A plank AB has mass 12 kg and length 2.4 m. A load of mass 8 kg is attached to the plank at the point C, where AC = 0.8 m. The loaded plank is held in equilibrium, with AB horizontal, by two vertical ropes, one attached at A and the other attached at B, as shown in Figure 2. (a) Find the tension in the rope attached at B. (4) The plank is now modelled as a non-uniform rod. With the new model, the tension in the rope attached at A is 10 N greater than the tension in the rope attached at B. (b) Find the distance of the centre of mass of the plank from A. (6)

A-Level Edexcel Maths Mechanics Forces: A plank AB has mass 12 kg and le

A plank AB has mass 12 kg and length 2.4 m - Edexcel - A-Level Maths Mechanics - Question 6 - 2008 - Paper 1

Question 6

A plank AB has mass 12 kg and length 2.4 m. A load of mass 8 kg is attached to the plank at the point C, where AC = 0.8 m. The loaded plank is held in equilibrium, w... show full transcript

Worked Solution & Example Answer:A plank AB has mass 12 kg and length 2.4 m - Edexcel - A-Level Maths Mechanics - Question 6 - 2008 - Paper 1

Step 1

Find the tension in the rope attached at B.

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Answer

To find the tension in the rope attached at B, we need to analyze the moments about point A. The total moment caused by the weights acting downwards must be equal to the moment caused by the tension at B.

First, we calculate the weight of the load and the plank:

Weight of the load: $W_{load} = 8g$ (where $g$ is the acceleration due to gravity)
Weight of the plank: $W_{plank} = 12g$

The total distance from A to the point of load (C) is $0.8$ m and from A to B is $2.4$ m.

Using the moment balance about point A: $8g imes 0.8 + 12g imes 1.2 = T_B imes 2.4$

Solving for $T_B$ : $T_B = rac{8g imes 0.8 + 12g imes 1.2}{2.4}$

Substituting the value of $g = 9.81 ext{ m/s}^2$ gives: $T_B = 85 ext{ N}$

Step 2

Find the distance of the centre of mass of the plank from A.

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Answer

To find the distance of the centre of mass of the plank from point A, we can use the following relation:

Given the new tension model, the tension in the rope at A is $T_A = T_B + 10$ N.

Now using moments about point A:

The equation becomes: $(X + 10) imes 0.8 + X imes 2.4 = 8g imes 0.8 + 12g imes X$

Using $g = 9.81 ext{ m/s}^2$ , we can simplify the equations and solve for $X$ . After calculations, we find: $X = 1.4 ext{ m}$

Thus, the distance of the centre of mass of the plank from A is 1.4 m.

A plank AB has mass 12 kg and length 2.4 m - Edexcel - A-Level Maths Mechanics - Question 6 - 2008 - Paper 1

Worked Solution & Example Answer:A plank AB has mass 12 kg and length 2.4 m - Edexcel - A-Level Maths Mechanics - Question 6 - 2008 - Paper 1

Find the tension in the rope attached at B.

Find the distance of the centre of mass of the plank from A.

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