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A box weighing 200 newtons is hanging from the ceiling. The value of angle 2 is 65°. Tensions T1 and T2 are 132.6 newtons and 130.0 newtons respectively. What is angle 1?

A box weighing 200 newtons is hanging from the ceiling The value of angle 2 is 65 Tensions T1 and T2 are 1326 newtons and 1300 newtons respectively What is angl class=

Respuesta :

Arnold11
According to Newtons third law vertical components of T₁ and T₂ should be equal to the weight of the box or:

T₁sin(θ₁) + T₂sin(θ₂)=200 N

Since θ₂=65°, T₁=132.6 N and T₂=130 N we need to solve for θ₁:

T₂sin(θ₂)=200 N - T₁sin(θ₁)

sin(θ₂)=(200-T₁sin(θ₁))/T₂

θ₂=sin⁻¹{(200-T₁sin(θ₁))/T₂}=37.9°

So the angle θ₂=37.9°.

Answer:

38.29

Explanation:

First you need to find the vertical component of T2 by using trig, sin65 = y/130  ... y = 130*sin65 then y for T2 is 117.8, so 200 - 117.8 tells us the vertical component of the tension of T1 which is 82.18.  We can then use trig on the T1 triangle to solve for theta 1 which I will call X here....sinX= 82.17/132.6 and therefore X= sin-1 (82.17/132.6) and X (theta 1) = 38.29

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