Question

A pile driver is a device used to drive stakes into the

Answer 1

Answer:

0.0483m or 48.3 mm

Explanation:

Let g = 10m/s2

At 8m, the pile has a potential energy of

P = mgh = 3000*10*8 = 240000 J

This energy is converted to kinetic energy once the pile drops down to the bottom:

$E = \frac{mv^2}{2} = 240000$

$v^2 = \frac{240000*2}{3000} = 160$

Taking gravity into consideration, the net force acting on the pile once it hits the ground is

$-5*10^6 + 10*3000 = -4970000 N$

Therefore the net deceleration is:

$a = F/m = -49700003000 = -1657 m/s^2$

We can find out how far it's driven into the ground with the following equation of motion:

$v^2 - v_0^2 = 2as$

where v = 0 is the final velocity, which is 0 because it stops, $v_0^2 = 160$ is the initial velocity when it hits the ground, a is the deceleration, and s is the distance it travels into the ground

$0 - 160 = 2*(-1657)s$

$s = \frac{-160}{2*(-1657)} = 0.0483m$ or 48.3 mm