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Help! M2 Moments problem.
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h2shin
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#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?
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#2
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#2
Hi there,
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While you're waiting for an answer, did you know we have 300,000 study resources that could answer your question in TSR's Learn together section?
We have everything from Teacher Marked Essays to Mindmaps and Quizzes to help you with your work. Take a look around.
If you're stuck on how to get started, try creating some resources. It's free to do and can help breakdown tough topics into manageable chunks. Get creating now.
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brianeverit
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#3
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#3
(Original post by h2shin)
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?
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?
For example if we take moments about B for the rod AB we have 2M=3mg
and for the rod BC
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