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 Newtons Second Law: 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

(i) the tension in the string AC

96%

114 rated

Answer

To find the tension in string AC, denoted as $T_{AC}$ , we can resolve the forces acting on the particle in both the horizontal and vertical directions.

Vertical Forces: The weight of the particle (8 N) acts downward, and the vertical component of the tension $T_{AC}$ acts upward. Thus, we have: $T_{AC} imes rac{1}{ ext{sin}(35°)} - 8 = 0$ Rearranging this gives us: $T_{AC} imes ext{sin}(35°) = 8$
Calculating $T_{AC}$ : $T_{AC} = rac{8}{ ext{sin}(35°)}$ Using a calculator, we find:

ightarrow T_{AC} ext{ (approximately)} = 13.95 ext{ N}$$

Step 2

(ii) the tension in the string BC

99%

104 rated

Answer

To find the tension in string BC, denoted as $T_{BC}$ , we will also resolve the forces acting on the particle:

Vertical Forces: The vertical component of $T_{BC}$ must also counteract the weight of the particle. Thus, we have: $T_{BC} imes ext{sin}(25°) = 8$
Calculating $T_{BC}$ : $T_{BC} = rac{8}{ ext{sin}(25°)}$ By calculating this, we find:

ightarrow T_{BC} ext{ (approximately)} = 18.92 ext{ N}$$

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

(i) the tension in the string AC

(ii) the tension in the string BC

Join the A-Level students using SimpleStudy...