Engineering

A pile driver, of mass 500 kg is allowed to fall from rest through a distance of 1.8 m on to a 200 kg concrete pile to drive it into the ground. Each impact drives the pile into the ground by a further 150 mm. Assuming that the pile driver remains in contact with the pile after impact and that momentum is conserved, use the principle of conservation of energy to calculate:

a. The kinetic energy of the driver and pile combination immediately after impact.
b. The change in potential energy of the driver and pile combination on moving into the ground.
c. The average ******ing force that brings the pile and driver to rest, ensuring use of the principle of conservation of energy.
(Assume acceleration due to gravity g=9.81m/s2)

d. Using D’Alembert’s principle, solve the same problem specified in c.

Any help in solving this would be greatly appreciated!

(edited 10 months ago)

Reply 1

Alex_H_

Original post

by Mindgate21

A pile driver, of mass 500 kg is allowed to fall from rest through a distance of 1.8 m on to a 200 kg concrete pile to drive it into the ground. Each impact drives the pile into the ground by a further 150 mm. Assuming that the pile driver remains in contact with the pile after impact and that momentum is conserved, use the principle of conservation of energy to calculate:
a. The kinetic energy of the driver and pile combination immediately after impact.
b. The change in potential energy of the driver and pile combination on moving into the ground.
c. The average ******ing force that brings the pile and driver to rest, ensuring use of the principle of conservation of energy.
(Assume acceleration due to gravity g=9.81m/s2)
d. Using D’Alembert’s principle, solve the same problem specified in c.
Any help in solving this would be greatly appreciated!

For part a, Using conservation of energy:
GPE of the driver = KE of driver + concrete after impact.
mgh = KE

For part b, using conservation of energy:
Change in PE of concrete + driver
PE = mgh

For part c,
Work done = force × distance moved by the pile
F = ma
--> a = W / md

I've left it for you to substitute in the values and complete the calculations