Rotational Equilibrium

[MDwannabe7]

---

Members don't see this ad.

Mass 1 is located at the far left end of a 90 cm beam. Mass 2 is located at the center of the beam, and mass 3 is located 30 cm from the center, on the right side. Mass 3 and mass 1 are the same. If the fulcrum is located 10 cm to the left of the center of the beam, what is the mass of mass 2 if the beam does not rotate?

The answer says, "In this configuration, the beam must rotate, regardless of the mass of mass 2."

I do not get it - any explanations?

 

[mosquitoman]

i think mass 2 can be any weight because it is directly in the center.. that is.. it doesnt have a lever arm

remember you do weight * distance from center

Fg1X1 = Fg2x2

for the one at center, x = 0

 

[MDwannabe7]

i think mass 2 can be any weight because it is directly in the center.. that is.. it doesnt have a lever arm

remember you do weight * distance from center

Fg1X1 = Fg2x2

for the one at center, x = 0

But mass 2 does have a lever arm, b/c the fulcrum is located 10 cm to the left of the center. What I don't understand is how it is impossible for this setup to be in rotational equilibrium...

 

[lixxx669]

suppose the mass of 1 and 3 is m, ignore 2 first,
clockwise torque= mgX40cm
countercolckwise torque=mgX35cm
the beam have the trand to rotate clockwise already, if you add 2, which is located on the right of fulcrum, will make it more rotate clock wise.
So it will rotate regardless the mass of 2

 

[KDMID]

Hi there,

I know I'm late in this thread, but I just got stuck on this problem in my prep. The explanations above do not clarify the confusion I seem to share with MDwannabe7. My interpretation of the problem is this: m1 is at the far left of the beam, 45 cm from the center. M3 is 30 cm to the left of the center. M2 is at the center of the beam. And, the fulcrum is 10 cm to the left of m2/the center of the beam. Kind of like the poor schematic below (^ = fulcrum). So, I thought, like MDwannabe, that if m2 was 5.5*m1, then it could be in equilibrium...

m1___________m3_____^___m2____________________

Am I misreading the problem and diagramming incorrectly? Anyone able to reword the scenario to think the like lixxx & others did above/explain how they got there? Thanks!

 

[lexw]

i think you diagrammed it incorrectly

Mass 1 is located at the far left end of a 90 cm beam.
Mass 2 is located at the center of the beam.
Mass 3 is located 30 cm from the center, on the right side.
The fulcrum is located 10 cm to the left of the center of the beam. Mass 3 and mass 1 are the same.

m1_____________^____c(m2)_______m3________________
(35) (0) (10) (40)

since m1 and m3 are the same and d is different it means that it wont be in equilibrium regardless of m2. only if m2 was on the left side would it balance out.

 

[makingthejump]

Torque = Force x Lever Arm
TorqueClockwise = Force x 40cm
TorqueCounterclockwise=Force x35cm

In words, the above means that there is greater torque in the clockwise direction so the beam will rotate clockwise. The question states that mass 2 is to the RIGHT of the fulcrum. Think about this...it is to the RIGHT which will only add to the Torque produced in the clockwise direction. You can't make mass 2 have a negative value b/c mass is a positive quantity, thus there is no value at which mass 2 can be that would make the beam not rotate b/c in all scenarios of this problem torque clockwise > torque counterclockwise and therefore yields clockwise rotation of the beam. Make sense?

 

[KDMID]

Thanks so much for the quick responses, lexw & making the jump. I guess I didnt read the first post on this thread carefully, though, & that's probably causing much of the confusion. It differs slightly to my problem. Here's what my book says, word for word:

Mass 1 is located at the far left end of a 90 cm beam. Mass 2 is located at the center of the beam, & mass 3 is located 30 cm from the center on the left side. Mass 3 & mass 1 are the same. If the fulcrum is located 10 cm to the left of the center of the beam, what is the mass of mass 2 if the beam does not rotate?

From this, I got the diagram I made above, where m3 is 20 cm to the left of the fulcrum, m2 is 10 cm to the right of the fulcrum, & m1 is 45 cm to the left. From that, I still get m2 being 5.5*m1 or m3. Maybe, they changed the problem for my edition of the book (I just got the newest one), but didn't change the answer from the old problem that still had m3 on the right side of the fulcrum?

m1___________m3_____^___m2____________________