Question

A 2 200-kg pile driver is used to drive a steel I-beam into the ground. The pile driver falls 4.20 m before coming into contact with the top of the beam, and it drives the beam 14.0 cm farther into the ground before coming to rest. Using energy considerations, calculate the average force the beam exerts on the pile driver while the pile driver is brought to rest.

Answer 1

Answer:

669042 N upward

Explanation:

$W_g$ = Work done by gravity on pile driver

$W_b$ = Work done by beam

u = Initial velocity

v = Final velocity

m = Mass of pile driver = 2200 kg

g = Acceleration due to gravity = 9.81 m/s²

h = Height the pile driver falls = 4.2 m

d = Bend in beam = 14 cm

Total work done = Change in Kinetic energy

$W_g+W_b=\frac{1}{2}m(v^2-u^2)\\\Rightarrow mg(h+d)+Fd=0\\\Rightarrow F=-\frac{mg(h+d)}{d}\\\Rightarrow F=-\frac{2200\times 9.81(4.2+0.14)}{0.14}\\\Rightarrow F=-669042\ N$

The force the beam exerts on the pile driver while the pile driver is brought to rest is 669042 N upward