Question

Determine the maximum weight of the flowerpot that can besupported without exceeding a cable tension of 50 lb in eithercable AB or AC.

Answer 1

Maximum weight = 76.64 lb

Step-by-step explanation:

In the second figure attached it can be seen the free body diagram of the problem.

The equation of equilibrium respect x-axis is

`\sum F_x = 0`

`F_(AC) * sin 30 - F_(AB) * (3)/(5) = 0`

`F_(AC) = 1.2 * F_(AB)`

So, cable segmet AC supports bigger tension than segment AB. If
`F_(AC) = 50 lb` then

`F_(AB) = (F_(AC))/(1.2)`

`F_(AB) = 41.67 lb`

The equation of equilibrium respect y-axis is

`\sum F_y = 0`

`F_(AB) * (4)/(5) + F_(AC) * cos 30 - W = 0`

`41.67 lb * (4)/(5) + 50 lb * cos 30 - W = 0`

`W = 76.64 lb`