Question

Два однакових шматочки криги летять назустріч одна одній з однаковими швидкостями і при зіткненні перетворюються на воду. Температура крижинок до удару - 12^0 С. Знайдіть швидкість крижинок . Вважайте, що при ударі вся кінетична енергія перетворюється на теплову.

Answer 1

Ответ:

Скорость льдинок равна ≈ 843 м/c

Объяснение:

Два одинаковых кусочка льда летят навстречу друг другу с одинаковыми скоростями и при столкновении превращаются в воду. Температура льдинок до удара -12°C. Найдите скорость льдинок. Считайте, что при ударе вся кинетическая энергия преобразуется в тепловую.

Дано:

t₀ = -12°C

c = 2100 Дж/(кг·°С)

λ = 330000 Дж/кг

V - ?

——————————————

Количество теплоты, требуемое для превращения кусочков льда в воду равно сумме кинетических энергий двух льдинок:

$Q = 2E_k$

Обозначим массу одного кусочка как m.

Теплота сначала потребуется для нагревания кусочков льда до температуры плавления, а затем на плавление:

$Q = Q_1+Q_2 = 2m\lambda + 2mc(t-t_0) = 2m(\lambda + c\Delta t)$

Кинетическая энергия одного кусочка льда:

$E_k = \dfrac{mV^2}{2}$

Тогда:

$2m(\lambda + c\Delta t) = mV^2 \ \Longrightarrow \ \boxed{ V = \sqrt{2(\lambda + c\Delta t)} }$

Расчет ([Дж] = [кг]·[м²]/[с²]):

V = √(2·(330000 Дж/кг + 2100 Дж/(кг·°С) · 12°С)) = √(2·(330000 Дж/кг + 25200 Дж/кг)) ≈ 843 м/c

#SPJ1

Answer 2

Problem Analysis

We are given that two identical pieces of ice are flying towards each other with the same speed. Upon collision, they transform into water. The temperature of the ice pieces before the collision is -12°C. We need to find the speed of the ice pieces. It is also mentioned that all the kinetic energy is converted into thermal energy upon collision.

Solution

To solve this problem, we can use the principle of conservation of energy. The initial kinetic energy of the ice pieces is converted into thermal energy upon collision.

The kinetic energy of an object can be calculated using the formula:

Kinetic Energy = (1/2) * mass * velocity^2

Since the two ice pieces are identical, their masses are the same. Let's assume the mass of each ice piece is 'm'.

The initial kinetic energy of each ice piece is given by:

Initial Kinetic Energy = (1/2) * m * velocity^2

Upon collision, the kinetic energy is converted into thermal energy. We can equate the initial kinetic energy to the thermal energy generated upon collision.

Initial Kinetic Energy = Thermal Energy

Now, let's calculate the thermal energy generated upon collision.

The thermal energy generated can be calculated using the formula:

Thermal Energy = mass * specific heat capacity * change in temperature

Since the ice is transforming into water, we need to consider the specific heat capacity of ice and water. The specific heat capacity of ice is 2.09 J/g°C, and the specific heat capacity of water is 4.18 J/g°C.

The change in temperature is the final temperature minus the initial temperature. In this case, the final temperature is 0°C, and the initial temperature is -12°C.

Change in temperature = 0°C - (-12°C) = 12°C

Now, let's equate the initial kinetic energy to the thermal energy and solve for the velocity.

(1/2) * m * velocity^2 = m * specific heat capacity * change in temperature

Simplifying the equation:

(1/2) * velocity^2 = specific heat capacity * change in temperature

Now, let's solve for the velocity.

Calculation

Let's substitute the values into the equation and solve for the velocity.

(1/2) * velocity^2 = 2.09 J/g°C * 12°C

(1/2) * velocity^2 = 25.08 J/g

Multiplying both sides by 2:

velocity^2 = 50.16 J/g

Taking the square root of both sides:

velocity = √(50.16 J/g)

Using the conversion factor 1 g = 0.001 kg:

velocity = √(50.16 J/g) = √(50.16 J/0.001 kg) = √(50,160 m^2/s^2) ≈ 224.1 m/s

Answer

The speed of the ice pieces is approximately 224.1 m/s.