Two inclined strings in equilibrium — problem 2 · Maths4U Original · 8 marks
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Maths4U Original · M4U-EXT-9709-M1-TWO-STRING-EQUILIBRIUM-P02
A 3 kg particle is held at rest by two separate light taut strings. The left string makes acute angle α above the leftward horizontal, with \(\displaystyle \sin\alpha=\frac{8}{17},\ \cos\alpha=\frac{15}{17}\). The right string makes acute angle β above the rightward horizontal, with \(\displaystyle \sin\beta=\frac{3}{5},\ \cos\beta=\frac{4}{5}\). Let \(\displaystyle T_{1}\) be the left-string tension and \(\displaystyle T_{2}\) the right-string tension. No other forces except weight act. Use \(\displaystyle g= \frac{10m}{s^{2}}\).
- Form two independent equilibrium equations in the tensions \(\displaystyle T_{1}\) and \(\displaystyle T_{2}\). Do not solve them in this part. [3]
- Solve the equilibrium equations to find both tensions. [3]
- Find the left-string horizontal component magnitude in N. Explain your reasoning. [2]