Two hanging masses and three strings

In summary, in this problem, two masses of m and M (where M = 2m) are connected by three strings. The first mass is suspended from a single vertical string held by two strings each at 45 degrees to the horizontal. One of the strings is attached to a fixed point and the other is attached to the second mass, which is then connected to a fixed point at an angle theta to the horizontal. The system is in equilibrium, with no net force acting on it. Using the equations F = ma and ΣF = 0, it can be determined that the y component of the two tensions in the diagonal strings supporting mass m is equal to mg, and the tension in the third string connecting mass M to
  • #1
Lennie
1
0

Homework Statement


Two masses m and M (where M = 2m) are attached with strings. One mass m is suspended from a single verticle string held by two strings each at 45 degrees to the horizontal. The suspending string to the left at 45 degrees is attached to a fixed point. The string on the right at 45 degrees is attached to another mass M which in turn is attached by a further to a fixed point above at an angle theta to the horizontal.
If the system is in equilibrium, determine the tension in the three strings in terms of m and g, and calculate the angle theta.[/B]

Homework Equations


F = ma

The Attempt at a Solution


As the system is in equilibrium i can say a=0 and therefore ΣF = 0.
The y component of the two tensions in the two diagonal strings supporting mass m should be equal to mg when summed. Assuming the tensions are still equal (not quite sure what effect the other mass M would have on this - mass M is what has thrown me) then the tension in the bottom two strings should be mg/√2 ?
The tension in the 3rd string connecting mass M with the fixed point ? My best quest was to say it is equal to √2mg as 2mg sin45 = T ?
I also don't know theta however and don't see a way of finding it, at this point I am almost sure i have absolutely none of this right! Any help on a method to solve this would be much appreciated!

P.s sorry for the lack of image, can't seem to find anything on the web which shows a similar situation.
 
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  • #2
Lennie said:
As the system is in equilibrium i can say a=0 and therefore ΣF = 0.
Good.

Lennie said:
The y component of the two tensions in the two diagonal strings supporting mass m should be equal to mg when summed.
Good.

Lennie said:
Assuming the tensions are still equal
No need to assume that... prove it!

Lennie said:
The tension in the 3rd string connecting mass M with the fixed point ? My best quest was to say it is equal to √2mg as 2mg sin45 = T ?
Why guess? Apply ΣF = 0 to mass M and solve for the unknowns.

Lennie said:
P.s sorry for the lack of image, can't seem to find anything on the web which shows a similar situation.
You can use the whiteboard to slap something together yourself.
 

1. What is the purpose of studying two hanging masses and three strings?

The purpose of studying two hanging masses and three strings is to understand basic principles of physics, such as gravity and tension, and to apply them in real-world scenarios. This experiment also helps to develop problem-solving skills and critical thinking.

2. How are the masses and strings arranged in this experiment?

In this experiment, two masses are suspended from a horizontal bar using three strings. The two masses are of equal weight and are hanging at equal distances from the center of the bar. The strings are attached to the masses and then to the bar, forming a triangle shape.

3. What factors affect the behavior of the two hanging masses and three strings?

The behavior of the two hanging masses and three strings is affected by several factors, including the weight of the masses, the length and tension of the strings, and the angle at which the strings are suspended. These factors can influence the equilibrium position, oscillation, and overall stability of the system.

4. How can the tension in the strings be calculated?

The tension in the strings can be calculated using the equation T = mg, where T is the tension, m is the mass, and g is the acceleration due to gravity. This equation assumes that the strings are massless and the masses are in equilibrium. If the strings have mass, their weight must also be taken into account.

5. What is the significance of the two hanging masses and three strings experiment in the field of physics?

The two hanging masses and three strings experiment is significant in the field of physics because it demonstrates the principles of equilibrium, tension, and oscillation. It also has practical applications, such as understanding the behavior of bridges and other structures that rely on tension to maintain stability.

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