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lisabon 2012 [21]
4 years ago
8

Air becomes a conductor when the electric field strength exceeds 3.01 × 106 N/C. Determine the maximum amount of charge that can

be carried by a metal sphere 5.0 m in radius. The value of the Coulomb constant is 8.99 × 109 N · m2 /C 2 . Answer in units of C.
Physics
1 answer:
Blizzard [7]4 years ago
3 0

Answer:

8.37×10⁻³ C.

Explanation:

The formula of electric field is given as

E = kq/r².......................... Equation 1

Where E = electric field, q = amount of charge, k = coulomb constant, r = radius of the sphere

make q the subject of the equation

q = Er²/k .................... Equation 2

Given: E = 3.01×10⁶ N/C, r = 5.0 m, k = 8.99×10⁹ Nm²/C².

Substitute into equation 2

q = (3.01×10⁶)(5²)/(8.99×10⁹)

q = (75.25/8.99)×10⁻³

q = 8.37×10⁻³ C.

Hence the maximum amount of charge = 8.37×10⁻³ C.

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Answer:

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v = A ω cos ω t

a = -A ω^2 sin ω t        

a (max) = -A ω^2     is the max acceleration (- can be ignored here)

ω = (K/ m)^1/2        for SHM

F = - K x^2     restoring force of spring

K = 4.34 / .0745^2 = 782 N / m

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Explanation:

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velocity of Gazelle (Vg) = 63,863.8 kg

mass of Lion and Gazelle (M) = 200,900.7 kg

velocity of Lion and Gazelle (V) = ?

The first figure below shows the motion of the Lion and Gazelle with their direction.

The second diagram shows the motion of the Lion and Gazelle with their directions rearranged to form a right angle triangle.

from the triangle formed we can get the velocity of the Lion and Gazelle immediately after collision using their momentum and Phytaghoras theorem

momentum = mass x velocity

momentum of the Lion = 169,169 x 77,377.3 = 13,089,840,463.7 kgm/s

momentum of the Gazelle = 31,731.7 x 63,863.8 = 2,026,506,942.46 kgm/s

momentum of the Lion and Gazelle = 200,900.7  x V

now applying Phytaghoras theorem we have

13,089,840,463.7 + 2,026,506,942.46 =  200,900.7 x V

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