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Tanzania [10]
3 years ago
6

A positive charge distribution exists within a nonconducting spherical region of radius a. The volume charge density ρ is not un

iform but varies with the distance r from the center of the spherical charge distribution, according to the relationship ρ=βr for 0<=0<=a, where β is a positive constant, and ρ=0, and r>a.A. Show that the total charge Q in the spherical region of radius a is βπa^4B. In terms of β,r,a and fundamential constants, determine the magnitude of the electric field at a point a from distance r from the center of the spherical charge distribution for each of the following cases.i. r>aii. r=aiii 0
Physics
1 answer:
baherus [9]3 years ago
5 0

A negative charge and a positive charge

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Starting from rest, a basketball rolls from the top to the bottom of a hill, reaching a translational speed of 6.1 m/s. Ignore f
tatiyna

Answer:

a) h=3.16 m, b)  v_{cm }^ = 6.43 m / s

Explanation:

a) For this exercise we can use the conservation of mechanical energy

Starting point. Highest on the hill

           Em₀ = U = mg h

final point. Lowest point

           Em_{f} = K

Scientific energy has two parts, one of translation of center of mass (center of the sphere) and one of stationery, the sphere

           K = ½ m v_{cm }^{2} + ½ I_{cm} w²

angular and linear speed are related

           v = w r

           w = v / r

            K = ½ m v_{cm }^{2} + ½ I_{cm} v_{cm }^{2} / r²

            Em_{f} = ½ v_{cm }^{2} (m + I_{cm} / r2)

as there are no friction losses, mechanical energy is conserved

             Em₀ = Em_{f}

             mg h = ½ v_{cm }^{2} (m + I_{cm} / r²)         (1)

             h = ½ v_{cm }^{2} / g (1 + I_{cm} / mr²)

for the moment of inertia of a basketball we can approximate it to a spherical shell

             I_{cm} = ⅔ m r²

we substitute

            h = ½ v_{cm }^{2} / g (1 + ⅔ mr² / mr²)

            h = ½ v_{cm }^{2}/g    5/3

             h = 5/6 v_{cm }^{2} / g

           

let's calculate

           h = 5/6 6.1 2 / 9.8

           h = 3.16 m

b) this part of the exercise we solve the speed of equation 1

          v_{cm }^{2} = 2m gh / (1 + I_{cm} / r²)

in this case the object is a frozen juice container, which we can simulate a solid cylinder with moment of inertia

              I_{cm} = ½ m r²

we substitute

             v_{cm } = √ [2gh / (1 + ½)]

             v_{cm } = √(4/3 gh)

let's calculate

             v_{cm } = √ (4/3 9.8 3.16)

             v_{cm }^ = 6.43 m / s

4 0
3 years ago
Suppose that the Sun started shrinking in size, without losing any mass. What would be the effect of the Sun's change on the orb
adell [148]

Answer:

F = G M m / R^2 gravitational force on planet of mass m.

None of these quantities change in the given hypothesis so

there will be no change in the orbit of mass m

3 0
2 years ago
Determine whether the given value is a statistic or a parameter. a homeowner measured the voltage supplied to his home on 20 day
Gelneren [198K]
<span>For this example, the value presented would be considered a statistic. The value is a statistic as it represents a numerical measurement of a sample. If it were a parameter, it would need to represent a numerical measurement of a population.</span>
4 0
3 years ago
Two 6 ohm resistors in parallel gives an equivalent resistance of
Mashcka [7]

Answer:

3 ohms

Explanation:

6×6/6+6 =3 .............

3 0
3 years ago
Find the mass of a sample of water if its temperature dropped 24.8 °C when it lost 870 J of
rosijanka [135]

Answer:

8.35 × 10^{-3} kg

Explanation:

Remember the formula for heat:

Q=mc\Delta T

You just need to solve for m, doing so you're left with:

m=\dfrac{Q}{c\Delta T}

Replace the variables with numbers and that's it.

7 0
2 years ago
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