Help with Retarding Force Homework Statement

[Ben_Walker1978]

Homework Statement

I need help with the following question:

A pile-driver has a hammer mass of 1000 kg which is dropped onto a pile from a height of 5 meters. The pile is driven 0.5 meters into the ground. The pile has a mass of 500 kg. Calculate the retarding force exerted by the ground on the combined mass of the pile and hammer.

Thanks,

Homework Equations

The Attempt at a Solution

So far i have this, this is for the hammer hitting the pile:

PE = Mgh

M = 1000Kg

g = 9.81 m/s

h = 5 meters

1000 x 9.81 x 5 = 49050 Joules

V^2 = 2gh

Square root of 2 x 9.81 x 5 = 9.9 m/s^1

Velocity = 9.9 m/s^1

But i am now stuck. How do i work out the pile going 0.5 meters into the ground. And the retarding force?
Can anyone help please?

 

[scottdave]

Have you learned about elastic and inelastic collisions? What do you know about the collision? What is conserved in the collision? Do the pile and the hammer move together as the pile drives into the ground?

 

[Ben_Walker1978]

Have you learned about elastic and inelastic collisions? What do you know about the collision? What is conserved in the collision? Do the pile and the hammer move together as the pile drives into the ground?

Hello,
Thanks for the reply.
I have not learned about the things you have mentioned. Yes i guess the pile and the hammer move in the ground together.

 

[scottdave]

They may be closer to an Elastic Collision, which would have some "bounce". You may want to read up on this. https://en.wikipedia.org/wiki/Elastic_collision

If they move into the ground together, you can use Conservation of Momentum to determine the initial speed at which they move. Kinetic Energy will not be conserved (note that Energy is always conserved, but it may not all remain as Kinetic).

Whichever way you solve, put your assumptions in your solution. Draw a diagram to show what forces are acting on the objects.