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Pile driven into the ground by a hammer question - HELP!!!!

I'm really struggling with the last part of this question:


A hammer of mass 100kg falls 4 metres onto a pile of mass 300kg and drives it 80mm into the ground.

a) Calculate the loss of energy on impact

b) Calculate the work done by the resistance of the ground

c) Calculate the average resistance to penetration


Please help!
The falling mass sees a decrease in it KE. It has max PE at the top.

Can you determine the energy loss ?

This was posted from The Student Room's Android App on my GT-I9100
Reply 2
E=mgh
E=100x9.81x4
E=3924J?
Reply 3
Interesting question and I would like to see the actual answer, do you happen to have it?

I spent a good while looking at it and this is what I did:

a) Calculate the loss of energy on impact
GPE is 100*9.81*4 = 3924J

Kinetic energy just before contact is therefore 3924J also.
From this velocity can be found to be 8.86m/s

From the conservation of momentum, initial momentum = 100*8.86 = 886Ns = final momentum = (100+300)*V

The final velocity is therefore 2.2m/s

The final Kinetic energy is 1/2 * 400* 2.2^2 = 986J

The energy that is lost is therefore 3924 - 986 = 2938J


b) Calculate the work done by the resistance of the ground

Kinetic energy + GPE = Work done by resistance

986 (worked out in part a) + 400*9.81*0.08 (height lost as pile penetrates ground) = 1300J



c) Calculate the average resistance to penetration


Work done =FS

1300/0.08 = 16250N



Hope at least some of that helps, im not too confident in my answers but thought I'd give it a go! If you find the correct answers please let me know!
Reply 4
Thank you so much!
Where the hell did you get 2.2 m/s as the final velocity?
Reply 6
There seems to be missing information in the question so solve it using e=0(plastic collision). If you still need it though
Please help
Help me on this
Original post by rub em out
Interesting question and I would like to see the actual answer, do you happen to have it?

I spent a good while looking at it and this is what I did:

a) Calculate the loss of energy on impact
GPE is 100*9.81*4 = 3924J

Kinetic energy just before contact is therefore 3924J also.
From this velocity can be found to be 8.86m/s

From the conservation of momentum, initial momentum = 100*8.86 = 886Ns = final momentum = (100+300)*V

The final velocity is therefore 2.2m/s

The final Kinetic energy is 1/2 * 400* 2.2^2 = 986J

The energy that is lost is therefore 3924 - 986 = 2938J


b) Calculate the work done by the resistance of the ground

Kinetic energy + GPE = Work done by resistance

986 (worked out in part a) + 400*9.81*0.08 (height lost as pile penetrates ground) = 1300J



c) Calculate the average resistance to penetration


Work done =FS

1300/0.08 = 16250N



Hope at least some of that helps, im not too confident in my answers but thought I'd give it a go! If you find the correct answers please let me know!


Are you sure for the answer on c?

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