Question

A pile driver of mass 300 kg is used to drive a pile of mass 500 kg vertically into the ground. The pile driver falls freely through a distance of 54.0 m, rebounding with a velocity relative to the pile and equal to the relative velocity immediately before impact. Determine: the velocity of the driver immediately before impact: the velocity of he pile immediately after the impact: the depth of penetration of the pile after impact given that the ground resisting force is constant and equal to 115 kN: (4 marks) the time taken for the penetration. ​

Answer 1

We can use the principle of conservation of energy to solve this problem. First, we need to find the velocity of the driver immediately before impact, which is 42.4 m/s. Next, we can find the velocity of the pile immediately after impact, which is 25.4 m/s. Then, we can use the work-energy principle to find the depth of penetration of the pile after impact, which is 5.24 m. Finally, we can use the kinematic equation to find the time taken for the penetration, which is 1.02 seconds.