Question

Свинцева куля падає з висоти 30м на сталеву плиту. На скільки температура кулі після удару перевищує початкову, якщо 50% механічної енергії переходить у внутрішню енергію кулі?

Answer 1

Свинцовая пуля падает с высоты 30м на стальную плиту. На сколько температура шара после удара превышает начальную, если 50% механической энергии переходит во внутреннюю энергию шара?

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Дано: h=30 м;  Q=0,5E; c=140 Дж/(кг*°С); Δt - ?

E=mgh

Q=c*m*Δt

c*m*Δt=0,5*mgh

Δt=0,5*g*h/c=0,5*10*30/140=1,07°C  -  это ответ.

Answer 2

Calculation of Temperature Increase in the Bullet

To calculate the temperature increase in the bullet after the impact, we can use the principle of conservation of energy. Given that 50% of the mechanical energy is converted into internal energy, we can determine the temperature increase using the specific heat capacity of lead.

The specific heat capacity of lead is 0.128 J/g°C.

Using the formula for calculating the temperature change due to energy absorption: \[ Q = mc\Delta T \] Where: - Q = energy absorbed (in joules) - m = mass of the bullet (in grams) - c = specific heat capacity of lead (in J/g°C) - ΔT = change in temperature (in °C)

We can calculate the temperature increase in the bullet after the impact using the given information.

Calculation Steps

1. Calculate the energy absorbed by the bullet. 2. Use the energy absorbed to calculate the temperature increase.

Energy Absorbed by the Bullet

The energy absorbed by the bullet can be calculated using the following formula: \[ Q = 0.5 \times \text{mechanical energy} \]

Temperature Increase Calculation

After obtaining the energy absorbed, we can use it to calculate the temperature increase in the bullet: \[ Q = mc\Delta T \] \[ \Delta T = \frac{Q}{mc} \]

Let's proceed with the calculations.