Question

A pile driver drives a post into the ground. The mass of the pile driver is 2 500 kg and it is dropped through a height of 8.0 m on each stroke. If the resisting force of the ground is 4.0 × 106 N, how far is the post driven in on each stroke?

Answer 1

Answer:

Distance, d = 0.049 meters

Explanation:

It is given that,

Mass of the pile, m = 2500 kg

It is dropped through a height of 8.0 m on each stroke, h = 8 m

The resisting force of the ground, $F=4\times 10^6\ N$

The work done in each stroke is equal to the potential energy of the pile driver such that,

$W=mgh$

Work done due to resistive force is :

$W=Fd$

So,

$Fd=mgh$

d is the distance covered by the post driven in on each stroke.

$d=\dfrac{mgh}{F}$

$d=\dfrac{2500\times 9.8\times 8}{4\times 10^6}$

d = 0.049 meters

So, on each stroke the post driven is 0.049 meters far. Hence, this is the required solution.