2. A 200 lb traffic light supported by two cables hangs in equilibrium. As shown in the figure below, let the weight of the light be represented by \vec{w} and the forces on the two cables \vec{F_1} and \vec{F_2}. Find \vec{F_1}, \vec{F_2} and the magnitudes of \vec{F_1} and \vec{F_2}.
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Step 1: The traffic light is in equilibrium, so the net force acting on it is zero. Show more…
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A 200-lb traffic light supported by two cables hangs in equilibrium. As shown in FIGURE $7.1 .19(b)$, let the weight of the light be represented by $\mathbf{w}$ and the forces in the two cables by $\mathbf{F}_{1}$ and $\mathbf{F}_{2}$. From Figure 7.1.19(c), we see that a condition of equilibrium is $$ \mathbf{w}+\mathbf{F}_{1}+\mathbf{F}_{2}=\mathbf{0} $$ See Problem 39. If $$ \begin{aligned} \mathbf{w} &=-200 \mathbf{j} \\ \mathbf{F}_{1} &=\left(\left\|\mathbf{F}_{1}\right\| \cos 20^{\circ}\right) \mathbf{i}+\left(\left\|\mathbf{F}_{1}\right\| \sin 20^{\circ}\right) \mathbf{j} \\ \mathbf{F}_{2} &=-\left(\left\|\mathbf{F}_{2}\right\| \cos 15^{\circ}\right) \mathbf{i}+\left(\left\|\mathbf{F}_{2}\right\| \sin 15^{\circ}\right) \mathbf{j} \end{aligned} $$ use $(7)$ to determine the magnitudes of $\mathbf{F}_{1}$ and $\mathbf{F}_{2}$. [Hint: Reread (iii) of Definition 7.1.1.]
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We have a traffic light hanging from two lightweight cables, each at a 45-degree angle from the vertical. The weight of the traffic light is denoted as (w). what is the tension in each cable
Nishant K.
a. What is the resultant force exerted by the two cables supporting the traffic light in figure? (5 points) b. What is the weight of the light? (5 points) c. If a 20-N wind blows on the traffic light to the right, what are the new tensions in each cable if the angles do not change? (5 points) 45.0° 45.0° 60.0 N 60.0 N
Adi S.
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