What is the work done by the ground in stopping the pile?

[bolei]

hi guys, i got a question about momentum, shouldn't be hard but I am not quite sure how to solve, please help me~~

A pile driver of mass 600kg moving vertically downwards with a speed of 20m/s strikes the top of a vertical pile of mass 6000kg without rebounding. the pile is driven 12cm into the ground by the blow.Calculate(i)the initial velocity of the pile, assuming conservation of momentum during the initial impact;(ii)the work done by ground resistance in stopping the pile.

actually I've already got the answer for(i), if not wrong,it's momentum = 12000J and initial-v = 1.82m/s,the question is how to do (ii)~

cheers guys

 

[Winzer]

To find the acceleration, how about :
$$v_{f}^2=v_{o}^2+2a(x_{f}-x_{o})$$?

The momentum for the most part is right(it should be 11946J) as well as the velocity.

 

[bolei]

yeah, but how about the question(ii)?

 

[Winzer]

In order to find the work done by the ground you must find the force that the ground exerts on the pile. So if you solve for a then you can get F=(6600kg)a. So it exert a force of F on the ground, then the ground must be exerting a force of -F on the pile(Newtons third law).
You now have the force and can use:

$$W=\int F ds$$ this simplfies to $$W=F\Delta x$$ since the force is constant