This time its a statics problem

In summary, the problem is a statics problem involving a nonuniform bar suspended at rest by two massless cords. The equations for equilibrium are T1 sin(theta1) + T2 sin(theta2) = mg and T1 cos(theta1) - T2 cos(theta2) = 0. To solve for the center of mass, the mass of the bar needs to be calculated, as well as the tension in each cord. Using the equation for equilibrium, the distance x from the left-hand end of the bar to its center of mass can be found, and then the center of mass can be determined by taking the average of the two ends of the bar.
  • #1
Cyrad2
13
0
A nonuniform bar is suspended at rest in a horizontal position by two massless cords as shown. One cord makes the angle theta1 = 36.9 with the vertical; the other makes the angle theta2 = 53.1 with the vertical. If the length L of the bar is 6.10m, compute the distance x from the left-hand end of the bar to its center of mass.

I keep getting stuck on this one. Basically all I know is that it's a statics problem, since it's at rest. So, I know that

T1 sin(theta1) + T2 sin(theta2) = mg
T1 cos(theta1) - T2 cos(theta2) = 0
where T1 and T2 are the tensions on the cords supporting the rod.

There are so many unknowns that I'm not sure where to go from here, but I've been playing around with:

T1sin(theta1)*X - T2sin(theta2)*(L-X) = 0
(Force1 * Distance1) == (Force2 * Distance2)

I would appreciate some suggestions and hints! (i'm not asking for anyone to solve it because the problem may be on my test tommarow). Thanks a bunch!
 
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  • #2
Here's what you need to do: 1. Calculate the mass of the bar, m = T1 sin(theta1) / g, where g is the gravitational acceleration (9.81 m/s2). 2. Calculate the tension in each cord, T1 = m * g / sin(theta1) and T2 = m * g / sin(theta2). 3. Using the equation for equilibrium (T1sin(theta1)*X - T2sin(theta2)*(L-X) = 0), solve for X. Once you have the value of X, you can find the center of mass by taking the average of the two ends of the bar: x_center_of_mass = (x + L)/2.
 
  • #3


Hi there,

It looks like you're on the right track with your equations. Since the bar is at rest, we can assume that the sum of all the forces acting on it is equal to zero. This means we can set up the following equations:

T1sin(theta1) + T2sin(theta2) = mg (equation 1)
T1cos(theta1) - T2cos(theta2) = 0 (equation 2)
T1sin(theta1)*x - T2sin(theta2)*(L-x) = 0 (equation 3)

We can solve for T1 and T2 by rearranging equation 2 and substituting into equation 1:

T1cos(theta1) = T2cos(theta2) (from equation 2)
T1 = T2cos(theta2)/cos(theta1) (substituting into equation 1)
T2sin(theta2) = mg - T1sin(theta1) (from equation 1)
T2 = (mg - T1sin(theta1))/sin(theta2) (substituting into previous equation)

Now we can substitute these values back into equation 3 and solve for x:

T1sin(theta1)*x - T2sin(theta2)*(L-x) = 0 (equation 3)
T1sin(theta1)*x - ((mg - T1sin(theta1))/sin(theta2))*sin(theta2)*(L-x) = 0 (substituting in values for T1 and T2)
T1sin(theta1)*x - (mg - T1sin(theta1))*(L-x) = 0 (simplifying)
T1sin(theta1)*x - mgL + T1sin(theta1)*L - T1sin(theta1)*x = 0 (expanding brackets)
T1sin(theta1)*L = mgL (cancelling out like terms)
x = (mgL)/(T1sin(theta1)) (solving for x)

Now we can plug in the values for mg, L, T1, and theta1 to get our final answer for x. I hope this helps! Good luck on your test tomorrow.
 

1. What is statics?

Statics is a branch of mechanics that deals with the study of objects at rest or in constant motion. It involves analyzing the forces acting on an object and predicting the resulting motion or equilibrium.

2. What types of problems can be solved using statics?

Statics can be used to solve problems related to structures, machines, and other physical systems. For example, it can be used to determine the stability of a building or the forces acting on a bridge.

3. How is statics different from dynamics?

While statics deals with objects at rest or in constant motion, dynamics deals with objects that are accelerating. This means that dynamics takes into account the forces that cause changes in motion, while statics focuses on the forces that maintain equilibrium.

4. What are some common applications of statics in real life?

Statics has many practical applications in engineering, architecture, and other fields. It is used in the design and analysis of structures such as buildings, bridges, and dams. It is also used in the development of machines and mechanical systems.

5. What are some key concepts to understand in statics?

Some key concepts in statics include Newton's laws of motion, force equilibrium, moment of a force, and free body diagrams. It is also important to understand vector operations and how to apply them to solve statics problems.

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