Um corpo indeformável em repouso é atingido por um projétil metálico com a velocidade de 300 m/s e a temperatura de 0 ºC. Sabe-se que, devido ao impacto, 1/3 da energia cinética é absorvida pelo corpo e o restante transforma-se em calor, fundindo parcialmente o projétil. O metal tem ponto de fusão t_f = 300 ºC, calor específico c = 0,02 cal/g ºC e calor latente de fusão L_f = 6 cal/g. Considerando 1 cal cong 4 J, a fração x da massa total do projétil metálico que se funde é tal que

Let's break down the problem step by step to find the correct answer.

First,<|begin_of_text|>199999610961the kinetic energy of the projectile is converted into heat energy, which is then used to melt part of the projectile. We know that 1/3 of the kinetic energy is absorbed by the body, and the remaining 2/3 is converted into heat energy.

Let's calculate the kinetic energy of the projectile:

$K = frac{1}{2}mv^2 = frac{1}{2}m(300)^2 = 45000m$ J

Since 1/3 of the kinetic energy is absorbed by the body, the remaining 2/3 is converted into heat energy:

$Q = frac{2}{3}K = frac{2}{3}(45000m) = 30000m$ J

Now, we need to find the mass of the projectile that melts. Let's use the heat energy equation:

$Q = mcDelta T + mL_f$

where $m$ is the mass of the projectile that melts, $c$ is the specific heat capacity of the metal, $Delta T$ is the temperature change, and $L_f$ is the latent heat of fusion.

Rearranging the equation to solve for $m$, we get:

$m = frac{Q}{cDelta T + L_f}$

Plugging in the values, we get:

$m = frac{30000}{0.02(300) + 6} = 0.25$ kg

Since the total mass of the projectile is 1 kg, the fraction of the mass that melts is:

$x = frac{0.25}{1} = 0.25$

Therefore, the correct answer is B) $x = 0.25$.

Explanation: The key to this problem is to recognize that 1/3 of the kinetic energy is absorbed by the body, and the remaining 2/3 is converted into heat energy. We then use the heat energy equation to find the mass of the projectile that melts. By rearranging the equation and plugging in the values, we find that the correct answer is B) $x = 0.25$.