Question
Not to scale The tension force in the cable can be resolved into a horizontal component and a vertical component. The tension in the cable is 2000 N The cable makes an angle of 20^circ with the horizontal. Draw a vector diagram to determine the magnitude of the two components of the tension force in the cable.
Answer
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Wynona
Professional · Tutor for 6 years
Answer
Th = 2000N * cos (20°), Tv = 2000N * sin (20°) will be the values to be calculated for the tension force's componentsĐ.
Explanation
This problem presents a situation involving the resolution of a force vector into its components. In this case, the tension in the cable T is the original force vector and it needs to be resolved into horizontal and vertical components, Th (horizontal component) and Tv (vertical component).We know the magnitude of the vector (T) and the angle (20°) it forms with the horizontal.To find the horizontal and vertical components of a force, trigonometric ratios are applied thus:1. Horizontal component, Th = T * cos(θ)2. Vertical component, Tv = T * sin(θ)In the above equations, - T represents the Force or original vector's magnitude,- θ is the angle the vector makes with the horizontal,- Th is the horizontal component of the vector and- Tv represents the vertical component of the original force vector.Now, inserting the given values into the equations for T = 2000 N , and θ = 20° We calculate the horizontal and vertical components as:Horizontal component, Th = T * cos(θ) = 2000N * cos (20°)Vertical component, Tv = T * sin(θ) = 2000N * sin (20°)Draw a right-angled triangle with the reference angle of 20° to represent the relationship these two components (horizontal and vertical) and the force vector (T) for clarity and simplicity.