What fraction of the sign's weight is supported by each string?

In summary, the problem involves a hemispherical sign with a diameter of 1 meter and uniform mass density, supported by two cables. To find the fraction of weight supported by each cable, the total torque must be 0. By setting up equations for the torque and the total weight, it is determined that the back cable supports 1/3 of the weight and the front cable supports 2/3 of the weight.
  • #1
decathlonist
I am stuck on one of the AP Physics problems. Could you please help me out and give some pointers on how to solve the following problem:

A hemispherical sign 1 m in diameter and of uniform mass density is supported by two strings. What fraction of the sign's weight is supported by each string?

[see attachment for the diagram]

Thank you
 

Attachments

  • diagram.bmp
    8.7 KB · Views: 804
Last edited by a moderator:
Physics news on Phys.org
  • #2
[searches in vain for an attachment...]
 
  • #3
I was able to down load the attachement without any trouble.

I shows a semicircle with two lines (the supporting cables) going up from (first cable) one end of a diameter and (2nd cable) 0.75 meters along (I assume) the diameter and so 0.25 meters from the other end.

Let W be the weight of the sign, F1 and F2 be the forces on the respective cables. Obviously F1+F2= W. The total torque must be 0 (about any point- in particular about the point of attachment of cable 1) so -W(1/2 meter) (the torque due to the weight of the sign)plus F_2(0.75) must be 0.
(0.75)F_2- 0.5 W= 0 or F_2= (0.5/0.75)W= (2/3)W.

From F_1+ F_2= W we get F_1+ (2/3)W= W or F_1= (1/3)W.

The cable at the back is supporting 1/3 of the weight and the one in front is supporting 2/3 of the weight.
 

FAQ: What fraction of the sign's weight is supported by each string?

1. What is the concept of weight distribution in relation to strings?

Weight distribution refers to the way in which the weight of an object is distributed or divided among the different strings supporting it. This concept is important in understanding how much weight each string is able to support.

2. How does the number of strings affect the weight distribution?

The more strings that are used to support an object, the more evenly distributed the weight will be. This means that each individual string will support a smaller fraction of the total weight.

3. What factors influence the amount of weight supported by each string?

The main factors that influence the weight supported by each string include the strength and thickness of the string, the angle at which the string is attached to the object, and the overall weight of the object.

4. Is the weight supported by each string always equal?

No, the weight supported by each string is not always equal. This depends on the factors mentioned above, as well as the distribution of weight within the object itself. In some cases, one string may be supporting more weight than the others.

5. How can weight distribution be calculated for a particular object?

Weight distribution can be calculated by considering the weight of the object and the number of strings supporting it, as well as the factors that influence the weight supported by each string. Using this information, a scientist can determine the fraction of the weight that is supported by each string.

Back
Top