Tackle Component
'mastering physics' homework question?
I can't get a picture of this problem up so I'll explain it as well as I can.
Basically a sign for a shop is attached to the wall and is held in place with a bolt (directly attaching its inner edge to the wall) and a rope which is attached between the wall and the outer edge of the sign at an angle of 20 degrees to the horizontal.
The sign is 3.2m long and has a mass of 12kg.
a) what is the tension in the rope
b)What is the horizontal and vertical components of the force, F, exerted by the bolt?
I'm really stuck at this and would appreciate any help if you could tell me how to tackle this problem.
Thanks x
(a).
∑τ at bolt = 0
- T L sin θ + m g (½ L) = 0
T = ½ m g / sin θ = ½ (12) (9.8) / sin 20°
T = 171.92 N
(b).
∑Fx = 0
H - T cos θ = 0
H - 171.92 cos 20° = 0
H = 161.552 N
∑Fy = 0
V + T sin θ - m g = 0
V + 171.92 sin 20° - (12) (9.8) = 0
V = 58.8 N
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let's check the answer;
∑τ at initial rope on the outer edge of sign = 0
V L - m g (½ L) = L(58.8 - ½ *12 * 9.8) = 0
∑Fx = H - T cos θ = 161.552 - 171.92 cos 20° = 0
∑Fy = T sin θ + V - mg = 171.92 sin 20° + 58.8 - (12)(9.8) = 0
All OK !