Question

A speedboat is towing a paraglider at a constant speed and height
on the end of a light rope of length 30m, which makes an angle q
with the horizontal. The forces acting on the paraglider are the
vertical lift, L, the horizontal drag, D, his weight, W and the
tension in the rope, T.

How to draw a vector diagram to show the object is in equilibrium?

Answer 1

Answer on Question# 54630- Physics / Mechanics- Kinematics

Question:

A speedboat is towing a paraglider at a constant speed and height on the end of a light rope of length $30\mathrm{m}$ , which makes an angle $\mathbf{q}$ with the horizontal. The forces acting on the paraglider are the vertical lift, L, the horizontal drag, D, his weight, W and the tension in the rope, T. How to draw a vector diagram to show the object is in equilibrium?

Answer:

By the Newton's second law of motion

$$m \vec {a} = \vec {F},$$

where $\vec{F}$ is the net force (i.e. is the vector sum of all the forces). According to the statement of the problem we have $\vec{v} = \overrightarrow{const}$ and $h = const$ (fig. 1). It means that a paraglider is in equilibrium. Hence, $\vec{a} = 0$ and the net force is also equals to zero. Namely,

$$\vec {F} = \vec {L} + \vec {W} + \vec {T} + \vec {D} = 0.$$

Fig. 1

The projections on the coordinate axes give

$$\left\{ \begin{array}{c} O y: 0 = L - W - T \sin (q); \\ O x: 0 = T \cos (q) - D. \end{array} \right. \Rightarrow$$ $$\left\{ \begin{array}{c} L = W + T \sin (q); \\ D = T \cos (q). \end{array} \right.$$

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