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3 years ago

If trees have leaves, then birds nests will increase. What the independent variable and the dependent variable?

Physics

1 answer:

Marianna [84]3 years ago

5 0

The amount of birds nests depends on whether or not the trees have more or less leaves.

The independent should be the trees/leaves.

The dependent variable should be the birds nests.

Hope this helped ^-^

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What is the most important safety rule in cycling?

Mekhanik [1.2K]

Answer:

Wear a helmet. Stay visible; use bike lights and/or wear bright clothes. Look and Signal; use hand signals to let drivers know where you're going, try to make eye contact with them and look before you go.

Explanation:

4 0

2 years ago

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A closely wound, circular coil with a diameter of 4.30 cm has 470 turns and carries a current of 0.460 A .

Nadusha1986 [10]

Hi there!

a)
Let's use Biot-Savart's law to derive an expression for the magnetic field produced by ONE loop.

$dB = \frac{\mu_0}{4\pi} \frac{id\vec{l} \times \hat{r}}{r^2}$

dB = Differential Magnetic field element

μ₀ = Permeability of free space (4π × 10⁻⁷ Tm/A)

R = radius of loop (2.15 cm = 0.0215 m)

i = Current in loop (0.460 A)

For a circular coil, the radius vector and the differential length vector are ALWAYS perpendicular. So, for their cross-product, since sin(90) = 1, we can disregard it.

$dB = \frac{\mu_0}{4\pi} \frac{id\vec{l}}{r^2}$

Now, let's write the integral, replacing 'dl' with 'ds' for an arc length:
$B = \int \frac{\mu_0}{4\pi} \frac{ids}{R^2}$

Taking out constants from the integral:
$B =\frac{\mu_0 i}{4\pi R^2} \int ds$

Since we are integrating around an entire circle, we are integrating from 0 to 2π.

$B =\frac{\mu_0 i}{4\pi R^2} \int\limits^{2\pi R}_0 \, ds$

Evaluate:
$B =\frac{\mu_0 i}{4\pi R^2} (2\pi R- 0) = \frac{\mu_0 i}{2R}$

Plugging in our givens to solve for the magnetic field strength of one loop:

$B = \frac{(4\pi *10^{-7}) (0.460)}{2(0.0215)} = 1.3443 \mu T$

Multiply by the number of loops to find the total magnetic field:
$B_T = N B = 0.00631 = \boxed{6.318 mT}$

Now, we have an additional component of the magnetic field. Let's use Biot-Savart's Law again:
$dB = \frac{\mu_0}{4\pi} \frac{id\vec{l} \times \hat{r}}{r^2}$

In this case, we cannot disregard the cross-product. Using the angle between the differential length and radius vector 'θ' (in the diagram), we can represent the cross-product as cosθ. However, this would make integrating difficult. Using a right triangle, we can use the angle formed at the top 'φ', and represent this as sinφ.

$dB = \frac{\mu_0}{4\pi} \frac{id\vec{l} sin\theta}{r^2}$

Using the diagram, if 'z' is the point's height from the center:

$r = \sqrt{z^2 + R^2 }\\\\sin\phi = \frac{R}{\sqrt{z^2 + R^2}}$

Substituting this into our expression:
$dB = \frac{\mu_0}{4\pi} \frac{id\vec{l}}{(\sqrt{z^2 + R^2})^2} }(\frac{R}{\sqrt{z^2 + R^2}})\\\\dB = \frac{\mu_0}{4\pi} \frac{iRd\vec{l}}{(z^2 + R^2)^\frac{3}{2}} }$

Now, the only thing that isn't constant is the differential length (replace with ds). We will integrate along the entire circle again:
$B = \frac{\mu_0 iR}{4\pi (z^2 + R^2)^\frac{3}{2}}} \int\limits^{2\pi R}_0, ds$

Evaluate:
$B = \frac{\mu_0 iR}{4\pi (z^2 + R^2)^\frac{3}{2}}} (2\pi R)\\\\B = \frac{\mu_0 iR^2}{2 (z^2 + R^2)^\frac{3}{2}}}$

Multiplying by the number of loops:
$B_T= \frac{\mu_0 N iR^2}{2 (z^2 + R^2)^\frac{3}{2}}}$

Plug in the given values:
$B_T= \frac{(4\pi *10^{-7}) (470) (0.460)(0.0215)^2}{2 ((0.095)^2 + (0.0215)^2)^\frac{3}{2}}} \\\\ = 0.00006795 = \boxed{67.952 \mu T}$

5 0

1 year ago

Read 2 more answers

Strong winds causing a vehicle to lose all control is called

mixer [17]

The answer to this question is "Buffeting". This is an unusual strong wind condition that resulted in the loss of vehicle control. This condition occurs in roads and bridges, across and along mountains that affected vehicles control. The drivers must be alert and put their full attention to overcome this condition.

4 0

2 years ago

An eagle is flying horizontally at a speed of 2.60 m/s when the fish in her talons wiggles loose and falls into the lake 4.60 m

sergij07 [2.7K]

Answer:

9.495 m/s

Explanation:

initial horizontal speed, ux = 2.60 m/s

initial vertical speed, uy = 0

height, h = 4.60 m

acceleration due to gravity, g = 9.8 m/s^2

Let the speed of fish is v as it hits the water level.

Use third equation of motion in vertical direction

$v^{2}= u^{2}+2as$

$v^{2}= 0^{2}+2\times 9.8\times 4.60$

v = 9.495 m/s

Thus, the fish hits the water level with the speed of 9.495 m/s.

8 0

3 years ago

The current in the wires of a circuit is 120.0 milliamps.If the voltage impressed across the ends of the circuit where tripled(w

ivanzaharov [21]

Answer:

Explanation:

Current in a wire is 120mA

I = 120mA = 120 × 10^-3 A

I = 0.12 A

If the voltage applied at across the wire is tripled

From ohms law

V=IR

R = V / I

Since R is constant

Then,

V / I = K

Then, we can say

V / I = V' / I'

Given that,

Initially

V = V and I = 120mA

Then, V' = 3V and I' =?

So,

V / I = V' / I'

V / 120 = 3V / I'

Cross multiply

V × I' = 120 × 3V

Divide both sides by V

I' = 120 × 3V / V

I' = 360mA

So, the current in the wire when the voltage was tripled is 360mA, the current was also tripled

3 0

3 years ago