A steel hammer weighing 25 kg falls from a certain height and drives a 50 kg pile into the ground to a depth

A steel hammer weighing 25 kg falls from a certain height and drives a 50 kg pile into the ground to a depth of 0.5 m. In this case, 50% of the hammer’s energy goes to heating the hammer and the pile. How high does the hammer fall?

Task data: m1 (weight of a steel hammer) = 25 kg; m2 (mass of the driven pile) = 50 kg; h2 (pile immersion depth) = 0.5 m; η (energy losses for heating the hammer and pile) = 50% (0.5).

We express the height from which the hammer should have fallen from the formula: η = Ap / Az = m2 * g * h2 / (m1 * g * h1) = m2 * h2 / (m1 * h1), whence h1 = m2 * h2 / (η * m1).

Let’s make a calculation: h1 = 50 * 0.5 / (0.5 * 25) = 2 m.

Answer: The hammer fell from a height of 2 m.