Final answer:
To determine the speed required to melt the bullet, we first need to calculate the energy transferred to the bullet during the collision with the pendulum. We can then use the specific heat capacity of lead and the mass of the bullet to determine the temperature increase due to the collision. By equating the heat transferred to the latent heat of fusion of lead, we can find the speed necessary to melt the bullet.
Step-by-step explanation:
To determine the speed required to melt the bullet, we first need to calculate the energy transferred to the bullet during the collision with the pendulum.
The mechanical energy dissipated in the collision can be calculated using the formulE = (1/2)mv^2 + (1/2)I*(v/L)^2
where E is the energy dissipated, m is the mass of the bullet, v is the speed of the bullet, I is the moment of inertia of the pendulum, and L is the length of the cord.
Since half of the kinetic energy lost in the collision went into the bullet, we can set the energy dissipated equal to the energy transferred to the bullet:
E = (1/2)m*v^2 = (1/2)*(10 g)*(v)^2
Next, we can calculate the temperature increase of the bullet due to the collision using the specific heat capacity of lead, the initial temperature of the bullet, and the mass of the bullet:
Q = m*C*(T_f - T_i)
where Q is the heat transferred, m is the mass of the bullet, C is the specific heat capacity of lead, T_f is the final temperature of the bullet, and T_i is the initial temperature of the bullet.
Finally, we can calculate the speed required to melt the bullet by equating the heat transferred to the latent heat of fusion of lead:
Q = mL = (25 J/g)*10 g
By solving these equations simultaneously, we can find the speed v that would be necessary to melt the bullet.