Question

Your are part of a team to help design the atrium of a new building.Your boss, the manager of the project, wants to suspend a 6.2 kg sculpture high over the room by hanging it from the ceiling using thin, clear fishing line (string) so that it will be difficult to see how the sculpture is held up. The only place to fasten the fishing line is to a wooden beam which runs around the edge of the room at the ceiling.The fishing line that she wants to use will hold 10 kg so she suggests attaching two lines to the sculpture to be safe. Each line would come from the opposite side of the ceiling to attach to the hanging sculpture. Her initial design has the first line making an angle of 12.67∘with the ceiling and the second line making an angle of 16.15∘ with the ceiling. She knows you took physics, so she asks you if her design can work.

How much force would the first line exert on the beam holding it up?
Assume that g=9.8 m/s−2.

Answer 1

The answer is below

Step-by-step explanation:

Given that the mass of the sculpture (m) = 6.2 kg,
`\theta_1=12.67^o,\theta_2=16.15^o`

`Sum\ of\ horizontal\ force\ is\ zero\ hence:\\\\T_1cos(\theta_1)=T_2cos(\theta_2)\\\\T_1=(T_2cos(\theta_2))/(cos(\theta_1))\\ \\Sum\ of\ vertical\ force\ is\ zero:\\\\T_1sin(\theta_1)+T_2sin(\theta_2)=mg\\\\(T_2cos(\theta_2))/(cos(\theta_1))sin(\theta_1)+T_2sin(\theta_2)=mg\\\\T_2=(mg)/((cos(\theta_2))/(cos(\theta_1))sin(\theta_1)+sin\theta_2) \\\\T_2=(6.2*9.81)/((cos(16.15))/(cos(12.67))sin(12.67)+sin16.15) =123.1\ N\\\\`

`T_1=(T_2cos(\theta_2))/(cos(\theta_1))=121.2\ N`