Question

A lead bullet moving 500 m/s hits a wooden block and stops. Find its change in temperature if 1/10 of the energy is changed to heat in the bullet.

Answer 1

A lead bullet moving $500\mathrm{m / s}$ hits a wooden block and stops. Find its change in temperature if 1/10 of the energy is changed to heat in the bullet.

(specific heat capacity of lead $c = 130\frac{J}{kg^{*}\circ C}$ )

Solution: the energy of the bullet before it enters the wooden block is the kinetic energy of a bullet:

$E_0 = \frac{mV_0^2}{2}, \quad V_0 = 500\frac{m}{s} - \text{velocity of the bullet before it stops}$

By condition, one tenth of energy changed to heat:

$$Q = \frac {1}{1 0} E _ {0} = \frac {1}{2 0} m V _ {0} ^ {2} (1)$$

Equation for the thermal process of bullet:

$$Q = c * m * \Delta t (2),$$

$c -$ specific heat capacity of lead,

$\Delta t -$ change in temperature

(1) $= (2)$

$$\frac {1}{2 0} m V _ {0} ^ {2} = c * m * \Delta t$$ $$\Delta t = \frac {V _ {0} ^ {2}}{2 0 c} = \frac {5 0 0 \frac {m}{S} * 5 0 0 \frac {m}{S}}{2 0 * 1 3 0 \frac {J}{k g * {}^ {\circ} C}} = 9 6. 1 5 {}^ {\circ} C$$

Answer: change in temperature is $96.15{}^{\circ}\mathrm{C}$