Question

Two small metal cubes with masses 2. 0 g and 4. 0 g are tied together by a 5. 0-cm-long massless string and are at rest on a frictionless surface. Each is charged to +2. 0 μc. What is the energy of this system? what is the tension in the string? the string is cut. What is the speed of each cube when they are far apart?.

Answer 1

The energy of the system, tension in the string, and speed of each cube are respectively; U = 0.72 J, T = 14 N and (V₂, V₄) = (-22, 14)

Calculation of energy and tension in a String

We are given;

Mass of cube 1; m₁ = 2 g

Mass of cube 2; m₂ = 4 g

Distance between cubes; d = 5 cm = 0.05 m

Charges of cubes; Q = q = +2. 0 μc = 2.0 × 10⁻⁶ C

A) Formula for the energy of the system is;

U = kQq/d

U = 8.99 × 10⁹ × (2.0 × 10⁻⁶ C)²/0.05 m

U = 0.03596/0.05

U = 0.72 J

B) Formula for the Tension is;

T = U/d

T = 0.72/0.05

T ≈ 14 N

C) Momentum is conserved, and as such the initial momentum is zero. Thus;

0 = (0.0020 × V₂) + (0.0040 × V₄)

⇒ V₂ = -2V₄

Energy is also conserved and so;

(½ × 0.0020 × (-2V₄)²) + (½ × 0.004 × (V₄)²) = 0.72 J

-0.0040V₄² + 0.002V₄² = 0.72 J

0.0060V₄² = 0.72 J

V₄² = 0.72/0.0060

V₄² = 120

V₄ = √120

V₄ ≈ 11 m/s

Recall that; V₂ = -2V₄

Thus;

V₂ = -2(11) m/s

V₂ = -22 m/s

Thus;

(V₂, V₄) = (-22, 14)

Read more about Conservation of Momentum at; brainly.com/question/7538238