Find out the average resistance of the ground:

In a construction of pile-driving for building, a pile driver of mass 25 kg freely drops through a height of 3 metre on the top of a pile having mass of 50 kg. If this is driven into the ground through 7.5 cm, find out the average resistance of the ground to pile driving and the amount of energy lost in impact.

Solution

W_H   =  Weight of pile-hammer (driver) = 25 × g N

V_H   = Velocity of driver before impact =

                                      = 7.67 m / sec.

W_P  = Weight of pile = 50 g N.

By Using principle of conservation of the momentum,

 (W_H  V_H )/g = ((W_H + W_P )/g) V_c

where, V_c is a common velocity of the pile along with hammer

∴ Vc  = 25 × 7.67 /75 = 2.56 m / sec.

Figure 8.7

Refer Figure showing ground resistance R

R′ = Net upward resistance = R - W_P  - W_H

                                                = R - (75 g )

∴ (R - 75 g ) × 7.5 = ( (25 + 50) × (2.56)²/2

∴ R - 75 × 9.81 =75 × (2.56)² /15

∴ R = 768.52 N

KE lost in impact = KE before impact - KE after impact

=25 × (7.67)² / 2 -75 × (2.56)² /2

= 735.36 - 245.76

= 489.60 N. m.