To estimate the kinetic energy acquired by the nail when struck by the hammer, we can use the principle of conservation of kinetic energy in an elastic collision. The principle states that the total kinetic energy before the collision should be equal to the total kinetic energy after the collision.
First, let's consider the initial kinetic energy of the hammer. We can calculate this using the formula:
Kinetic Energy (K.E.) = (1/2) * mass * velocity^2
Given that the initial mass of the hammer is 550 g (which is equivalent to 0.55 kg) and the initial velocity is 5.1 m/s, we can calculate the initial kinetic energy of the hammer:
K.E. of the hammer = (1/2) * 0.55 kg * (5.1 m/s)^2
Next, we need to consider the final kinetic energy after the collision. Since the collision is approximately elastic, we assume that the total kinetic energy before and after the collision is the same.
Now, let's consider the kinetic energy acquired by the nail. Given that its mass is 15 g (which is equivalent to 0.015 kg) and we assume it starts with negligible initial velocity, we can consider its initial kinetic energy to be zero.
Thus, the total kinetic energy after the collision is equal to the kinetic energy of the nail:
K.E. of the nail = K.E. of the hammer
So, to estimate the kinetic energy acquired by the 15 g nail, we can simply calculate the initial kinetic energy of the hammer using the formula provided earlier.