Question

The picture has a weight of 10 lb and is to be hunged over the smooth pin B. If the string is attached to the frame at points A and C, and the maximum force the string can support is 15 lb. Determine the shortest string that can be safely used.

SIT. 0: The picture has a weight of 10 lb and is to be hunged over the smooth pin B. If a string is attached to the frame at points A and C, and the maximum force the string can support is 15lb: in 42) Determine the shortest string that can be safely used? A. 20.3" B. 19.1" C.18.8" D. 22.6"

Answer 1

Step 1: Given Data

Weight = 10 lb

Length of longer side = 18"

Axial Tension Capacity of String = 15lb

Step 2: Free body diagram of Internal Forces

T T B C 10 - 9 in.

Here, θ = The angle of inclination of the string with horizontal at the state when it is at maximum tensile capacity.

It is to be observed that the only variables in this system are the Thread Length (L) and the Tension in thread (T). For the Length to be shortest the tension, T, has to be maximum i.e. 15 lb.

Length is dependent on the angle of inclination, therefore we can analyze the system as shown below,

TCose B TCose T А. С 9 in 9 in 10 + 2TSino

Step 3: It can be seen that the net force in the Y direction is zero, so the sum, 10+2TSinθ = 0

Here T=15 lb,

On Solving we get,   θ = -19.47 degrees

For the length to be shortest, we can use the above diagram,

LCosθ = 9

Therefore the shortest half length is = L=9.545", Total length of string is,   L = 19.1".