Answer:
P = VI
Explanation:
the power is equal to the current × voltage
Dispersion angle = 0.3875 degrees.
Width at bottom of block = 0.09297 cm
Thickness of rainbow = 0.07038 cm
Snell's law provides the formula that describes the refraction of light. It is:
n1*sin(θ1) = n2*sin(θ2)
where
n1, n2 = indexes of refraction for the different mediums
θ1, θ2 = angle of incident rays as measured from the normal to the surface.
Solving for θ2, we get
n1*sin(θ1) = n2*sin(θ2)
n1*sin(θ1)/n2 = sin(θ2)
asin(n1*sin(θ1)/n2) = θ2
The index of refraction for air is 1.00029, So let's first calculate the angles of the red and violet rays.
Red:
asin(n1*sin(θ1)/n2) = θ2
asin(1.00029*sin(40.80)/1.641) = θ2
asin(1.00029*0.653420604/1.641) = θ2
asin(0.398299876) = θ2
23.47193844 = θ2
Violet:
asin(n1*sin(θ1)/n2) = θ2
asin(1.00029*sin(40.80)/1.667) = θ2
asin(1.00029*0.653420604/1.667) = θ2
asin(0.39208764) = θ2
23.08446098 = θ2
So the dispersion angle is:
23.47193844 - 23.08446098 = 0.38747746 degrees.
Now to determine the width of the beam at the bottom of the glass block, we need to calculate the difference in the length of the opposite side of two right triangles. Both triangles will have a height of 11.6 cm and one of them will have an angle of 23.47193844 degrees, while the other will have an angle of 23.08446098 degrees. The idea trig function to use will be tangent, where
tan(θ) = X/11.6
11.6*tan(θ) = X
So for Red:
11.6*tan(θ) = X
11.6*tan(23.47193844) = X
11.6*0.434230136 = X
5.037069579 = X
And violet:
11.6*tan(θ) = X
11.6*tan(23.08446098) = X
11.6*0.426215635 = X
4.944101361 = X
So the width as measured from the bottom of the block is: 5.037069579 cm - 4.944101361 cm = 0.092968218 cm
The actual width of the beam after it exits the flint glass block will be thinner. The beam will exit at an angle of 40.80 degrees and we need to calculate the length of the sides of a 40.80/49.20/90 right triangle. If you draw the beams, you'll realize that:
cos(θ) = X/0.092968218
0.092968218*cos(θ) = X
0.092968218*cos(40.80) = X
0.092968218*0.756995056 = X
0.070376481 = X
So the distance between the red and violet rays is 0.07038 cm.
Answer:
Approximately 1.62 × 10⁻⁴ V.
Explanation:
The average EMF in the coil is equal to
,
Why does this formula work?
By Faraday's Law of Induction, the EMF 
induced in a coil (one loop) is equal to the rate of change in the magnetic flux 
through the coil.
.
Finding the average EMF in the coil is similar to finding the average velocity.
.
However, by the Fundamental Theorem of Calculus, integration reverts the action of differentiation. That is:
.
Hence the equation
.
Note that information about the constant term in the original function will be lost. However, since this integral is a definite one, the constant term in 
won't matter.
Apply this formula to this question. Note that , the magnetic flux through the coil, can be calculated with the equation
.
For this question,
is the strength of the magnetic field. 
is the area of the coil.
is the number of loops in the coil. 
is the angle between the field lines and the coil. - At
, the field lines are parallel to the coil, 
. - At
, the field lines are perpendicular to the coil, 
.
Initial flux: 
.
Final flux: 
.
Average EMF, which is the same as the average rate of change in flux:
.
Answer:
W = 55.12 J
Explanation:
Given,
Natural length = 6 in
Force = 4 lb, stretched length = 8.4 in
We know,
F = k x
k is spring constant
4 = k (8.4-6)
k = 1.67 lb/in
Work done to stretch the spring to 10.1 in.
![W = \dfrac{k}{2}[x^2]_6^{10.1}](https://tex.z-dn.net/?f=W%20%3D%20%5Cdfrac%7Bk%7D%7B2%7D%5Bx%5E2%5D_6%5E%7B10.1%7D)
W = 55.12 J
Work done in stretching spring from 6 in to 10.1 in is equal to 55.12 J.
Explanation:
a. moving a 145 kg aluminum sculpture across a horizontal steel platform
b. pulling a 15 kg steel sword across a horizontal steel shield
c. pushing a 250 kg wood bed on a horizontal wood floor
d. sliding a 0.55 kg glass amulet on a horizontal glass display case
