Question

Помогите!!!!!! Небольшое тело с положительным зарядом q1 и массой m=300г закреплено на высоте H1=50 см над неподвижным точечным зарядом q2=5мкКл. Верхнее тело освобождают, и оно начинает падать вертикально вниз. Когда тело оказалось на высоте H2=30 см над точечным зарядом, его КИНЕТИЧЕСКАЯ энергия стала равной W=120мДж. Заряд q1 тела равен ...мкКл.

Answer 1

Кинетическая энергия "верхнего" тела Е кинетическая будет равна разности общей энергии тела Е общ. в положении 1 и 2.
Е₁ = Е₁ (потенц.) + Е₁ (элстат.)
Е₂ = Е₂ (потенц.) + Е₂ (элстат)

ΔЕ общ. = Е кинетическая = Е₁ - Е₂ = mg(ΔH) + kq₁xq₂(1/R₂ - 1/R₁).

q₁ = [E кинетическая - mgΔH]÷kq₂[(R₁ - R₂)/(R₁×R₂)].
Осталось подставить значения из условия.
q₁ = [0,12  - 0,3×10×0,2] ÷ 9×10⁹×5×10⁻⁶(0,2/0,15) = 8 мкКл.

Ответ: 8 мкКл

Answer 2

Calculation of the Charge q1

To find the value of the charge q1, we can use the principle of conservation of energy. The initial potential energy of the body at height H1 is equal to the final kinetic energy of the body at height H2.

The potential energy of the body at height H1 is given by the equation:

PE1 = m * g * H1

where m is the mass of the body (300 g = 0.3 kg), g is the acceleration due to gravity (approximately 9.8 m/s^2), and H1 is the height above the point charge q2 (50 cm = 0.5 m).

The final kinetic energy of the body at height H2 is given as 120 mJ (millijoules).

KE2 = W = 120 mJ = 120 * 10^-3 J

Since the body is falling vertically downwards, the change in potential energy is equal to the work done by the electric field between the two charges q1 and q2.

PE1 - PE2 = W = q1 * V

where V is the potential difference between the two charges.

Now, we need to find the potential difference V. The potential difference between two point charges can be calculated using the equation:

V = k * (q1 / r1 - q2 / r2)

where k is the Coulomb's constant (approximately 9 * 10^9 Nm^2/C^2), q1 and q2 are the charges, and r1 and r2 are the distances between the charges and the body, respectively.

In this case, the distance r1 is equal to H1 (0.5 m) and the distance r2 is equal to H2 (0.3 m).

Substituting the values into the equation, we get:

PE1 - PE2 = q1 * V

m * g * H1 - KE2 = q1 * (k * (q1 / r1 - q2 / r2))

Now we can solve this equation to find the value of q1.