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tino4ka555 [31]
3 years ago
11

A rain gutter is to be constructed from a metal sheet of width 30 cm by bending up one-third of the sheet on each side through a

n angle θ . How should θ be chosen so that the gutter will carry the maximum amount of water?
Physics
1 answer:
GarryVolchara [31]3 years ago
7 0

Answer:

60

Explanation:

The volume of the water carried will be proportional to the cross-sectional area. The cross-section is a trapezoid with height 10sint, where t represents theta. The top of the trapezoid is 10+(2)(10cost), i.e. 10 + 20cost. The base of the trapezoid is 10.

Area of trapezoid = (average of bases) times (height)

= ([10 + (10 +20cost)] / 2 ) 10 sint

= (10 + 10cost)(10sint)

= 100sint + 100sintcost, call this A(t). You need to maximize. So differentiate and set equal to zero.

dA/dt = -100sin(t)^2+100cos(t)+100cos(t)^2 = 0, divide by 100:

-sin(t)^2 + cos(t) + cos(t)^2 = 0, replace sin^2 by 1-cos^2

2cos(t)^2 + cos(t) - 1 = 0, factor

(1+cos(t))(2cos(t)-1)=0, so  

cos(t)=1, t=0 that give a min (zero area) not a max, or

cos(t) = 1/2, so t=60 degrees. This gives the max.

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A spherical capacitor contains a charge of 3.50 nC when connected to a potential difference of 210.0 V. Its plates are separated
Lelu [443]

Incomplete question as we have not told to find what quantity.The complete question is here

A spherical capacitor contains a charge of 3.50 nC when connected to a potential difference of 210.0 V. Its plates are separated by vacuum and the inner radius of the outer shell is 5.00 cm.calculate: (a) the capacitance; (b) the radius of the inner sphere; (c) the electric field just outside the surface of the inner sphere.

Answer:

(a) C=16.7pF

(b) r_{a} =3.749cm

(c) E=2.24*10^{4} N/C

Explanation:

Given data

Q=3.50nC\\V=210V\\r_{b}=5.0cm

For part (a)

The Capacitance given by:

C=\frac{Q}{V}\\ C=\frac{3.50*10^{-9} C}{210V}\\C=1.6666*10^{-11}F\\or\\C=16.7pF

For part (b)

The Capacitance of coordinates is given as

C=\frac{4\pi e}{\frac{1}{r_{a} }-\frac{1}{r_{b} } }\\ So\\{\frac{1}{r_{a} }-\frac{1}{r_{b} } }=\frac{4\pi *8.85*10^{-12} }{1.666*10^{-11}}=6.672m^{-1} \\ \frac{1}{r_{a} }=6.672+(1 /0.05)\\\frac{1}{r_{a} }=26.672\\r_{a} =1/26.672\\r_{a} =0.0375m\\r_{a} =3.749cm

For part (c)

The electric field according to Gauss Law is given by:

EA=\frac{Q}{e}\\ E=\frac{Q}{4\pi er_{a}^{2}  }=\frac{kQ}{r_{a}^{2}}\\  E=\frac{9*10^{9}*3.50*10^{-9} }{(0.0375m)^{2} }\\ E=2.24*10^{4} N/C

7 0
3 years ago
An object with a mass of 9 kg weighs 14.4 N on the Moon. What is the
erma4kov [3.2K]

Answer:

1.6 m/s²

Explanation:

Weight equals mass times acceleration due to gravity.

F = mg

14.4 N = (9 kg) g

g = 1.6 m/s²

7 0
3 years ago
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a place that is typically cold because of an increase in altitude would most likely have what type of climate? dry climate mild
Marta_Voda [28]
A place that is cold because of an increase in altitude has a mountain area climate or simply, mountain climate. An area that is high in altitude typically has a colder temperature because of the increased amount of rainfall they have. Also, air tends to cool as it rises in temperature. 
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3 years ago
You are given a parallel plate capacitor that has plates of area 29 cm2 which are separated by 0.0100 mm of nylon (dielectric co
GalinKa [24]

Answer:

20.60 kV

Explanation:

Capacitance of parallel plates without dielectric between them is:

C=\frac{\varepsilon_{0}A}{d}

with d the distance between the plates, A the area of the plates and ε₀ the constant 8.85419\times10^{-12}\frac{C^{2}}{Nm^{2}}, so :

C_0=\frac{(8.85419\times10^{-12})(0.0029)}{0.0100\times10^{-3}}=2.57\times10^{-9} F

But the dielectric constant is defined as:

k=\frac{C}{C_{0}}

With C the effective capacitance (with the dielectric) and Co the original capacitance (without the dielectric). So, the new capacitance is:

C=kC_0

But capacitance is related with voltage by:

C=\frac{Q}{V}

with Q the charge and V the voltage, using the new capacitance and solving for V:

kC_0=\frac{Q}{V}

V=\frac{Q}{kC_0}=\frac{0.18\times10{-3}}{(3.4)(2.57\times10^{-9})}=20599.68V=20.60 kV

4 0
2 years ago
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If a box has a length of 10.0 cm, a width of 20.0 cm, and a height of 5.00 cm, then what is its volume in m^3?
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Explanation:

Solution,

Given:-

  • Length=10 cm
  • Width= 20 cm
  • Height= 5 cm
  • Volume =?

Now,

By using the formula of volume of a cuboid, we have

  • volume=length×width×height
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  • volume=1000 cm³
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  • volume=(1×10⁴) cm³

Hence, last option is the correct answer.

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