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:
Total length of spring 0.647 m
Explanation:
We have given mass of the person m = 150 kg
Acceleration due to gravity
Spring constant k = 10000 N/m
Nominal length of spring = 0.50
According to hook's law
x = 0.147 m
So total length of spring = 0.50+0.147 = 0.647 m
People are asleep at 3 am so energy would be less then.
Answer:
g'(10) =
Explanation:
Since g is the inverse of f ,
We can write
g(f(x)) = x <em> </em><em>(Identity)</em>
Differentiating both sides of the equation we get,
g'(f(x)).f'(x) = 1
g'(10) = --equation[1] Where f(x) = 10
Now, we have to find x when f(x) = 10
Thus 10 = + 2
= 8
x =
Since f(x) = + 2
f'(x) = -
f'() = -4 × 4 = -16
Putting it in equation 1, we get:
We get g'(10) = -
Answer:
PE=4900J
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Explanation:
P.E=m×g×h
Given m = 50 Kg , h = 10 m.
P.E=50×10×9.8
P.E=50×98=4900J
Hence increase in potential energy is 4900J.