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inessss [21]
3 years ago
7

A particle moves along the x axis so that when t is greater than zero, it's position function is given by cos square root of t.

what is the velocity of the particle at the first instance when the particle is at the origin?
Physics
1 answer:
faust18 [17]3 years ago
4 0
The position is a cosine function, so the particle is at the origin
whenever the cosine is zero.
 
The first point where the cosine is zero occurs when the angle is  π/2 .
That happens when √t = π/2 , so t = π² / 4 is the point where we need
the particle's speed.

Speed is the first derivative of the position.
The derivative with respect to 't' of cos(√t) is [ -1 / (2√t) sin(√t) ] . (chain derivative.)

The speed when [ t = π² / 4 ] is . . .

-1 / 2√(π² / 4) times sin(√(π² / 4)) = -(1 / π) times sin(π/2) = -(1/π) times (1) = -(1/π) .

The first time when the particle is at the origin, it's moving backwards,
into [ -x ] territory, and its speed is (1/π) = about 0.3183... . (rounded)

There you have its speed and direction, so you have its velocity.
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Explanation:

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A spherical capacitor contains a charge of 3.40 nC when connected to a potential difference of 240.0 V. Its plates are separated
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Answer:

A) 1.4167 × 10^(-11) F

B) r_a = 0.031 m

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A) The formula for capacitance is given by;

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B) To find the radius of the inner sphere,we will make use of the formula for capacitance of spherical coordinates.

C = (4πε_o)/(1/r_a - 1/r_b)

Rearranging, we have;

(1/r_a - 1/r_b) = (4πε_o)/C

ε_o is a constant with a value of 8.85 × 10^(−12) C²/N.m

Plugging in the relevant values, we have;

(1/r_a - 1/0.041) = (4π × 8.85 × 10^(−12) )/(1.4167 × 10^(-11))

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1/r_a = 7.8501 + 24.3902

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C) Formula for Electric field just outside the surface of the inner sphere is given by;

E = kQ/r_a²

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E = (8.99 × 10^(9) × 3.4 × 10^(-9))/0.031²

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Answer with Explanation:

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Metal volume flow  rate,Q=0.03m^3/min

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Let 1 for the top and 2 for the bottom

d_=0.030 m

h_2=0

A_1=\frac{\pi d^2}{4}=\frac{3.14\times (0.030)^2}{4}

A_1=7.065\times 10^{-4} m^2

v_1=\frac{Q}{A_1}=\frac{5\times 10^{-4}}{7.065\times 10^{-4}}

v_1=0.708 m/s

Pressure at the top and bottom of the sprue is atmospheric

h_1+\frac{v^2_1}{2g}=h_2+\frac{v^2_2}{2g}

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0.2+\frac{(0.708)^2}{2\cdot 9.8}=0+\frac[v^2_2}{2\cdot 9.8}

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\eta=0.004 N.s/m^2

\rho=2700 kg/m^3

Substitute the values then we get

Reynolds number=\frac{2.1\times 0.03\times 2700}{0.004}

Reynolds number=42525

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