Question

пуля массой 10Г летящая со скоростью V равно 10 м секунду попадает в льдину определить массу растаявшего при этом льда если известно что 50% кинетической энергии пули перешло в тепло? Начальная темп. Льда0°

Answer 1

Problem Analysis

We are given the following information: - Mass of the bullet (m) = 10 g = 0.01 kg - Velocity of the bullet (V) = 10 m/s - 50% of the kinetic energy of the bullet is transferred as heat to the ice - Initial temperature of the ice = 0°C

We need to determine the mass of the melted ice after the bullet hits it.

Solution

To solve this problem, we can use the principle of conservation of energy. The initial kinetic energy of the bullet is converted into heat energy when it hits the ice. We can equate the initial kinetic energy of the bullet to the heat energy gained by the ice.

The initial kinetic energy of the bullet can be calculated using the formula:

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

Let's calculate the initial kinetic energy of the bullet:

Kinetic Energy = (1/2) * 0.01 kg * (10 m/s)^2

Now, since 50% of the kinetic energy of the bullet is transferred as heat to the ice, we can calculate the heat energy gained by the ice:

Heat Energy = 0.5 * Kinetic Energy

Finally, we can use the heat energy gained by the ice to determine the mass of the melted ice. We know that the heat energy gained by the ice is equal to the heat required to raise the temperature of the ice from 0°C to its melting point (0°C), and then to melt the ice completely. The heat required to raise the temperature of the ice can be calculated using the formula:

Heat Required = mass * specific heat capacity * temperature change

The specific heat capacity of ice is approximately 2.09 J/g°C.

Let's calculate the heat required to raise the temperature of the ice:

Heat Required = mass * 2.09 J/g°C * (0°C - 0°C)

Since the ice is already at 0°C, there is no temperature change.

Now, we can equate the heat energy gained by the ice to the heat required to raise the temperature of the ice and melt it completely:

Heat Energy = Heat Required

We can rearrange the equation to solve for the mass of the melted ice:

mass = Heat Energy / (2.09 J/g°C)

Let's substitute the values and calculate the mass of the melted ice.

Calculation

Given: - Mass of the bullet (m) = 10 g = 0.01 kg - Velocity of the bullet (V) = 10 m/s - Specific heat capacity of ice = 2.09 J/g°C - Initial temperature of the ice = 0°C

Kinetic Energy = (1/2) * 0.01 kg * (10 m/s)^2

Heat Energy = 0.5 * Kinetic Energy

Heat Required = mass * 2.09 J/g°C * (0°C - 0°C)

mass = Heat Energy / (2.09 J/g°C)

Substituting the values:

Kinetic Energy = (1/2) * 0.01 kg * (10 m/s)^2 = 0.5 J

Heat Energy = 0.5 * 0.5 J = 0.25 J

Heat Required = 0.25 J / (2.09 J/g°C) = 0.119 g

Therefore, the mass of the melted ice is approximately 0.119 grams.

Answer

The mass of the melted ice, when a bullet with a mass of 10 grams and a velocity of 10 m/s hits it, and 50% of the bullet's kinetic energy is transferred as heat to the ice, is approximately 0.119 grams.