Answer to Question #86092 in Classical Mechanics for Shawn Dickson

Question

A mass of 1.5 tonnes is suspended 1.5m above a stake. How far into the ground will the stake go if if the mass is allowed to fall and 30% of the energy upon impact is lost due to heat and if ground resistance is 300kn

Answer 1

The work against ground resistance is

$$W=\eta mgh=(1-0.3)1500(9.8)(1.5)=15435 J$$

Needed depth is

$$h=W/F=15435/300000= 0.051 m = 5.1 cm$$