In the centripetal movement, what happens with velocity is that it will remain constant, always pointing in its tangential direction of the trajectory. Said speed, although constant, will have a constant direction that will generate an acceleration that will always point towards the center of the circle radius. Both vectors as the turn is performed will always be perpendicular to each other.

4 0

3 years ago

Two identical particles, each with a mass of 4.5 mg and a charge of 30 nC, are moving directly toward each other with equal spee

e-lub [12.9K]

Answer:

r₁ = 20.5 cm

Explanation:

In this exercise we can use the conservation of energy

the gravitational power energy is always attractive, the electrical power energy is repulsive if the charges are of the same sign

starting point.

Em₀ = U_g + U_e + K = $-G \frac{m_1m_2}{r} +k \frac{q_1q_2}{r} - 2 ( \frac{1}{2} m v^2)$

the two in the kinetic energy is because they are two particles

final point. When it is detained

Em_f = U_g + U_e = $-G \frac{m_1m_2}{r_1} + k \frac{q_1q_2}{r_1}$

the energy is conserved

Em₀ = em_f

the charges and masses of the two particles are equal

$-G \frac{m^2}{r} + k \frac{q^2}{r} + m v^2 = - G \frac{m^2}{r_1} + k \frac{q^2}{r_1}$

sustitute the values

-6.67-11 (4.5 10-3) ² / 0.25 - 9, 109 (30 10-9) ² / 0.25 + 4.5 10-3 4² = - 6.67 10- 11 (4.5 10-3) ² / r1 -9 109 (30 10-9) ² / r1

-5.4 10⁻¹⁵ + 3.24 10⁻⁵ - 7.2 10⁻⁵ = -1.35 10⁻¹⁵ / r₁ + 8.1 10⁻⁶ / r₁

We can see that the terms that correspond to the gravitational potential energy are much smaller than the terms of the electric power, which is why we depress them.

3.24 10⁻⁵ - 7.2 10⁻⁵ = 8.1 10⁻⁶ / r₁

-3.96 10⁻⁵ = 8.1 10⁻⁶ / r₁

r₁ = 8.1 10⁻⁶ /3.96 10⁻⁵

r₁ = 2.045 10⁻¹ m

r₁ = 20.5 cm

4 0

3 years ago