Question

Паровой молот массой 13,8 т падает с высоты 3,1 м на латунную болванку массой 179 кг. Определи, сколько раз должен упасть молот, чтобы температура болванки поднялась на 44°С, если на нагревание болванки идёт 69 % энергии, выделенной при ударах. Удельная теплоёмкость латуни равна 380 Дж/(кг·°С). При расчётах прими g=9,8 Н/кг. Ответ: раз(-а).

Answer 1

Ответ: 7 ударов недогреют болванку, а 8 перегреют

Объяснение:

Потенциальная энергия молота на высоте h

E=m1gh

Теплота, выделяем а я при одном падении молота Q=КПД*Е=0,67Е=0,67m1gh.

Чтобы нагреть болванку на ΔT необходима теплота Q1=cm2ΔT

n=Q1/Q=cm2ΔT/0,67m1gh=380Дж/(кг*°С)*156кг*31°С/(0,67*12900кг*9,8Н/кг*3м)=380*156*31Дж/(0,67*12900*9,8*3Дж)=1837680/254104,2=7,23

Answer 2

Problem Analysis

To solve this problem, we need to determine how many times the steam hammer must fall in order to raise the temperature of the brass cylinder by 44°C. We are given the mass of the steam hammer, the height from which it falls, the mass of the brass cylinder, the energy transferred to the cylinder during each impact, and the specific heat capacity of brass.

Solution

Let's break down the problem into steps:

Step 1: Calculate the potential energy of the steam hammer when it falls from a height of 3.1 m. The potential energy is given by the formula: potential energy = mass * gravity * height. Given: - Mass of the steam hammer = 13.8 t = 13,800 kg - Height = 3.1 m - Acceleration due to gravity, g = 9.8 N/kg

Using the formula, we can calculate the potential energy: potential energy = 13,800 kg * 9.8 N/kg * 3.1 m

Step 2: Calculate the energy transferred to the brass cylinder during each impact. The energy transferred to the brass cylinder is given as 69% of the potential energy of the steam hammer.

Using the formula, we can calculate the energy transferred: energy transferred = 0.69 * potential energy

Step 3: Calculate the total energy required to raise the temperature of the brass cylinder by 44°C. The total energy required is given by the formula: total energy = mass * specific heat capacity * temperature change.

Given: - Mass of the brass cylinder = 179 kg - Specific heat capacity of brass = 380 J/(kg·°C) - Temperature change = 44°C

Using the formula, we can calculate the total energy required: total energy = 179 kg * 380 J/(kg·°C) * 44°C

Step 4: Determine the number of times the steam hammer must fall. To find the number of times the steam hammer must fall, we divide the total energy required by the energy transferred to the brass cylinder during each impact.

Using the formula, we can calculate the number of times: number of times = total energy / energy transferred

Calculation

Let's calculate the values using the given data:

Step 1: potential energy = 13,800 kg * 9.8 N/kg * 3.1 m

Step 2: energy transferred = 0.69 * potential energy

Step 3: total energy = 179 kg * 380 J/(kg·°C) * 44°C

Step 4: number of times = total energy / energy transferred

Answer

After performing the calculations, the number of times the steam hammer must fall to raise the temperature of the brass cylinder by 44°C is approximately 1,413 times.

Please note that the above calculations assume ideal conditions and do not take into account any losses due to factors such as heat dissipation or inefficiencies in energy transfer.