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-

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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