The equilibrium condition allows finding the result for the tension in cable 3 of the system is:
T₃ = 66.7 N
Given parameters
- Mass of the dog md = 4.0 kg
To find
Newton's second law gives the relationship between the force, the mass and the acceleration of the bodies, in the spatial case that the acceleration is zero, it is called the equilibrium condition.
∑ F = 0
Where F is the force.
The free body diagram is a diagram of the forces without the details of the bodies, in the attachment we see a free body diagram of each part of the system.
Let's apply the equilibrium condition to each body.
Cat
x-axis
T₂ - T₁ cos θ₁ = 0
T₂ = T₁ cos θ₁
y-axis
T₁ sin θ₁ - [tex]W_{cat}[/tex] = 0
T₁ sin θ₁ = [tex]W_[cat}[/tex]
Dog
x-axis
T₃ cos θ₃ - T₂ = 0
T₂ = T₃ cos θ₃
y-axis
T₃ sin θ₃ - [tex]W_{dog}[/tex]= 0
T₃ sin θ₃ te3 = [tex]W_{dog}[/tex]
We look for the Tension of cable 2.
T₂ = T₁ cos θ₁
[tex]W_{cat}[/tex] =T₁ sin θ₁
We solve.
T₂ = [tex]W_{cat}[/tex] cot θ₁
T₂ = 2.0 9.8 cot 20
T₂ = 53.85 N
We solve the dog equation.
T₂ = T₃ cos θ₃
[tex]W_{dog}[/tex] = T₃ sin θ₃
We resolve
[tex]\frac{W_{dog}}{T_2 } = tan \theta_3[/tex]
θ₃ = tan⁻¹ [tex]\frac{W_{dog}}{T_2}[/tex]
θ₃ = tan⁻¹ ( [tex]\frac{4.0 \ 9.8 }{53.85}[/tex])
θ₃ = 36º
Now we look for cable 3 tension.
[tex]W_{dog}[/tex] = T₃ sin θ₃
T₃ = [tex]\frac{W_{dog}}{sin \theta_3}[/tex]
T₃ = [tex]\frac{4.0 \ 9.8 }{sin 36}[/tex]
T₃ = 66.7 N
In conclusion using the equilibrium condition we can find the tension in cable 3 is:
T₃ = 66.7 N
Learn more here: brainly.com/question/17915050
