Question

С какой скоростью должна лететь свинцовая пуля, чтобы при ударе о преграду она расплавилась, если температура пули до удара 570С ? При ударе в тепло превращается 40% энергии пули.

Answer 1

КПД=(c*m*(t-t1)+L*m)/((m*v^2)/2); v^2=(c*(t-t1)+L)*2; v=((c*(t-t1)+L*)*2)^0,5.;c-уд. теплоемкость свинца , t- температура мплавления свинца, t1=57, L- уд. теплота плавления свинца! Наверно так решается!!

Answer 2

Calculating the Speed Required for a Lead Bullet to Melt Upon Impact

To calculate the speed required for a lead bullet to melt upon impact, we can use the equation for kinetic energy and the energy conversion during impact.

The kinetic energy of the bullet can be calculated using the formula: \[ KE = \frac{1}{2}mv^2 \] where: - \( KE \) = kinetic energy - \( m \) = mass of the bullet - \( v \) = velocity of the bullet

The energy converted into heat upon impact can be calculated using the formula: \[ E_{heat} = \frac{40}{100} \times KE \] where: - \( E_{heat} \) = energy converted into heat - \( 40/100 \) represents the 40% of energy converted into heat

The temperature change of the bullet can be calculated using the formula: \[ E_{heat} = mc\Delta T \] where: - \( m \) = mass of the bullet - \( c \) = specific heat capacity of lead - \( \Delta T \) = change in temperature

By equating the two expressions for \( E_{heat} \), we can solve for the velocity \( v \) required for the bullet to melt upon impact.

Calculation Steps

1. Calculate the kinetic energy of the bullet using the given temperature and the specific heat capacity of lead. 2. Calculate the energy converted into heat upon impact. 3. Equate the energy converted into heat to the change in temperature of the bullet to solve for the velocity.

Let's proceed with the calculations.

Calculation

1. Calculate the kinetic energy of the bullet: - Given temperature of the bullet before impact: \( T = 570^\circ C \) - Specific heat capacity of lead: \( c = 128 J/kg \cdot K \) - Mass of the bullet: Let's assume a typical mass for a lead bullet, which is around 7.0 grams or 0.007 kg.

Using the formula \( KE = \frac{1}{2}mv^2 \), we can solve for the velocity \( v \).

2. Calculate the energy converted into heat upon impact: - Given energy conversion factor: 40%

Using the formula \( E_{heat} = \frac{40}{100} \times KE \), we can calculate the energy converted into heat.

3. Equate the energy converted into heat to the change in temperature of the bullet to solve for the velocity: - Given change in temperature: \( \Delta T = T_{final} - T_{initial} \) - Final temperature of the bullet: The melting point of lead is 327.5°C.

Using the formula \( E_{heat} = mc\Delta T \), we can solve for the velocity \( v \).

Conclusion

By following these steps, we can calculate the speed required for a lead bullet to melt upon impact.