Question 1. A hammer of mass 500 kg is held 10 m above and is going to collide with a pile of mass 1000 kg. The hammer is dropped with gravity and then after the collision, the hammer and the pile have the common velocity and the pile is driven into the ground 0.2 m below. For the figure, please visit here. (a) What is the momentum of the hammer before the collision? (b) Find the total kinetic energy before and after the collision? Account for the difference. (c) Find the energy lost from the moment after collision until the moment that the pile is driven 0.2 m into the ground. (d) Hence, find the resistive force. My answers: (a) First should find the velocity of the hammer before the collision. Two ways to find, (i) Apply the motion formula, first use s = ut + 1/2 at2 where u = 0, a = 10, s = 10 to find t. And then use v = u + at with the t just found to find v which is the velocity of the hammer before the collision. (ii) Apply potential energy = kinetic energy gained potential energy = mgh = kinetic energy = 1/2 mv2 where h = 10, m = 500, g = 10. Then also can find the answer. After finding the v, find the momentum of the hammer. (b) The total kinetic energy before the collision is just equal to the potential energy of the hammer before impact. To find the total kinetic energy after the collision, should find the common velocity of the hammer and the pile after the collision by the conservation of momentum. Using m1 * u = (m1 + m2) * v. The difference is because some energy is lost due to the sound energy of the impact and the internal energy gained by the hammer and the pile. (c) The energy lost = mgh where m = 1000 + 500 = 1500, h = 0.2, g = 10. (d) The resistive force = energy lost / h where h = 0.2 Question 2. A man of mass 50 kg is above the water surface by 6 m. Then he is going to jump into the water. Suppose that the average resistive force of the water is 1500 N, what is the depth that the man can dive into the water surface (Neglect the man's height, assume he is a point mass)? My answer: First should find the potential energy of the man which is equal 3000 J. After that the depth of the man below the water surface = 3000 / 1500 = 2 m.