A pile driving hammer of mass 0.5T falls 2.4m from rest onto a pile of mass 125kg. There is no renounce. The pile is driven into the ground 150mm. Calculate the common velocity after impact and the average resisting force of ground in bringing the pile and driver to rest
Common velocity after impact = (2*0.5*2.4)/(0.5+125) = 0.936 m/s
Average resisting force of ground = (0.5*2.4*0.936)/(150*10^-3) = 8.6 kN
velocity of hammer on hitting ground = sqrt (2 * 9.81 * 2.4)
= 47 m/s
so momentum of hammer = m v = (0.5 *1000 kg I assume you mean) * 47
= 23,500 kg m/s
That will be the total momentum of pile and hammer after impact
(500 + 125 ) v = 23500
v = 37.6 m/s at impact (your "common velocity")
average speed during stop = 37.6 / 2 = 18.8 m/s
so time to stop = 0.150 meters / 18.8 = 0.00798 seconds to stop
average force = change in momentum / time to stop = 23500 /.00798
= 2,945,333 Newtons