Find the tension in these two ropes?

Question

A camper hangs a 23kg pack between two trees, using two separate pieces of rope of different lengths. The left rope makes a 19 degree angle with the vertical left tree. The right rope makes an angles of 62 degrees with the vertical right tree. What is the tension in both the left and right ropes?

Answer 1

m = mass of the pack = 23 kg

θ₁ = angle of the left rope = 19° (to vertical)

θ₂ = angle of the right rope = 62° (to vertical)

g = acceleration by gravity = 9.8 m/s²



T₁ = tension in the left rope = ?

T₂ = tension in the right rope = ?



The horizontal components of the tensions in the rope equal each other.

T₁×sin(θ₁) = T₂×sin(θ₂)

so

T₁ = T₂×sin(θ₂)/sin(θ₁) . . . . . . . . . . . . . . . . . equation 1



The vertical components of the tensions in the ropes add up to the weight of the pack.

T₁×cos(θ₁) + T₂×cos(θ₂) = m×g . . . . . . . . . . equation 2



Substitute equation 1 into equation 2.

(T₂×sin(θ₂)/sin(θ₁))×cos(θ₁) + T₂×cos(θ₂) = m×g

T₂×[sin(θ₂)×cos(θ₁)/sin(θ₁) + cos(θ₂)] = m×g

T₂ = m×g / [sin(θ₂)×cos(θ₁)/sin(θ₁) + cos(θ₂)]



Filling in the numbers, you get:

T₂ = (23 kg)×(9.8 m/s²) / [sin(62°)×cos(19°)/sin(19°) + cos(62°)]

T₂ = 74.3 N



Filling in the numbers into equation 1, you get:

T₁ = (74.3 N)×sin(62°)/sin(19°)

T₁ = 201.5 N

Answer 2

so which you have 2 ropes too short to omit the load? Get extra rope is the least difficult way. to connect 2 ropes to make one the suitable way is to apply a fisherman's knot, that's incredibly 2 a million/2 hitches - one on each and each end formed around the status element of the different. while drawn at the same time the two lock at the same time, and value approximately 30% of power. in case you pass the loose ends around two times in the previous forming the hitches that's easy to undo, and weakens the line somewhat much less - that 2d version is the rescue version of this knot. Splicing is suitable , yet while this could be a commonplace difficulty purely get some longer ropes! while your ropes are long adequate use a pull down truckie's hitch. that's the place the rope is taken down around a rail (you have used a around turn and 2 a million/2 hitches with a thumb stopper knot on the different element of course) or ring it comes decrease back up, the loop formed and the hitch made, then the load end is taken backtrack to the rail etc. and via alternately leaning in this and taking over the slack you are able to draw down a lot of rigidity. a lot so as which you will overwhelm the load! you have been warned. Then shield the tip with a pair of hitches around the backside element of the ropes, so it can not slide and it won't come loose - in case you stacked your load actual interior the 1st place. solid success. Edit I forgot to show that a bowline reduces your ropes load means to under a million/2 it incredibly is unique score. very few knots do no longer cost a minimum of a third of a rope's power. same for twine, braid etc.

Answer 3

tricky situation. search at the search engines. that might help!