A particle of weight 8 N is attached at C to the ends of two light inextensible strings AC and BC. The other ends, A and B, are attached to a fixed horizontal ceiling. The particle hangs at rest in equilibrium, with the strings in a vertical plane. The string AC is inclined at 35° to the horizontal and the string BC is inclined at 25° to the horizontal, as shown in Figure 1. Find (i) the tension in the string AC, (ii) the tension in the string BC.

A-Level Edexcel Maths Mechanics Forces: A particle of weight 8 N is atta

A particle of weight 8 N is attached at C to the ends of two light inextensible strings AC and BC - Edexcel - A-Level Maths Mechanics - Question 2 - 2013 - Paper 1

Question 2

A particle of weight 8 N is attached at C to the ends of two light inextensible strings AC and BC. The other ends, A and B, are attached to a fixed horizontal ceilin... show full transcript

Worked Solution & Example Answer:A particle of weight 8 N is attached at C to the ends of two light inextensible strings AC and BC - Edexcel - A-Level Maths Mechanics - Question 2 - 2013 - Paper 1

Step 1

Find (i) the tension in the string AC

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Answer

To find the tension in string AC, we can use the equilibrium of forces acting on the particle. Since the system is in equilibrium, we can set up the following equations based on the vertical and horizontal components:

The vertical forces:

$T_{AC} imes rac{1}{ ext{cos}(35°)} = 8$ (weight acting downwards)
The horizontal components:

$T_{AC} imes ext{sin}(35°) = T_{BC} imes ext{sin}(25°)$ (for equilibrium in horizontal force)

Using the first equation, we can express $T_{AC}$ :

$T_{AC} = \frac{8}{\text{cos}(35°)}$

Step 2

Find (ii) the tension in the string BC

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Answer

To find the tension in string BC, we utilize the equation set up from the horizontal components of the forces:

From the previous step, we substitute our value for $T_{AC}$ into the horizontal equilibrium equation:

$T_{AC} \cdot \text{sin}(35°) = T_{BC} \cdot \text{sin}(25°)$

By rearranging the equation to solve for $T_{BC}$ and substituting the value of $T_{AC}$ we found:

$T_{BC} = \frac{T_{AC} \cdot \text{sin}(35°)}{\text{sin}(25°)}$

This gives us the tension in string BC.

A particle of weight 8 N is attached at C to the ends of two light inextensible strings AC and BC - Edexcel - A-Level Maths Mechanics - Question 2 - 2013 - Paper 1

Worked Solution & Example Answer:A particle of weight 8 N is attached at C to the ends of two light inextensible strings AC and BC - Edexcel - A-Level Maths Mechanics - Question 2 - 2013 - Paper 1

Find (i) the tension in the string AC

Find (ii) the tension in the string BC

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