A plank AB has mass 40 kg and length 3 m - Edexcel - A-Level Maths Mechanics - Question 2 - 2005 - Paper 1

To find the tension at C, we start with the equilibrium of the vertical forces acting on the system. We can express the equilibrium condition as:

$T + 3T = 40g + 20g$

where:

• $T$ is the tension at A,
• $3T$ is the tension at C,
• $40g$ is the weight of the plank,
• $20g$ is the weight of the load.

Simplifying this equation:

$4T = 60g$

Thus, the tension can be calculated as follows:

$T = 15g$

Substituting $g$ as 9.81 m/s²:

$T = 15 \times 9.81 = 147.15 \, \text{N}$

Now, for the tension at C, we get:

$T_C = 3T = 3(15g) = 45g = 441.15 \text{N}$

So, the tension in the rope at C is approximately 441 N.