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3 years ago

What effect will be produced on a capacitor if the separation between the plates is increased

Physics

1 answer:

soldi70 [24.7K]3 years ago

7 0

It will decrease the capacitance because we know nothing about the charge.

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Find the area of the part of the plane 5x 3y z = 15 that lies in the first octant.

Lunna [17]

This part of the plane lies above a triangle with boundaries $x=0$ and $y=0$ along the coordinate axes, as well as the line

$z=0 \implies 5x + 3y = 15 \implies y = \dfrac{15 - 5x}3$

When $y=0$ , we have $15-5x=0\implies x=3$ . So this triangle is the set

$T = \left\{(x,y)\in\Bbb R^2 ~:~ 0\le x\le3 \text{ and } 0\le y\le\dfrac{15-5x}3\right\}$

Also, when $x=0$ , we have $y=\frac{15}3=5$ . So the triangle has length 3 and width 5, hence area 1/2•3•5 = 15/2.

Let $z=f(x,y) = 15 - 5x - 3y$ . Then the area of the plane over $T$ is

$\displaystyle \iint_T dA = \iint_T \sqrt{1 + \left(\frac{\partial f}{\partial x}\right)^2 + \left(\frac{\partial f}{\partial y}\right)^2} \, dx \, dy$

We have

$\dfrac{\partial f}{\partial x} = -5 \implies \left(\dfrac{\partial f}{\partial x}\right)^2 = 25$

$\dfrac{\partial f}{\partial y} = -3 \implies \left(\dfrac{\partial f}{\partial y}\right)^2 = 9$

$\implies\displaystyle \iint_T dA = \sqrt{35} \iint_T dx\,dy = \boxed{\frac{15\sqrt{35}}2}$

since the integral

$\displaystyle \iint_TdA$

is exactly the area of $T$ , 15/2.

8 0

2 years ago

A 56.0kg ice skater spins about a vertical axis through her body with her arms horizontally outstretched, making 2.50 turns each

Arada [10]

Answer:

Net force = 129.4, Force as multiple of weight of her hand = 18.84

Explanation:

Given Data:

Total body weight = 56.0 kg ;

no. of turns = 2.5/second ;

hand to hand distance = 1.5m ;

weight of hand = 1.25% of body weight ;

Solution:

mass of hand = $\frac{1.25}{100}$ *56 = 0.7kg ;

radius = d/2 = 1.5/2 = 0.75m ;

Now we need to find velocity, as we know that velocity can be calculated by dividing distance by time

v = d/t = $\frac{2.5*2*3.14*0.75}{1}$ = 11.775 m/s or 12 m/s;

The formula to calculate force is given as

F = mv²/r = (0.7*11.775²)/0.75 = 129.4 N

To calculate force as multiple of weight on her hand, we need to calculate the gravitational force W on her hand first.

W = gm = 9.81 * 0.7 = 6.867 N

Now the wieght on her hand can be represented by

$\frac{Force_{net} }{weight of hand}$ = 129.4 / 6.867 = 18.84

3 0

3 years ago

Which light is most sensitive to the eyes?

san4es73 [151]

Answer:

Our eyes are most sensitive to the wavelengths corresponding to the yellow and green colors of the spectrum. Flashy signs and some fire engines are painted in a yellowish-green color to attract our attention.

6 0

2 years ago

3. Calculate the momentum of a 1200kg car with a velocity of 25m/s.

antiseptic1488 [7]

momm=massxvelocity

momm=1200x2.5=120x25=600x5=3000kgm/s

4 0

3 years ago

A woman is riding a jet ski at a speed of 26 m/s and notices a seawall straight ahead. the farthest she can lean the craft in or

castortr0y [4]

she can stop about 16 feet before hitting it

7 0

3 years ago