Calculating the tension in the backstay of a sailboat...?

Question

An intro physics question... should be pretty simple and I'd really appreciate any help!

The mast of a sailboat is supported at bow and stern by stainless steel wires, the forestay and backstay, anchored x = 10.0 m apart.

a) The L = 12.4-m long mast weighs 817 N and stands vertically on the deck of the boat. The mast is positioned 3.70 m behind where the forestay is attached. The tension in the forestay is 520 N. Calculate the tension in the backstay.

b) Calculate the force that the mast exerts on the deck.

Thanks so much. I will be checking frequently for answers. Thank you so so so much!

The first offered answer was wrong... first off, 10m - 3.7 = 6.3m... Dang, I was so excited too. Anybody else?

Answer 1

a) The L = 12.4-m long mast weighs 817 N and stands vertically on the deck of the boat. The mast is positioned 3.70 m behind where the forestay is attached. The tension in the forestay is 520 N. Calculate the tension in the backstay.

Let α be the angle between the mast and the forestay.
α = arctan(3.7/12.4) = 16.614°
Fx = 520sin16.614° = 148.68 N
Fy = 520cos16.614° = 498.29 N
let β be the angle between the mast and the backstay.
β = arctan(10.0 - 3.7)/12.4) = 26.934°
The horizontal force exerted on the mast by the forestay must be balanced by the force exerted on the mast by the backstay:
Fx = 148.68 N
Fy = 148.68/tan(26.934°) = 292.64 N
The tension in the backstay, F is
F = 148.68/sin(26.934°) = 328.24 N

B) the force the mast exerts on the deck
Ft = 817 + 328.24 + 498.29 = 1,643.53 N

Answer 2

for a
firstly find the lengths of the wires by drawing two triangles with hight 12.4m, one has length 8.3m (10m -3.7m) and the other has length 3.7m.
I will use Ff for forestay tension, Lf for forestay length, and Fb, Lb for the backstay.
As the mast is stationary the net force is zero, hence Ff x Lf =Fb x Lb.
from the triangles Lf = 12.9m and Lb = 13.9m, therefore
Fb =483N

I am not entirely sure with b
but I would assume that it is 817N, which is the mass of mast as this is the force that it is excerting on the deck

Answer 3

Backstay Tension

Answer 4

That's a good question, I was wondering the same thing myself

Answer 5

It is possible, however I'm not convinced