Help! M2 Moments problem.

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h2shin
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#1
Report Thread starter 7 years ago
#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?
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TSR Learn Together
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#2
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#2
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brianeverit
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#3
Report 7 years ago
#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?
i don't agree with your moments about B.
For example if we take moments about B for the rod AB we have 2M=3mg
and for the rod BC 2R=mg+F\sqrt3
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