Resistance of wood to falling knifeWatch

#1
An open knife edge of mass M is dropped from a height h on a wooden floor. If the blade penetrates a distance s into the wood, the average resistance offered by wood to blade is?

The answer is Mg[1+(h/s)] but I don't get how.

I thought the equation should be
Mg(h+s) = KE right before hitting the wood + (Resistance x s)
and the KE right before hitting the wood would be equal to lost in potential energy for the height fallen, so KE = Mgh. Therefore, the equation becomes
Mg(h+s) = Mgh + (Resistance x s) so
[(Mgs)/s)] = Resistance

Could someone please tell me why I'm wrong?
1
1 year ago
#2
(Original post by RyanCWY)
...
Work done bringing knife to rest (KE = 0) at x = 0 (GPE = 0), equals initial GPE of mg(h + s). So Fs = mg(h + s) => F = mg(1 + h/s).
0
1 year ago
#3
(Original post by RyanCWY)
Mg(h+s) = KE right before hitting the wood + (Resistance x s)
and the KE right before hitting the wood would be equal to lost in potential energy for the height fallen, so KE = Mgh. Therefore, the equation becomes
Mg(h+s) = Mgh + (Resistance x s) so
[(Mgs)/s)] = Resistance

Could someone please tell me why I'm wrong?
The knife loses of GPE, with no nett change in KE (it starts and finishes with none). The only other (other than by gravity) work done on it is by the resistance of the wood, .
0
1 year ago
#4
(Original post by RyanCWY)
I thought the equation should be
Mg(h+s) = KE right before hitting the wood + (Resistance x s)
That's the error. The knife starts and ends with a KE of 0.

You cannot have the KE when the knife hits the wood in the equation because it came from the GPE on the LHS and is entirely lost by the end. Your equation should be:

Energy lost = negative work done

Note that the energy lost is entirely GPE, as the knife starts and ends with no KE.

The work done by the wood's resistance on the knife is negative, as the force is opposite to the direction of travel of the knife (it slows it). We account for the work being negative by putting the loss of GPE in the equation.
1
1 year ago
#5
Surely it depends on the heat of the knife and it's material as well?
0
1 year ago
#6
(Original post by niteninja1)
Surely it depends on the heat of the knife and it's material as well?
We're given the depth to which the knife penetrates, which will vary with different materials / conditions.
0
#7
(Original post by Physics Enemy)
Work done bringing knife to rest (KE = 0) at x = 0 (GPE = 0), equals initial GPE of mg(h + s). So Fs = mg(h + s) => F = mg(1 + h/s).
I get it now thankss
1
#8
(Original post by RogerOxon)
That's the error. The knife starts and ends with a KE of 0.

You cannot have the KE when the knife hits the wood in the equation because it came from the GPE on the LHS and is entirely lost by the end. Your equation should be:

Energy lost = negative work done

Note that the energy lost is entirely GPE, as the knife starts and ends with no KE.

The work done by the wood's resistance on the knife is negative, as the force is opposite to the direction of travel of the knife (it slows it). We account for the work being negative by putting the loss of GPE in the equation.
Thankss
0
1 year ago
#9
(Original post by RyanCWY)
KE right before hitting the wood ...
To add, if you want to do the Q by considering knife's point of contact with floor:

W (KE = GPE = 0) = KE (poc) + GPE (poc)
=> Fs = mgh + mgs = mg(h + s)
=> F = mg(1 + h/s)

I think this is what you were shooting for.
0
X

new posts
Latest
My Feed

Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

see more

See more of what you like onThe Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

University open days

• Solent University
Mon, 25 Mar '19
• Cardiff University
Wed, 27 Mar '19
• University of Portsmouth
Wed, 27 Mar '19

Poll

Join the discussion

Where do you need more help?

Which Uni should I go to? (149)
18.53%
How successful will I become if I take my planned subjects? (79)
9.83%
How happy will I be if I take this career? (136)
16.92%
How do I achieve my dream Uni placement? (114)
14.18%
What should I study to achieve my dream career? (79)
9.83%
How can I be the best version of myself? (247)
30.72%