Year 11 Maths - Specialist Statics of a Particle

Forces and Triangle of Forces

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Questions

Question 1

61412

A particle of mass 4kg is suspended by two strings attached to two points in the same horizontal plane. If the two strings make angles with the horizontal, find the tension in each string.

Answer

$T_1=T_2=2 \sqrt2 \,kg\,wt$

Worked Solution

$$\begin{aligned}
&\triangle ABC\ \text{is the triangle}\\
&\text{of the resolved forces.}\\
&\begin{aligned}A B&=T_{1}, \quad B C=T_{2}\ \text{and}\\ A C&=4 \text{kgwt.}\\
\angle A B C&=90^{\circ}\\
T_{1}&=T_{2} ( \text{isosceles}\ \Delta)\\
\frac{T_{2}}{4}&=\cos 45^{\circ}\\
T_{2}&=4 \times \frac{\sqrt{2}}{2}\\
\therefore\ T_{1}&=T_{2}=2 \sqrt{2} \mathrm{~kgwt} .\end{aligned}
\end{aligned}
$$

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