# momentum

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Thread starter 3 years ago
#1
A wooden stake of mass 4 kg is to be driven vertically downwards into the ground
using a mallet of mass 6 kg. The speed of the mallet just prior to impact is 10 m/s
After impact the mallet remains in contact with the stake.
1) Find the speed with which
the stake begins to enter the ground.
2) If the ground offers a constant resistance to motion of 1000 N, how far will the
stake penetrate the ground on each blow? (Take g = 10 ms-2)

I can do part one, it's 6m/s but part 2 I don't really know what to do. I tried doing mv = Ft, 10x6 = 1000t t = 0.06s
I then tried to suvat using s = (u+v/2)t and got 0.18m but the answer says 0.20m, how am I supposed to approach it?

Thanks
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3 years ago
#2
(Original post by bl64)
A wooden stake of mass 4 kg is to be driven vertically downwards into the ground
using a mallet of mass 6 kg. The speed of the mallet just prior to impact is 10 m/s
After impact the mallet remains in contact with the stake.
1) Find the speed with which
the stake begins to enter the ground.
2) If the ground offers a constant resistance to motion of 1000 N, how far will the
stake penetrate the ground on each blow? (Take g = 10 ms-2)

I can do part one, it's 6m/s but part 2 I don't really know what to do. I tried doing mv = Ft, 10x6 = 1000t t = 0.06s
I then tried to suvat using s = (u+v/2)t and got 0.18m but the answer says 0.20m, how am I supposed to approach it?

Thanks
I would recommend first drawing a labelled diagram of the forces acting on the combined 10kg mass immediately after impact (and immediately before the tip of the stake pierces the ground). The forces are 10g acting downwards and 1000N acting upwards (resisting motion). Then use Fnet = ma to find a. Then use v^2 = u^2 + 2as to find s, setting v to 0.

Your mv = Ft approach failed because that equation applies to the transfer of momentum in the instant that the mallet strikes the stake, not during the subsequent period when the combined mallet and stake move downwards against the resistance of the ground.
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Thread starter 3 years ago
#3
(Original post by old_engineer)
I would recommend first drawing a labelled diagram of the forces acting on the combined 10kg mass immediately after impact (and immediately before the tip of the stake pierces the ground). The forces are 10g acting downwards and 1000N acting upwards (resisting motion). Then use Fnet = ma to find a. Then use v^2 = u^2 + 2as to find s, setting v to 0.

Your mv = Ft approach failed because that equation applies to the transfer of momentum in the instant that the mallet strikes the stake, not during the subsequent period when the combined mallet and stake move downwards against the resistance of the ground.
Thank you very much
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