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mixer [17]
3 years ago
15

A sphere of radius R contains charge Q spread uniformly throughout its volume. Find an expression for the electrostatic energy c

ontained within the sphere itself.
Physics
1 answer:
tensa zangetsu [6.8K]3 years ago
7 0

Answer:

E = \frac{3kQ^2}{5R}

Explanation:

Let the sphere is uniformly charge to radius "r" and due to this charged sphere the electric potential on its surface is given as

V = \frac{kq}{r}

now we can say that

q = \frac{Q}{\frac{4}{3}\pi R^3} (\frac{4}{3}\pi r^3)

q = \frac{Qr^3}{R^3}

now electric potential is given as

V = \frac{k\frac{Qr^3}{R^3}}{r}

V = \frac{kQr^2}{R^3}

now work done to bring a small charge from infinite to the surface of this sphere is given as

dW = V dq

dW = \frac{kQr^2}{R^3} dq

here we know that

dq = \frac{3Qr^2dr}{R^3}

now the total energy of the sphere is given as

E = \int dW

E = \int_0^R  \frac{kQr^2}{R^3} (\frac{3Qr^2dr}{R^3})

E = \frac{3kQ^2}{R^6} (\frac{R^5}{5} - 0)

E = \frac{3kQ^2}{5R}

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Ann [662]

Meter #2 is more precise.

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4 0
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21) A youngster having a mass of 50.0 kg steps off a 1.00 m high platform. If she keeps her legs fairly rigid and comes to rest
zlopas [31]

Answer:

-22,150 N

Explanation:

When the youngster jumps off the platform, during the fall her initial potential energy is converted into kinetic energy, according to the law of conservation of energy. Therefore, we can write:

mgh=\frac{1}{2}mu^2

where the term on the left is the potential energy while the term on the right is the kinetic energy, and where

m = 50.0 kg is the mass of the youngster

g=9.8 m/s^2 is the acceleration due to gravity

h = 1.00 m is the heigth of the platform

u is the speed of the youngster as she reaches the floor

Solving for u,

u=\sqrt{2gh}=\sqrt{2(9.8)(1.00)}=4.43 m/s

Then, when the youngster hits the floor, the force exerted on her during the deceleration is given by:

F=\frac{\Delta p}{\Delta t}=\frac{m(v-u)}{\Delta t}

where \Delta p is her change in momentum, and where

m is the mass

v = 0 is the final velocity (she comes to a stop)

u = 4.43 m/s is the initial velocity

\Delta t=10.0 ms =0.010 s is the duration of the collision

Substituting,

F=\frac{(50.0)(0-4.43)}{0.010}=-22150 N

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6 0
3 years ago
Two 5.0 kilogram objects have different gravitational potential energies. What property of the objects must differ?
ipn [44]

Answer:

Height.

Explanation:

Potential energy can be defined as an energy possessed by an object or body due to its position.

Mathematically, potential energy is given by the formula;

P.E = mgh

Where,

P.E represents potential energy measured in Joules.

m represents the mass of an object.

g represents acceleration due to gravity measured in meters per seconds square.

h represents the height measured in meters.

Hence, the property of the object (having a mass of 5 kilograms) which must differ to have different gravitational potential energies is the height from which they are falling from.

The object having the higher height would have a greater gravitational potential energy than the lower object.

7 0
2 years ago
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