Prooving a system will travel up to 180 degrees

In summary, the equation for the system is weight of pan and tray multiplied by sin2 θ / [x(h-xsin2 θ)] and the RHS side of the equation is not clear.
  • #1
physicsodyssey
11
6

Homework Statement


To prove that system will travel freely upto 180 degree
m2 is counterweight and m1 is mass of pan (=3kg)
i have attched the fbd or another link http://www.imagebam.com/image/54bb5a394377595

Homework Equations


m1(h + a sin θ) g x = m2 y h g
m2 = 9.13 kg

The Attempt at a Solution


we are stuck at the following equation
Pwg ≥( m1 x^2 + m2 y^2) sin2 θ / [ x(h-xsin2 θ)]
LHS is weight of pan and arm and if LHS>RHS, system will rotate freely
is this correct? can you pls explain it properly because it will clear my concepts.
Thanks.
 

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  • #2
Hello, welcome to PF :smile:

Could you clarify the problem statement a bit more? The diagram is difficult to read, I see no forces, what is what, what is the pivot point, what is a, what is P w (pr Pw ?), etc.
 
  • #3
a is the length of bearing housing(the middle block which is the reference axis) hence a sin θ is added to h for balancing. my issue is the second equation. i cannot understand the RHS side.LHS is simply the wt of pan and tray.(ρwg).
can you help me with the equation on RHS
( m1 x^2 + m2 y^2) sin2 θ / [ x(h-xsin2 θ)]
Thanks a lot for a warm welcome in this wonderful community.
 
  • #4
Still lost -- or rather not "in":

The thing on the right is a pan. What is a pan ? The thing in the middle is a bearing housing. Interesting. Does it pivot around some axis ? What axis ?

If the LHS was the weight of the pan and arm and now is the weight of the pan and tray, how come m1 doesn't feature in it ? What tray ?
What is s ?

What does the equation m1(h + a sin θ) g x = m2 y h g represent ? I see something in kg m3 /s2

What is ##\theta## ? What's the blue horizontal line ? And the black sloping line just underneath ?

THe fat black lines to L and R ? The thin black lines (where the h are mentionsed) ?

What is dangling from the bearing housing ? Where is the reference point for a ?

Are lengths measured in meters ?

What has to rotate 180 degrees ? Doesn't it bum into the fat line on the left ?
 

Related to Prooving a system will travel up to 180 degrees

What does it mean to prove a system will travel up to 180 degrees?

Proving that a system will travel up to 180 degrees means demonstrating that the system is capable of rotating or moving in a full half-circle, from its starting point to the opposite point, without any limitations or obstacles.

Why is it important to prove a system will travel up to 180 degrees?

Proving that a system can travel up to 180 degrees is important for ensuring that the system is functional and capable of completing a full range of motion. It also allows for accurate predictions and analysis of the system's behavior.

What factors are involved in proving a system will travel up to 180 degrees?

The factors involved in proving a system will travel up to 180 degrees can vary depending on the specific system. However, some common factors include the design and mechanics of the system, any external forces or constraints, and the range of motion of the system's components.

How do scientists typically prove that a system will travel up to 180 degrees?

Scientists typically use a combination of mathematical calculations, computer simulations, and physical experiments to prove that a system will travel up to 180 degrees. This allows for a thorough and accurate analysis of the system's capabilities.

What are some potential limitations or challenges in proving a system will travel up to 180 degrees?

Some potential limitations or challenges in proving a system will travel up to 180 degrees include external factors such as friction or other forces that may affect the system's motion. Additionally, the complexity of the system and its components may also pose challenges in accurately predicting its range of motion.

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