Homework #3 Problem 2
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Kevan Chao
Feb 15, 2012, 8:32:28 PM2/15/12
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(I)Alright, so I know Shear Stress = F/A, with the F=force parallel to the cross sectional area.
That in mind, the answer I got for part a.) was 8.9 MPa.
I got that by taking the (700N) / 2 = 350 N per leg.
And I know area of a circle = (pi)*r^2 = pi*(d/2)^2 = pi*(0.005m / 2)^2 = 1.9635 * 10^-5 m^2
So then since the are 2 nails I multiply the A by 2,
Sheer Stress=F/A = (350 N) / [2*1.9635*10^-5 m] = 8.913 MPa
If this is wrong, please tell me, as that is probably why i'm not getting part (II), which is my main question
(II)
Now for part II, the only differenc is that there's 4 nails. All I should need to do is multiply the area of the nail by 4 and solve for sheer. But I dont get an answer that's provided.
My work: Sheer Stress = F/A = 350N / (4*1.9635*10^-5 m) = 4.456 MPa.
It's not an answer choice. Can you please help? Thanks a lot.
That in mind, the answer I got for part a.) was 8.9 MPa.
I got that by taking the (700N) / 2 = 350 N per leg.
And I know area of a circle = (pi)*r^2 = pi*(d/2)^2 = pi*(0.005m / 2)^2 = 1.9635 * 10^-5 m^2
So then since the are 2 nails I multiply the A by 2,
Sheer Stress=F/A = (350 N) / [2*1.9635*10^-5 m] = 8.913 MPa
If this is wrong, please tell me, as that is probably why i'm not getting part (II), which is my main question
(II)
Now for part II, the only differenc is that there's 4 nails. All I should need to do is multiply the area of the nail by 4 and solve for sheer. But I dont get an answer that's provided.
My work: Sheer Stress = F/A = 350N / (4*1.9635*10^-5 m) = 4.456 MPa.
It's not an answer choice. Can you please help? Thanks a lot.
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Mitul
Feb 16, 2012, 9:59:27 AM2/16/12
to BMED2540
Hi,
Your understanding of the problem is almost perfect. Remember that
since the Force is a vector, the nails in line with the vector will
bear the same force. Which means that the 2 nails shall bear force F
each. While in case 2 there are 2 sets of nails and hence each set
would bear only half the force each.
The Lecture today should have solved your doubt but in any case hope
this helps too
Cheers.
Mitul
Your understanding of the problem is almost perfect. Remember that
since the Force is a vector, the nails in line with the vector will
bear the same force. Which means that the 2 nails shall bear force F
each. While in case 2 there are 2 sets of nails and hence each set
would bear only half the force each.
The Lecture today should have solved your doubt but in any case hope
this helps too
Cheers.
Mitul
Kevan Chao
Feb 16, 2012, 2:02:01 PM2/16/12
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Ah I figured it out. He's standing on one leg, so I wasn't supposed to divide his weight by two. Dangit. Knew something funny was going on when there was no answer choice less than 43.3 N for part II. thanks anyhow
Kevan Chao
Feb 18, 2012, 11:06:14 PM2/18/12
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Mitul,
I submitted my assignment and it says I got question 2, part a incorrect, but part b correct. Please explain how I am wrong.
So basically, from what I understand the answer to part a should be: Stress= F/A = 700 / (2[1.96*10^-5]) = 17.8 MPa
And Part B, which has 4 screws, should be: Stress = F/A = 700/(4[1.96*10^-5]) = 8.93 MPa
How the heck is the answer to part a 35.7 MPa??
I submitted my assignment and it says I got question 2, part a incorrect, but part b correct. Please explain how I am wrong.
So basically, from what I understand the answer to part a should be: Stress= F/A = 700 / (2[1.96*10^-5]) = 17.8 MPa
And Part B, which has 4 screws, should be: Stress = F/A = 700/(4[1.96*10^-5]) = 8.93 MPa
How the heck is the answer to part a 35.7 MPa??
Mitul
Feb 19, 2012, 2:04:01 PM2/19/12
to BMED2540
What is the formula for area you are using ?? The screw has a circular
cross section so the area should be pi*R*R, for the first case
cross section so the area should be pi*R*R, for the first case
Kevan Chao
Feb 21, 2012, 11:30:58 AM2/21/12
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Right. So if the diameter is 5mm=0.005m, then the radius=0.0025m
So A = pi*(0.0025)(0.0025) = 1.96*10^-5 m^2
F = 700N. Taking into account there are two nails,
Sheer Stress = F/A = 700N/(2*1.96*10^-5 m^2) = 17.8 MPa.
For four nails,
Sher Stress = F/A = 700N/(4*1.96*10^-5) = 8.93 MPa
So A = pi*(0.0025)(0.0025) = 1.96*10^-5 m^2
F = 700N. Taking into account there are two nails,
Sheer Stress = F/A = 700N/(2*1.96*10^-5 m^2) = 17.8 MPa.
For four nails,
Sher Stress = F/A = 700N/(4*1.96*10^-5) = 8.93 MPa
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