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Lemur [1.5K]
3 years ago
15

Two 1.0 g balls are connected by a 2.0-cm-long insulating rod of negligible mass. One ball has a charge of +10 nC, the other a 4

charge of - 10 nC. The rod is held in a 1.0 * 10 N/C uniform electric field at an angle of 30° with respect to the field, then released. What is its initial angular acceleration?
Physics
1 answer:
Irina18 [472]3 years ago
5 0

Answer:

  α = 5 10⁻³ rad / s²

Explanation:

For this exercise we can use Newton's second law for rotational movement, where the force is electric

             τ = I α

Where the torque is

             τ = F x r = F r sin θ

Strength is

              F = q E

The moment of inertia of a small ball, which we approximate to a point is

             I = m r²

We replace

            2 (q E) r sin θ   = 2m r² α

The number 2 is because the two forces create the same torque

             α = q E sin θ / m r

Let's reduce the magnitudes to the SI system

           m = 1.0g = 1.0 10⁻³ kg

           L = 2.0 cm = 2.0 10⁻² m

           q = 10 nc = 10 10⁻⁹ C

           E = 1.0 10 N / C

           r = L / 2

           r = 1.0 10⁻² m

Let's calculate

           α = 10 10⁻⁹ 1.0 10 sin 30 / 1.0 10⁻³ 1.0 10⁻²

           α = 5 10⁻³ rad / s²

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HOPE THIS HELPS YOU MATE!!
I HAVE ALSO GIVEN THE EXPLANATION THINKING THAT IT MIGHT HELP YOU.
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Answer:

The mass of the solid is 16 units.

The center of mass of the solid lies at (0.6875, 0.3542, 2.021)

Work:

Density function: ρ(x, y, z) = 8

x-bounds: [0, 1], y-bounds: [0, x], z-bounds: [0, x+y+3]

The mass M of the solid is given by:

M = ∫∫∫ρ(dV) = ∫∫∫ρ(dx)(dy)(dz) = ∫∫∫8(dx)(dy)(dz)

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Then integrate with respect to y:

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Now we have to find the center of mass of the solid which requires calculating the center of mass in the x, y, and z dimensions.

The z-coordinate of the center of mass Z is given by:

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= ∫∫[4(x+y+3)²](dx)(dy)

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Then integrate with respect to y:

∫[4x²y+24xy+4xy²+4y³/3+12y²+36y]dx, evaluate y from 0 to x

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Finally integrate with respect to x:

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The y-coordinate of the center of mass Y is given by:

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<em>Calculate the integral then divide the result by 16.</em>

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= ∫∫[8xy+8y²+24y](dx)(dy)

Then integrate with respect to y:

∫[4xy²+8y³/3+12y²]dx, evaluate y from 0 to x

= ∫[20x³/3+12x²]dx

Finally integrate with respect to x:

[5x⁴/3+4x³], evaluate x from 0 to 1

= 5/3+4

Y = (5/3+4)/16 = <u>0.3542</u>

<u />

The x-coordinate of the center of mass X is given by:

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<em>Calculate the integral then divide the result by 16.</em>

First integrate with respect to z:

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X = 11/16 = <u>0.6875</u>

<u />

The center of mass of the solid lies at (0.6875, 0.3542, 2.021)

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