The ends X and Y of an inextensible strings 27m long are fixed at two points on the same horizontal line which are 20 m apart. A particle of mass 7.5 kg is suspended from a point P on the string 12 m from X. (a) Illustrate this information in a diagram. (b) calculate, correct to two decimal places, <YXP and <XYP. (c) Find, correct to the nearest hundredth, the magnitudes of the tensions in the string. [take g=10 ms^(−2) ]


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Question Number 173245 by pete last updated on 08/Jul/22

$The ends X and Y of an inextensible strings 27 m$ $long are fixed at two points on the same$ $horizontal line which are 20 m apart .$ $A particle of mass 7.5 kg is suspended$ $from a point P on the string 12 m from X .$ $(a) Illustrate this information in a diagram .$ $(b) calculate, correct to two decimal$ $places, < YXP and < XYP .$ $(c) Find, correct to the nearest hundredth,$ $the magnitudes of the tensions in the$ $string . [take g = 10 {ms}^{- 2}]$
	Answered by mr W last updated on 09/Jul/22

	Commented by mr W last updated on 09/Jul/22

	$\cos α = \frac{20^{2} + 12^{2} - 15^{2}}{2 \times 20 \times 12} = \frac{319}{480}$ $α = \cos^{- 1} \frac{319}{480} \approx 48.35 °$ $\cos β = \frac{20^{2} + 15^{2} - 12^{2}}{2 \times 20 \times 15} = \frac{481}{600}$ $β = \cos^{- 1} \frac{481}{600} \approx 36.71 °$ $\frac{T_{1}}{\cos β} = \frac{T_{2}}{\cos α} = \frac{m g}{\sin (α + β)}$ $m g = 7.5 \times 10 = 75 N$ $\Rightarrow T_{1} = \frac{\cos β m g}{\sin (α + β)} = 60.35 N$ $\Rightarrow T_{2} = \frac{\cos α m g}{\sin (α + β)} = 50.03 N$
	Commented by pete last updated on 09/Jul/22

	$Thank Sir W$
	Commented by Tawa11 last updated on 11/Jul/22

	$Great sir$
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