A projectile (mass = 0.269 kg) is fired at and embeds itself in a target (mass = 1.34 kg). (The target is initially stationary). The target (with the projectile in it) flies off after being struck. What percentage of the projectile's incident kinetic energy does the target (with the projectile in it) carry off after being struck?
To find the percentage of the projectile's incident kinetic energy carried off by the target, we need to compare the kinetic energy before and after the collision.
1. Calculate the initial kinetic energy of the projectile:
The kinetic energy (KE) of an object is given by the equation KE = (1/2) * mass * velocity^2. We need to know the velocity of the projectile. If it is not given directly, we'll need more information to determine it.
2. Calculate the final velocity of the combined target and projectile:
Conservation of momentum tells us that the total momentum before the collision is equal to the total momentum after the collision. Since the target is initially stationary, we only need to consider the momentum of the projectile.
The initial momentum of the projectile (p_initial) is given by p_initial = mass_projectile * velocity_projectile.
The final momentum of the combined target and projectile (p_final) is given by p_final = (mass_projectile + mass_target) * velocity_final.
Since the target and projectile stick together after the collision, their final velocity will be the same. Therefore, we can rewrite the equation as p_final = (mass_projectile + mass_target) * velocity_final = (mass_projectile + mass_target) * velocity_final.
3. Use the principle of conservation of kinetic energy:
The principle of conservation of energy tells us that the total kinetic energy before the collision is equal to the total kinetic energy after the collision.
The initial kinetic energy (KE_initial) is given by KE_initial = (1/2) * mass_projectile * velocity_projectile^2.
The final kinetic energy (KE_final) is given by KE_final = (1/2) * (mass_projectile + mass_target) * velocity_final^2.
4. Calculate the percentage of kinetic energy carried off by the target:
To find the percentage of the projectile's incident kinetic energy carried off by the target, we'll compare the final and initial kinetic energies. The percentage is given by:
(KE_final / KE_initial) * 100
This will give us the proportion of the initial kinetic energy carried off by the target after the collision.