Question

Write this tension as a vector in both the cases.

Answer 1

The tension acting on point A is represented by the equation $\vec {T}_{A} = T_{AB}\cdot \left(-\frac{6.150}{10.483}\,\hat{i} - \frac{5.8}{10.483}\,\hat{j} + \frac{6.2}{10.483}\,\hat{k} \right)$ and the tension acting on point B is represented by the equation $\vec {T}_{B} = T_{AB}\cdot \left(\frac{6.150}{10.483}\,\hat{i} +\frac{5.8}{10.483}\,\hat{j} - \frac{6.2}{10.483}\,\hat{k} \right)$.

How to express a tension in vector form

Vectors are numbers characterized by magnitude and direction. In this question we must represents a tension in the form of a vector. Please notice that tension is a reactive force caused by the action of an external force, often indirectly, in which the string is elongated.

The total length of the string is found by Pythagorean Theorem:

$l_{AB} = \sqrt{[2.5\,m +(5.8\,m)\cdot \sin 39^{\circ}]^{2}+(5.8\,m)^{2}+(6.2\,m)^{2}}$

$l_{AB} \approx 10.483\,m$

First, the tension acting on point A is:

$\vec {T}_{A} = T_{AB}\cdot \left(-\frac{6.150}{10.483}\,\hat{i} - \frac{5.8}{10.483}\,\hat{j} + \frac{6.2}{10.483}\,\hat{k} \right)$

Lastly, the tension acting on point B is:

$\vec {T}_{B} = T_{AB}\cdot \left(\frac{6.150}{10.483}\,\hat{i} +\frac{5.8}{10.483}\,\hat{j} - \frac{6.2}{10.483}\,\hat{k} \right)$

The tension acting on point A is represented by the equation $\vec {T}_{A} = T_{AB}\cdot \left(-\frac{6.150}{10.483}\,\hat{i} - \frac{5.8}{10.483}\,\hat{j} + \frac{6.2}{10.483}\,\hat{k} \right)$ and the tension acting on point B is represented by the equation $\vec {T}_{B} = T_{AB}\cdot \left(\frac{6.150}{10.483}\,\hat{i} +\frac{5.8}{10.483}\,\hat{j} - \frac{6.2}{10.483}\,\hat{k} \right)$.

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