic energy when the glider is at this position:
</span>
<span>And then we can find the corresponding velocity:
</span>
<span>
c) </span><span>the magnitude of the maximum acceleration of the glider;
</span>
For a simple harmonic motion, the magnitude of the maximum acceleration is given by
where
The angular frequency is:
and so the maximum acceleration is
d) <span>the </span>acceleration<span> of the </span>glider<span> at x= -0.015</span><span>m
For a simple harmonic motion, the acceleration is given by
</span>
<span>where x(t) is the position of the mass-spring system. If we substitute x(t)=-0.015 m, we find
</span>
<span>
e) </span><span>the total mechanical energy of the glider at any point in its motion. </span><span>
we have already calculated it at point b), and it is given by
</span>
Answer:
<em>B) 1.0 × 10^5 V</em>
Explanation:
<u>Electric Potential Due To Point Charges </u>
The electric potential produced from a point charge Q at a distance r from the charge is
The total electric potential for a system of point charges is equal to the sum of their individual potentials. This is a scalar sum, so direction is not relevant.
We must compute the total electric potential in the center of the square. We need to know the distance from all the corners to the center. The diagonal of the square is
where a is the length of the side.
The distance from any corner to the center is half the diagonal, thus
The total potential is
Where V1 and V2 are produced by the +4\mu C charges and V3 and V4 are produced by the two opposite charges of . Since all the distances are equal, and the charges producing V3 and V4 are opposite, V3 and V4 cancel each other. We only need to compute V1 or V2, since they are equal, but they won't cancel.
The total potential is