Question

Паровой молот массой 19 т падает с высоты 4,7 м на медную болванку массой 249 кг. Определи, сколько раз должен упасть молот, чтобы температура болванки поднялась на 46°С, если на нагревание болванки идёт 65 % энергии, выделенной при ударах. Удельная теплоёмкость меди равна 380 Дж/(кг·°С). При расчётах прими g=9,8 Н/кг. Ответ: раз(-а).​

Answer 1

Ответ:

Дано

m1=12,9т=12900кг

h=3м

m2=156 кг

ΔT=31°C

КПД=67%

с=380Дж/(кг*°С)

g=9,8 Н/кг

Найти количество ударов молота n.

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

Ответ: 7 ударов недогреют болванку, а 8 перегреют

Объяснение:

Answer 2

Problem Analysis

To determine the number of times the steam hammer must fall in order to raise the temperature of the copper ingot by 46°C, we need to calculate the amount of energy required to raise the temperature of the ingot and compare it to the energy available from the hammer strikes.

Calculation Steps

1. Calculate the energy required to raise the temperature of the copper ingot. 2. Calculate the energy available from the hammer strikes. 3. Divide the energy required by the energy available to determine the number of hammer strikes needed.

Solution

1. Calculate the energy required to raise the temperature of the copper ingot: - Mass of the copper ingot (m): 249 kg - Specific heat capacity of copper (c): 380 J/(kg·°C) - Change in temperature (ΔT): 46°C

The energy required (Q) can be calculated using the formula: Q = m * c * ΔT

Substituting the given values: Q = 249 kg * 380 J/(kg·°C) * 46°C

Calculating the energy required: Q = 249 * 380 * 46 J

The energy required to raise the temperature of the copper ingot is Q = 4,303,320 J.

2. Calculate the energy available from the hammer strikes: - Mass of the steam hammer (m_hammer): 19,000 kg - Height of the fall (h): 4.7 m - Acceleration due to gravity (g): 9.8 m/s²

The potential energy (PE) of the steam hammer can be calculated using the formula: PE = m_hammer * g * h

Substituting the given values: PE = 19,000 kg * 9.8 m/s² * 4.7 m

Calculating the potential energy: PE = 19,000 * 9.8 * 4.7 J

The potential energy available from the hammer strikes is PE = 849,860 J.

3. Divide the energy required by the energy available to determine the number of hammer strikes needed: Number of hammer strikes = Q / PE

Substituting the calculated values: Number of hammer strikes = 4,303,320 J / 849,860 J

Calculating the number of hammer strikes: Number of hammer strikes ≈ 5.06

Therefore, the steam hammer must fall approximately 5 times in order to raise the temperature of the copper ingot by 46°C.

Note: The calculated number of hammer strikes is an approximation and may not be a whole number due to rounding.