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Two small metal cubes with masses 2.0 g and 4.0 g are tied together by a 4.7-cm-long massless string and are at rest on a frictionless surface. Each is charged to +2.5 μC .
What is the energy of this system?
Express your answer using two significant figures.
What is the tension in the string?
Express your answer using two significant figures.
The string is cut. What is the speed of each sphere when they are far apart?
Hint: There are two conserved quantities. Make use of both.
Express your answers using two significant figures. Enter your answers numerically separated by a comma.
(v2g,v4g)=_____m/s

Respuesta :

Answer:

1.2J

26 N

(-28, 14) m/s

Explanation:

energy

U = kQq / d = 8.99*10^9 * (2.5*10^-6C)² / 0.047m

U = 0.0562/0.047

U = 1.20 J

to two significant figures

tension

T = kQq / d²

T = U / d

T = 1.2 / 0.047

T = 25.53 N = 26 N to 2 sf

Momentum is conserved, and the initial momentum is zero:

0 = 0.0020 * V2 + 0.0040 * V4

so

V2 = -2 * V4

Energy is also conserved:

½ * 0.0020 * (-2V4)² + ½ * 0.0040 * (V4)² = 1.2 J

-½ * 0.0080 * V4² + ½ * 0.0040 * V4² = 1.2 J

-0.0040V4² + 0.002V4² = 1.2 J

0.0060V4² = 1.2 J

V4² = 1.2/0.0060

V4² = 200

V4 = √200

V4 = 14 m/s

and since V2 = -2 * V4

V2 = -28 m/s

(V2, V4) = (-28, 14)

The energy of this system is 1.2J

The  tension in the string is 26 N

The speed of each sphere when they are far apart is (-28, 14) m/s

Calculation of energy, tension, and speed:

The energy should be

U = kQq / d

= 8.99*10^9 * (2.5*10^-6C)² / 0.047m

U = 0.0562/0.047

U = 1.20 J

The tension should be

T = kQq / d²

T = U / d

T = 1.2 / 0.047

T = 25.53 N

= 26 N

The speed should be

Since Momentum should be conserved, and the initial momentum is zero:

So,

0 = 0.0020 * V2 + 0.0040 * V4

Now

V2 = -2 * V4

Due to this, Energy is also conserved:

½ * 0.0020 * (-2V4)² + ½ * 0.0040 * (V4)² = 1.2 J

-½ * 0.0080 * V4² + ½ * 0.0040 * V4² = 1.2 J

-0.0040V4² + 0.002V4² = 1.2 J

0.0060V4² = 1.2 J

V4² = 1.2/0.0060

V4² = 200

V4 = √200

V4 = 14 m/s

and now V2 = -2 * V4

V2 = -28 m/s

(V2, V4) = (-28, 14)

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