Back
to top
Help! M2 Moments problem.
Watch this threadPage 1 of 1
Go to first unread
Skip to page:
h2shin
Badges:
9
Rep:
?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#1
Hello!
I am stuck on a problem, I've taken it as far as I can but no progress
A uniform rod of length 2𝑎 runs from A to B and has mass 𝑘𝑚 where 𝑘=3. The rod is fixed at the point A and is freely hinged to another uniform rod of length 2𝑎 and mass 𝑚 at the point B. Both rods are in equilibrium with the first rod horizontal and the second inclined at angle 𝜃=30∘ to the vertical, with its unhinged end in contact with the rough floor. The coefficient of friction between the rod and the floor is 𝜇.
https://isaacphysics.org/api/images/...hinged_rod.svg
So I labelled all the forces like so in this picture:
https://isaacphysics.org/api/images/...inged_rod2.svg
And by resolving and equating the forces I have
4mg = M + R
N = F
Taking pivot around A I have
(11/2)mg + Fsqrt(3) = 3R
Moments about B
2M + Fsqrt(3) = (5/2)mg + R
3M + Nsqrt(3) = (13/2)mg
So I need to find minimum mew, so that F <= mewR
Now when I try to solve the equations, all I end up with is (11/2)mg + Fsqrt(3) = 3R and really don't know how to progress.
Any Ideas?
I am stuck on a problem, I've taken it as far as I can but no progress
A uniform rod of length 2𝑎 runs from A to B and has mass 𝑘𝑚 where 𝑘=3. The rod is fixed at the point A and is freely hinged to another uniform rod of length 2𝑎 and mass 𝑚 at the point B. Both rods are in equilibrium with the first rod horizontal and the second inclined at angle 𝜃=30∘ to the vertical, with its unhinged end in contact with the rough floor. The coefficient of friction between the rod and the floor is 𝜇.
https://isaacphysics.org/api/images/...hinged_rod.svg
So I labelled all the forces like so in this picture:
https://isaacphysics.org/api/images/...inged_rod2.svg
And by resolving and equating the forces I have
4mg = M + R
N = F
Taking pivot around A I have
(11/2)mg + Fsqrt(3) = 3R
Moments about B
2M + Fsqrt(3) = (5/2)mg + R
3M + Nsqrt(3) = (13/2)mg
So I need to find minimum mew, so that F <= mewR
Now when I try to solve the equations, all I end up with is (11/2)mg + Fsqrt(3) = 3R and really don't know how to progress.
Any Ideas?
0
reply
h2shin
Badges:
9
Rep:
?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#2
Oh above, after moments about B, I took moments about C as well.
They all just give me the same thing, I i suppose it's reassuring all the equations are consistent, just no way to find the mew!
They all just give me the same thing, I i suppose it's reassuring all the equations are consistent, just no way to find the mew!
0
reply
h2shin
Badges:
9
Rep:
?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#3
ghostwalker
Badges:
17
?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#4
Report
#4
(Original post by h2shin)
No one with any ideas?
No one with any ideas?
Your problem is that you are treating the whole structure ABC as one thing and that's not generating enough information. BUT each of the two parts AB, BC is itself in static equilibrium.
E.g. You can take moments about B for just AB, which will give you M, and thus you can work out R from your initial equation. And so on.
On a quick calculation I got mu to be:
Spoiler:
Show
1
reply
h2shin
Badges:
9
Rep:
?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#5
(Original post by ghostwalker)
When mu is a minimum, you'll have
Your problem is that you are treating the whole structure ABC as one thing and that's not generating enough information. BUT each of the two parts AB, BC is itself in static equilibrium.
E.g. You can take moments about B for just AB, which will give you M, and thus you can work out R from your initial equation. And so on.
On a quick calculation I got mu to be:
When mu is a minimum, you'll have
Your problem is that you are treating the whole structure ABC as one thing and that's not generating enough information. BUT each of the two parts AB, BC is itself in static equilibrium.
E.g. You can take moments about B for just AB, which will give you M, and thus you can work out R from your initial equation. And so on.
On a quick calculation I got mu to be:
Spoiler:
Show
AHH!! Right. I thought that was to do with it but the random x's and y's were confusing the hell out of me as well. thanks!
So it's exactly like a connected newton's third law system problem in M1 just in two dimension! with forces at B just cancelling out when you look at the whole system and taken out of the picture when I take pivot around B to equate the torque.
So simple but you helped me get there
0
reply
ghostwalker
Badges:
17
?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#6
Report
#6
(Original post by h2shin)
AHH!! Right. I thought that was to do with it but the random x's and y's were confusing the hell out of me as well. thanks!
AHH!! Right. I thought that was to do with it but the random x's and y's were confusing the hell out of me as well. thanks!
PS: I used the equations you posted without checking them to work out my answer.
0
reply
h2shin
Badges:
9
Rep:
?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#7
(Original post by ghostwalker)
np.
PS: I used the equations you posted without checking them to work out my answer.
np.
PS: I used the equations you posted without checking them to work out my answer.
The internal forces all cancelled out / were not relevant to the torque that's being calculated.
Thanks so much, this question was annoying me the whole day.
Just because the connected objects problem was taken from 1 dimension to 2 it just completely threw me off. argh.
0
reply
X
Page 1 of 1
Go to first unread
Skip to page:
Quick Reply
