Is the Triangular Lamina Stable When Suspended from Point C?

In summary, the conversation discusses a uniform triangular lamina with specific measurements and its suspension under gravity. The angle between BC and the downwards vertical is being calculated and the center of gravity is being found through a coordinate system. The slope of the line through the center of gravity and (2,0) is also mentioned. The conversation also mentions a question from a professor about the spelling of "lamina" backwards.
  • #1
BLUE_CHIP
A uniform triangular lamina ABC where AB = 1m and BC = 2m and it is right angled at B. It is suspended from C and hangs freely under gravity. Calculate the angle between BC and the downwards vertical.

Need help fast pls cheers:smile:
 
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  • #2
Find the center of gravity of the lamina.
The center of gravity will hang directly below C.

Easy way to find the center of gravity: Set up a coordinate system so that B is at (0,0), A is at (0,1), C is at (2, 0). Take the "average" of the three points. Find the slope of the line through (2,0) and the center of gravity and remember that slope = tan of angle the line makes with BC (x-axis).
(I get a remarkably simple result!)

(Off the subject: I once had a professor who put (on the FINAL exam!) the question "What is "lamina" spelled backwards?"! One student got really angry with him because the question "didn't make sense".)
 
  • #3


The stability of equilibrium in this scenario can be determined by observing the angle between BC and the downwards vertical. In this case, since the lamina is suspended from point C, the angle between BC and the downwards vertical can be calculated using trigonometric principles.

First, we can use the Pythagorean theorem to find the length of AC, which is the hypotenuse of the right triangle. AC = √(AB² + BC²) = √(1² + 2²) = √5m.

Next, we can use the sine function to find the angle between BC and the downwards vertical. sinθ = opposite/hypotenuse = BC/AC = 2/√5.

Using a calculator, we can find the value of this angle to be approximately 63.4 degrees. This means that the lamina is hanging at an angle of 63.4 degrees from the downwards vertical.

In terms of stability, this angle indicates that the lamina is not perfectly stable as it is not hanging straight down. However, it also does not have a very large angle, which could indicate instability. Overall, the stability of the equilibrium in this scenario would depend on the specific conditions and forces acting on the lamina.
 

FAQ: Is the Triangular Lamina Stable When Suspended from Point C?

What is stability of equilibrium?

The stability of equilibrium refers to the tendency of a system to return to its original state after being disturbed. In other words, it is the ability of a system to maintain its balance or steady state.

How is stability of equilibrium determined?

The stability of equilibrium is determined by analyzing the behavior of a system after a small disturbance. If the system returns to its original state, it is considered stable. If it moves away from its original state, it is considered unstable.

What are the different types of equilibrium?

There are three types of equilibrium: stable, unstable, and neutral. A stable equilibrium is when a system returns to its original state after a small disturbance. An unstable equilibrium is when a system moves away from its original state after a small disturbance. A neutral equilibrium is when a system remains in its new state after a small disturbance.

How does the concept of stability of equilibrium apply to real-life situations?

The concept of stability of equilibrium can be seen in various real-life situations such as the stability of buildings during earthquakes, the stability of financial markets, and even the stability of relationships. In each case, the system must be able to return to its original state after being disturbed in order to maintain stability.

What factors can affect the stability of equilibrium?

There are several factors that can affect the stability of equilibrium, such as external forces, changes in the environment, and the strength of the system's internal forces. Additionally, the type of equilibrium and the initial conditions of the system can also impact its stability.

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