Question

Металический шар упал с высоты 26 метров на свинцовую пластину массой 1кг и остановился.при этом пластина нагрелась на 3.2с чему равна масса шара если на нагревание пластины пошло 80% выделившегося при ударе количество теплоты?

Answer 1

За почерк извиняй , на бумаге быстрее все таки

Answer 2

Calculation of the Mass of the Metal Ball

To calculate the mass of the metal ball, we can use the principle of conservation of energy. The potential energy of the ball when it is at a height of 26 meters is converted into kinetic energy as it falls, and then into heat energy when it collides with the lead plate.

The potential energy of the ball can be calculated using the formula:

Potential Energy = Mass * Gravity * Height

Given that the height is 26 meters and the mass of the lead plate is 1 kg, we can calculate the potential energy:

Potential Energy = 1 kg * 9.8 m/s^2 * 26 m = 254.8 Joules [[1]].

Since the ball comes to a stop after colliding with the lead plate, all of its kinetic energy is converted into heat energy. The heat energy can be calculated using the formula:

Heat Energy = Kinetic Energy = 0.5 * Mass * Velocity^2

Since the ball comes to a stop, its final velocity is 0. Therefore, we can calculate the initial kinetic energy:

Initial Kinetic Energy = Heat Energy = 0.5 * Mass * Velocity^2

Given that the plate heats up by 3.2 degrees Celsius, we can assume that all the heat energy generated by the collision is absorbed by the plate. Let's denote the heat energy absorbed by the plate as Q.

According to the problem statement, 80% of the heat energy generated during the collision is absorbed by the plate. Therefore, we can write:

Q = 0.8 * Heat Energy

Substituting the formula for heat energy, we get:

Q = 0.8 * (0.5 * Mass * Velocity^2)

Now, we need to find the relationship between the heat energy absorbed by the plate and the change in temperature of the plate. This relationship is given by the specific heat capacity of the material. The specific heat capacity of lead is approximately 0.13 J/g°C [[2]].

The change in temperature of the plate can be calculated using the formula:

Change in Temperature = Q / (Mass of the Plate * Specific Heat Capacity of Lead)

Given that the mass of the plate is 1 kg and the change in temperature is 3.2°C, we can calculate the heat energy absorbed by the plate:

Q = (Mass of the Plate * Specific Heat Capacity of Lead) * Change in Temperature

Substituting the values, we get:

Q = (1 kg * 0.13 J/g°C) * 3.2°C = 0.416 Joules

Now, we can equate the two expressions for Q and solve for the mass of the ball:

0.8 * (0.5 * Mass * Velocity^2) = 0.416 Joules

Simplifying the equation, we get:

0.4 * Mass * Velocity^2 = 0.416 Joules

Since the final velocity of the ball is 0, we can solve for the initial velocity using the equation of motion:

Final Velocity^2 = Initial Velocity^2 + 2 * Acceleration * Distance

Given that the distance is 26 meters and the acceleration due to gravity is 9.8 m/s^2, we can calculate the initial velocity:

0 = Initial Velocity^2 + 2 * (-9.8 m/s^2) * 26 m

Simplifying the equation, we get:

Initial Velocity = sqrt(2 * 9.8 m/s^2 * 26 m) = 20.2 m/s

Substituting the values into the equation for heat energy, we get:

0.4 * Mass * (20.2 m/s)^2 = 0.416 Joules

Simplifying the equation, we get:

Mass = 0.416 Joules / (0.4 * (20.2 m/s)^2) = 0.052 kg

Therefore, the mass of the metal ball is approximately 0.052 kg.

Note: The calculations provided above assume ideal conditions and neglect any losses due to friction or air resistance.